Rotodynamic Pumps

NEW AGE

ROTODYNAMIC PUMPS(Centrifugal and Axial)

Non-met allic Containment Gas

o

K.M. Srinivasan

(f.D

NEW AGE INTERNATIONAL PUBLISHERS


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K.M. SrinivasanB.E.(Hons), PhD.(USSR)

Dean (R&D) Mechanical Sciences Department of Mechanical Engineering Kumaraguru College of Technology Coimbatore, Tamil Nadu

PUBLISHING FOR ONE WORLD

NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERSNew Delhi Hangalorc Chennai Cochin Guwahati Hydcrabad .Ialandhar Kolka!a Lucknow Mumbai Ranch; Visit us at www.newagepublishers.corn

Copyright 2008, New Age International (P) Ltd., Publishers Published by New Age International (P) Ltd., Publishers All rights reserved. No part of this ebook may be reproduced in any form, by photostat, microfilm, xerography, or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of the publisher. All inquiries should be emailed to [email protected]

ISBN (13) : 978-81-224-2976-3

PUBLISHING FOR ONE WORLD

NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS 4835/24, Ansari Road, Daryaganj, New Delhi - 110002 Visit us at www.newagepublishers.com

THIS BOOK is dedicated to My Parents Sri. K. MUTHUSAMY PILLAI And Smt. K.T. SAMBOORNAM As well as To my Professor and guide Dr. Dr. A.A. LOMAKIN And Dr. PAPIR Dr. A.N. PAPIR Polytechnic, Leningrad Polytechnic, Leningrad, K-21, USSR (at present called as St. Petersburg Polytechnic, St. Petersburg, Russia) Who brought me to this level

Comp-1/Newage/Pump-co.pm6.529.12.07

3.1.08


PREFACEIt was my very long felt ambition to provide a detailed and full information about the theory, design, testing, analysis and operation of different types of rotodynamic pumps namely Centrifugal, Radial, Diagonal and Axial flow types. I have learned a lot during the period 195962 about pumps at PSG College of Technology, Coimbatore, while working as Senior Research Assistant for CSIR Scheme on Pumps, Turbo chargers and flow meters. At the same time, I was undergoing training in foundry, pattern making, moulding, production, testing and design for different pumps at PSG Industrial Institute, Coimbatore and also during the period 1967 and 1975. I cannot forget my study at Leningrad Polytechnic, Leningrad K-21, USSR (now St. Petersburg Polytechnic, St. Petersburg, Russia), for my doctorate degree in pumps. Dr. A.A Lomakin, Dr. A.N. Papir, Dr. Gurioff, Dr. N.N. Kovaloff, Dr. A.N. Smirnoff, Dr. Staritski, Dr. Gorgidjanyan, Dr. Gutovski are the key professors who made me to know more about pumps from fundamentals to updated technology. I am very much grateful to Dr. A.A Lomakin and Dr. A.N. Papir, who were my professors and guides for my doctorate degree in pumps. As a consultant, for different pump industries in India and abroad, I could understand the field problems. My experience, since 1959 till date, has been put up in this book to enable the readers in industries, and in academic area, to design, to analyze and to regulate the pumps. Complete design process for pumps, losses and efficiency calculation, based on boundary layer theory for axial flow pumps are also given. Computer programmes for the design of pump and for profile loss estimation for axial flow pumps are also given. All the design examples in the last chapter are real working models. The results are also given with pump drawings. I do hope that the reader will be in a position to understand, design, test and analyze pumps, after going through this book. I shall be very much honoured if my book is useful in attaining this. I am grateful to my wife Smt. S. Nalini, my sons Sri S. Muthuraman and Sri S. Jaganmohan and my daughter Smt. S. Nithyakala, who were very helpful in preparing the manuscript and drawings. Last but not the least I am grateful to the editorial department of M/s New Age International (P) Ltd. Publishers for their untiring effort to publish the book in a neat and elegant form, in spite of so many problems they come across while formulating this book from the manuscript level to this level. Constructive criticisms and suggestions are highly appreciated for further improvement of the book.

K.M. SRINIVASAN


CONTENTSPREFACE (vii)

1 INTRODUCTION1.1 Principle and Classification of Pumps 1 1.1.1 Principle 1 1.1.2 Classification of Pumps 1

15

2 PUMP PARAMETERS2.1 Basic Parameters of Pump 6 2.1.1 Quantity of Flow or Discharge (Q) of a Pump 6 2.1.2 Total Head or Head of a Pump (H) 6 2.1.3 Total Head of a Pump in a System 7 2.1.4 Power (N) 11 2.1.5 Efficiency () 11 2.2 Pump Construction 12 2.3 Losses in Pumps and Efficiency 15 2.3.1 Hydraulic Loss and Hydraulic Efficiency (h) 15 2.3.2 Volumetric Loss and Volumetric Efficiency (v) 15 2.3.3 Mechanical Loss and Mechanical Efficiency (m) 16 2.3.4 Total Losses and Overall Efficiency (h) 16 2.4 Suction Conditions 16 2.5 Similarity Laws in Pumps 19 2.5.1 Similarity Laws 19 2.5.2 Specific Speed (ns) 22 2.5.3 Unit Specific Speed (nsq) 23 2.6 Classification of Impeller Types According to Specific Speed (ns) 24 2.7 Pumping Liquids Other than Water 26 2.7.1 Total Head, Flow Rate, Efficiency and Power Determination for Pumps 26 2.7.2 Effect of Temperature 27 2.7.3 Density Correction ( or ) 27 2.7.4 Viscosity Correction 28 2.7.5 Effect of Consistency on Pump Performance 32 2.7.6 Special Consideration in Pump Selection 33(ix)

633

(x)

CONTENTS

3 THEORY OF ROTODYNAMIC PUMPS3.1 Energy Equation using Moment of Momentum Equation for Fluid Flow through Impeller 34 3.2 Bernoullis Equation for the Flow through Impeller 35 3.3 Absolute Flow of Ideal Fluid Past the Flow Passages of Pump 38 3.4 Relative Flow of Ideal Fluid Past Impeller Blades 40 3.5 Flow Over an Airfoil 43 3.6 Two Dimensional Ideal Flow 45 3.6.1 Velocity Potential 45 3.6.2 Rotational and Irrotational Flow 45 3.6.3 Circulation and Vorticity 47 3.7 Axisymmetric Flow and Circulation in Impeller 48 3.7.1 Circulation in Impellers of Pump 49 3.7.2 Vorticity and Circulation Around Impeller Blades 49 3.8 Real Fluid Flow after Impeller Blade Outlet Edge 50 3.9 Secondary Flow between Blades 51 3.10 Flow of a Profile in a Cascade SystemTheoretical Flow 52 3.11 Fundamental Theory of Flow Over Isolated Profile 53 3.12 Profile Construction as per N.E. Jowkovski and S.A. Chapligin 55 3.13 Development of Thin Plate by Conformal Transformation 58 3.14 Development of Profile with Thickness by Conformal Transformation 58 3.15 Chapligins Profile of Finite Thickness at Outlet Edge of the Profile 59 3.16 Velocity Distribution in Space between Volute Casing and Impeller Shroud 61 3.17 Pressure Distribution in the Space between Stationary Casing and Moving Impeller Shroud of Fluid Machine 63

3464

4 THEORY AND CALCULATION OF BLADE SYSTEMS INCENTRIFUGAL PUMP4.1 4.2 4.3 4.4 Introduction 65 One Dimensional Theory 65 Velocity Triangles 66 Impeller Eye and Blade Inlet Edge Conditions 69 4.4.1 Inlet Velocity Triangle 70 4.4.2 Normal or Radial or Axial Entry of Fluid at Impeller Inlet 72 Outlet Velocity Triangle: Effect due to Blade Thickness 73 4.5.1 Outlet Velocity Triangle: Effect of Finite Number of Blades 74 Slip Factor as per Stodola and Meizel 75

65129

4.5 4.6

CONTENTS

(xi)

4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19

4.6.1 Slip Factor as Defined by Karl Pfliderer 77 4.6.2 Slip Factor as per Proscura 79 Coefficient of Reaction () 81 Selection of Outlet Blade Angle (2) and its Effect 83 Effect of Number of Vanes 86 Selection of Eye Diameter D0, Eye Velocity C0, Inlet Diameter of Impeller D1 and Inlet Meridional Velocity Cm1 89 Selection of Outlet Diameter of Impeller (D2) 92 Effect of Blade Breadth (B2) 92 Impeller Design 103 Determination of Shaft Diameter and Hub Diameter 106 Determination of Inlet Dimensions for Impeller 107 Determination of Outlet Dimensions of Impeller 108 Development of Flow Passage in Meridional Plane 109 Development of Single Curvature BladeRadial Blades 111 Development of Double Curvature Blade System 113 4.19.1 Importance of Diagonal Impellers 113 4.19.2 A General Solution for the Flow through the Vane System 114 4.19.3 Axisymmetric Flow of Fluid 115 4.19.4 Flow Line and Vortex Line in Axisymmetric Flow 116 4.19.5 Differential Equation for the Cross-section of Vane with the Flow Surface 118 4.19.6 Construction of Vane Surface when Wu = 0 118 4.19.7 Construction of Vane Under Equal Velocity Construction 120 4.19.8 Construction of Vane Surface Under Equal Velocity Flow for the Given w(s) 121 4.19.9 Conformal Transformation of Vane Surface 125 4.19.10 The Method of Error Triangles 126

5 SPIRAL CASINGS (VOLUTE CASINGS)5.1 5.2 5.3 5.4 5.5 5.6 5.7

130146

Importance of Spiral Casings 130 Volute Casing at the Outlet of the Impeller 131 Method of Calculation for Spiral Casing 132 Design of Spiral Casing with Cur = Constant and Trapezoidal Cross-section 134 Calculation of Trapezoidal Volute Cross-section Under Constant Velocity of Flow CV = Constant (Constant Velocity Design) 135 Calculation of Circular Volute Section with Cur = Constant 137 Design of Circular Volute Cross-section with Constant Velocity (CV) 138

(xii)

CONTENTS

5.8 5.9 5.9 5.9 5.10 5.11 5.12 5.13 5.14

Calculation of Diffuser Section of Volute Casing 139 (A) Design of Diffuser 140 (B) Calculation of Spiral Part of Diffuser Passage 141 (C) Calculation of Diverging Cone Part of the Diffuser 142 Return Guide Vanes 143 Design of Suction Casing at Inlet of the Impeller 144 Straight Convergent Cone 144 Spiral Type Approach Ring 144 Effect due to Volute 146

6 LOSSES IN PUMPS6.1 6.2 6.2 6.2 6.2 6.3 6.3 6.4 Introduction 147 (A) Mechanical Losses 147 (B) Losses due to Disc Friction (Nd ) 147 (C) Losses Stuffing Box (NS) 149 (D) Bearing Losses (NB) 154 (A) Leakage Flow through the Clearance between Stationary and Rotatory Wearing Rings 154 (B) Leakage Flow through the Clearance between Two Stages of a Multistage Pump 159 Hydraulic Losses 161

147163

7 AXIAL AND RADIAL THRUSTS7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 Introduction 164 Axial Force Acting on the Impeller 165 Axial Thrust in Semi-open Impellers 167 Axial Thrust due to Direction Change in Bend at Inlet 168 Balancing of Axial Thrust 169 Axial Thrust taken by Bearings 170 Radial Vanes at Rear Shroud of the Impeller 170 Axial Thrust Balancing by Balancing Holes 171 Axial Thrust Balancing by Balance Drum and Disc 172 Radial Forces Acting on Volute Casing 177 Determination of Radial Forces 177 Methods to Balance the Radial Thrust 180

164181

8 MODEL ANALYSIS8.1 Introduction 182 8.1.1 Real Fluid Flow Pattern in Pumps 187

182194

CONTENTS

(xiii)

8.2 8.3 8.4

Similarity of Hydraulic Efficiency 191 Similarity of Volumetric Efficiency 192 Similarity of Mechanical Efficiency 193

9 CAVITATION IN PUMPS9.1 9.2 9.3 9.4 9.5 9.6 Suction Lift and Net Positive Suction Head (NPSH) 195 Cavitation Coefficient (s) Thomas Constant 200 Cavitation Specific Speed (C) 201 Cavitation Development 201 Cavitation Test on Pumps 203 Methods Adopted to Reduce Cavitation 211

195215

10 AXIAL FLOW PUMP10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 10.9 10.10 10.11 10.12 10.13 10.14

216292

Operating Principles and Construction 216 Flow Characteristics of Axial Flow Pump 218 Kutta-Jowkovski Theorem 218 Real Fluid Flow over a Blade 222 Interaction between Profiles in a Cascade System 223 Curved Plates in a Cascade System 224 Effect of Blade Thickness on Flow Over a Cascade System 233 Method of Calculation of Profile with Thickness in a Cascade System 234 (A) Pump Design by Direct Method (Jowkovskis Method, Lift Method) 243 (B) Design of Axial Flow Pump as per Jowkovskis Lift Method Another Method 247 Flow with Angle of Attack 255 Correction in Profile Curvature due to the Change from Thin to Thick Profile 256 Effect of Viscosity 259 Selection of Impeller Diameter and Speed 260 Selection of Hub Ratio 261 l

10.15 Selection of Aspect Ratio at Periphery 263 t peri 10.16 Calculation of Hydraulic Losses and Hydraulic Efficiency 268 10.17 Calculation of Profile Losses using Boundary Layer Thickness (**) 271 10.17.1 Notations and Abbreviations 271 10.17.2 Determination of Profile Losses and Hydraulic Efficiency 274 10.17.3 Determination of Momentum Boundary Layer Thickness (**) 277 10.17.4 Computer Programme 283 10.18 Cavitation in Axial Flow Pumps 283

(xiv)

CONTENTS

10.19 Radial Clearance between Impeller and Impeller Casing 288 10.20 Calculation for Axial Flow Diffusers 289 10.21 Axial Thrust 291

11 TESTING, PERFORMANCE EVALUATION AND REGULATIONOF PUMPS 293338 11.1 Introduction 293 11.2 Pump PerformanceRelation between Total Head and Quantity of Flow 293 11.3 Pump Testing 301 11.4 Systems and Arrangements 306 11.5 Combined Operation of Pumps and Systems 310 11.6 Stable and Unstable Operation in a System 312 11.7 Reverse Flow in Pump 315 11.8 Effect of Viscosity on Performance 317 11.9 Pump Regulation 232 11.10 Effect of the Pump Performance when Small Changes are made in Pump Parts 336

12 PUMP CONSTRUCTION AND APPLICATION12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 Classification 339 Pumps for Clear Cold Water and for Non-Corrosive Liquids 339 Other Pumps 346 Axial Flow Pumps 354 Condensate Pumps 357 Feed Water Pumps 361 Circulating Pumps 363 Booster Pumps 365 Pump for Viscous and Abrasive Liquids 370

339374

13 DESIGN OF PUMP COMPONENTSDesign No. D1-A : Design of a Single Stage Centrifugal Pump 375 Design No. D1-A1 : Computer Programming in C++ for Radial Type Centrifugal Pump Impeller and Volute 381 Design No. D1-B : Design of a Multistage Centrifugal Pump 395 Design No. D2 : Spiral Casing Design 409 D2-A : Spiral Casing Design Under Cur = Constant and Trapezoidal Cross-Section 411 D2-B : Spiral Casing Design with CV = Constant and Trapezoidal Cross-section 414 D2-C : Design of Suction Volute 417

375486

CONTENTS

(xv)

Design No. D3 Design No. D4 Design No. D5 Design No. D6 Design No. D7 Design No. D8

: Design of Axial Flow Pump 418 : Correction for Profile Thickness by Increasing Blade Curvature () 427 : Calculation of Correction for Blade Thickness using Thickness Coefficient () 429 : Design of Axial Flow Pump 431 : Profile Losses Calculation 473 : Design of Axial Flow Pumpas per method Suggested by Prof. N.E. Jowkovski 482

APPENDICESAppendix II : ISI Standards Appendix III : Units of MeasurementConversion Factorsy Appendix I : Equations Relating Cy, max , for Different Profiles l

487508487 495 502

LITERATUREREFERENCES INDEX

509518 519520


1INTRODUCTION1.1 PRINCIPLE AND CLASSIFICATION OF PUMPS 1.1.1 PrincipleNewtons First law states that Energy can neither be created nor be destroyed, but can be transformed from one form of energy to another form. Different forms of energy exists namely, electrical, mechanical, fluid, hydraulic and pneumatic, pressure, potential, dynamic, wave, wind, geothermal, solar, chemical, etc. A machine is a contrivance, that converts one form of energy to another form. An electric motor converts electrical energy to mechanical energy. An internal combustion engine converts chemical energy to mechanical energy, etc. A pump is a machine which converts mechanical energy to fluid energy, the fluid being incompressible. This action is opposite to that in hydraulic turbines. Most predominant part of fluid energy in fluid machines are pressure, potential and kinetic energy. In order to do work, the pressure energy and potential energy must be converted to kinetic energy. In steam and gas turbines, the pressure energy of steam or gas is converted to kinetic energy in nozzle. In hydraulic turbine, the potential energy is converted to kinetic energy in nozzle. High velocity stream of fluid from turbine nozzle strikes a set of blades and makes the blades to move, thereby fluid energy is converted into mechanical energy. In pumps, however, this process is reversed, the movement of blade system moves the fluid, which is always in contact with blade thereby converting mechanical energy of blade system to kinetic energy. For perfect conversion, the moving blade should be in contact with the fluid at all places. In other words, the moving blade system should be completely immersed in fluid.

1.1.2 Classification of Pumps1.1.2.1 Classification According to Operating PrinciplePumps are classified in different ways. One classification is according to the type as positive displacement pumps and rotodynamic pumps. This classification is illustrated in Fig. 1.1. In positive placement pumps, fluid is pushed whenever pump runs. The fluid movement cannot be stopped, otherwise the unit will burst due to instantaneous pressure rise theoretically to infinity, practically exceeding the ultimate strength of the material of the pump, subsequently breaking the material. The motion may be rotary or reciprocating or combination of both.

2

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)

PU M PS PUMPS

Posi i D i acem ent Pumps t ve spl Positive Displacement P um ps

Ot her P um ps Other Pumps

R otodynam i Pumps c Rotodynamic P um ps

Reciprocating Type

Rotary Type

Jet Pump Hydraulic Ram

Centrifugal, Mixed and Axial Flow Regenerative

Piston plunger

Vane, Lobe Screw, Gear Perialistic, Metering, Diaphram, Radial piston, Axial piston

Fig. 1.1. Pump classfication

The principle of action, in all positive displacement pumps, is purely static. These pumps are also called as static pumps. The pumps, operated under this principle, are reciprocating, screw, ram, plunger, gear, lobe, perialistic, diaphram, radial piston, axial piston etc. In rotodynamic pumps, however, the energy is transferred by rotary motion and by dynamic action. The rotating blade system imparts a force on the fluid, which is in contact with the blade system at all points, thereby making the fluid to move i.e., transferring mechanical energy of the blade system to kinetic energy of the fluid. Unlike turbine, where pure pressure or potential energy is converted to kinetic energy, in pumps, the kinetic energy of the fluid is converted into either, pressure energy or potential energy or kinetic energy or the combination of any two or all the three forms depending upon the end use in spiral or volute casing, which follows the impeller. In domestic, circulating and in agricultural pumps, the end use is in the form of potential energy i.e., lifting water from low level to high level. In process pumps, used for chemical industries, the fluid is pumped from one chamber under pressure to another chamber under pressure. These chambers may be at the same level (only pressure energy conversion) or may be at different levels (pressure and potential energy conversion). Pumps used for fire fighting, for spraying pesticides, must deliver the liquid at very high velocity i.e., at very high kinetic energy. These pumps convert all available energy at the outlet of the impeller into very high kinetic energy. In turbines, the fluid is water or steam or chemical gas-air mixture at constant pressure and temperature, whereas, pumps deal with fluid at different temperatures and viscosities such as water, acids, alkaline, milk, distilled water, and also cryogenic fluids, like liquid hydrogen, liquid oxygen, liquid nitrogen, liquid ammonia, which are in gaseous form under normal temperatures. Pumps are also used to pump solid-liquid, liquid-gas or solid-liquid-gas mixtures, with different percentage of concentration called consistency. Hence pumps are applied in diversified field, the pumping fluid possessing different property, namely, viscosity, density, temperature, consistency, etc.

INTRODUCTION

3

A third category of pump, called jet pump, wherein, the fluid energy input i.e., high head low discharge of fluid is converted into another form of fluid energy i.e., low head and high discharge. These pumps are used either independently or along with centrifugal pumps. The reverse of Jet pump is Hydraulic Ram wherein low head and high discharge of water is converted into high head and low discharge. Hydraulic Rams are installed at hills near a stream or river. The natural hill slope is the low head input energy. Large quantity of water at low head is taken from the river. A portion of water is pumped at high pressure and is supplied to a nearby village as drinking water. Remaining water is sent back to the river. This system does not need any prime mover like diesel or petrol engine or electric motor. Repair and maintenance is easy, in hydraulic ram since moving part is only the ram.

1.1.2.2 Classification According to Head and DischargeAnother classification of pump is according to the head and discharge or quantity of flow to be pumped. Any customer, who is in need of a pump specifies only these two parameters. A quick selection of the pump is made referring standard charts for selecting the pump. Fig.1.2 gives the selection of pump according to head and discharge.10000 H.m PISTON 1000

CENTRIFUGAL 100

10 AXIAL 1 10 100 1000 10000 100000 3 Q.m /hr

Fig. 1.2. Pump selection as per head and discharge

1.1.2.3 Classification According to Specific SpeedMost accurate method of pump selection is based on the non-dimensional parameter called specific speed which takes into account speed of the pump along with head and discharge. Specific speed, ns = 3.65n Q H 3/ 4

...(1.1)

where nsspecific speed, nspeed in rpm, Qdischarge in m3/sec, Hhead in m. If pressure rise is known instead of total head then p = H, where ppressure rise of pumping fluid in N/m2 and specific weight of the fluid at the given temperature in N/m3. It is essential that all parameters must be

4


converted to equivalent water parameters before substituting them in equation 1.1. Fig.1.3, illustrates the pump selection according to the specific speed of the pump.Centrifugal (radial flow) Low ns = 50 80 b2 Medium n s = 80 150 b2 High ns = 150 300 b2

Diagonal and mixed flow ns = 300 500

Propeller and axial flow n s = 500 1000

b2D2

D2

D2

D2

D0

D0

D0

D0

D0

D2 = 2,5 to 1,8 D0 HQ

D2 = 2 to 1,8 D0

D2 = 1,8 to 1,4 D0

D2 = 1,4 to 1,2 D0

D2 = 0,8 D0

HQNh

HQN Qh

HQQ N Q

HQNQ Q h

Q

Q Nh

Q

Q

Q h

Fig. 1.3. Classification according to specifc speed

From Fig.1.3, it is evident that, at low specific speeds, centrifugal pumps; at medium specific speeds, mixed flow pumps and at high specific speeds, axial flow pumps are used. All of them are classified as rotodynamic pumps. At very low specific speeds, however, positive displacement pumps are used. Referring to the equation (1.1), it is seen that positive displacement pumps are used for very high head-very low discharge conditions. Ship propellers and aircraft propellers are of very high specific speed units beyond 1200 i.e., used for very low head-very high discharge conditions.

1.1.2.4 Classification According to Direction of Flow in ImpellerAnother classification of pumps is according to the direction of flow of fluid in impeller of the pump such as radial or centrifugal flow, mixed or diagonal flow and axial flow. Fig.1.4, illustrates the position of blade system in the impeller passage of a pump. Considering the flow of fluid in impeller, (Fig.1.4) if the flow direction is radial (2-1) and (3-1) i.e., perpendicular to the axis of rotation, the pump is called radial flow centrifugal pump. If the flow is axial (6-5) i.e., parallel to the axis of rotation, the pump is called axial flow pump. If the flow is partly axial and partly radial (4-2) and (4-3) i.e., diagonal, it is called mixed flow pump or diagonal flow pump. It is evident, from the Fig.1.4, that all these pumps are rotodynamic pumps i.e., rotary blade passage and dynamic action of blade system in the fluid passage.

D2

INTRODUCTION

5

b2 b2 a2 a2

Outlet, Delivery of water Inlet, entry of water IVDs

1 2 3

D2

I a1 II

III a1

D 3

D1

D3

D2

Ds

6

5 4 Shaft

90 axis

(a) Radial

(b) Mixed

(c) Axial

(d) Relative location

Fig. 1.4. Position of blade system in different types of impellers

21 Centrifugal Radial flow very high head and very low flow. 31 Centrifugal Radial flow high head and low flow. 42 Mixed flow Medium head and medium flow low range. 43 Diagonal flow Medium head and medium flow higher range. 65 Axial flow, propeller low head and high flow. Radial type centrifugal pumps have higher impeller diameter ratio (outlet to inlet diameter) and the blade is longer. Mixed flow pumps have medium diameter ratio and axial flow pumps have equal inlet and outlet diameters. This indicates that radial flow pumps work mostly by centrifugal force and partly by dynamic force, whereas, in axial flow pumps, the pressure rise is purely by hydrodynamic action. In mixed and diagonal flow pumps, however, the pressure rise is partly by centrifugal force and partly by hydrodynamic force.

2PUMP PARAMETERS2.1 BASIC PARAMETERS OF PUMPA pump is characterised by three parameters i.e., 1. Total head (H), 2. Discharge or quantity of flow (Q), and 3. Power (N).

2.1.1 Quantity of Flow or Discharge (Q) of a PumpQuantity of flow or rate of flow or discharge (Q) of a pump is the flow of fluid passing through the pump in unit time. The rate of flow or discharge in volumetric system is expressed as

unit weight flow unit volume flow i.e., m3/sec, m3/hr, lit/sec etc., and in gravimetric system as i.e., unit time unit time tons/day, kg/hr, kg/sec etc. The relation between gravimetric or weight (W) and volumetric (Q) flow rate is given by W = Q where is specific weight of the fluid.

2.1.2 Total Head or Head of a Pump (H)Total head of a pump (H) is defined as the increase in fluid energy received by every kilogram of the fluid passing through the pump. In other words, it is the energy difference per unit weight of the fluid between inlet and outlet of the pump. Referring to Fig. 2.1, the energy difference per unit weight of the fluid (E) between inlet (E1) and outlet (E2) will beZ2 p2 = pd Z2 H =Z2 Z1 Hd Z1

G X2

V

+ Hs X1

Hs

H

Z1

p1 = ps

Fig. 2.1. Head measurement in pumps6

PUMP PARAMETERS

7

Einlet Eoutlet where

p1 C2 + Z1 + 1 = E1 = 2g p2 C2 + Z2 + 2 = E2 = 2g

...(2.1)

p the pressure in N/m2 (PascalPa) Z the level or position above or below reference level in m C the flow velocity of the fluid in m/sec specific weight of the fluid in kg/m3 (or) N/m3 g acceleration due to gravity in m/sec2 Suffix 1 indicates inlet condition of the pump 2 indicates outlet condition of the pump Total head H will be H = (E2 E1) =

(C22 C12 ) ( p2 p1 ) + (Z2 Z1) + 2g

...(2.2)

and is expressed as

kgf.m N.m or = m. kgf N

2.1.3 Total Head of a Pump in a SystemA pump installation consists of pump and system. Pumps are selected to match the given condition of the system, which depends upon the system head (Hsy), quantity of flow (Q), density (), the viscosity (), consistency (C), temperature (T), and corrosiveness of the pumping liquid. If the pumping liquid is other than water at different temperatures and pressures such as milk, distilled water, acid, alkaline solutions, as well as liquid ammonia, liquid oxygen, liquid hydrogen, liquid nitrogen or any other chemical solutions under higher temperatures and pressures, solid-liquid solution, liquid-gas solutions etc., the pump parameters in liquid must be changed into equivalent water parameters. The quantity (Q) and the total head (H) of the pump must coincide with the conditions of external system such as pressure, and location of the system. Normally the pump is selected with 2 to 4% higher value in total head than the normal value of system head. A system consists of pipelines with fittings such as gate valve or butterfly valve or non-return valve or any other valve along with bends, tee joints, reducers etc., at the delivery line of the pump as well as foot valve, strainer, bend, etc., at the suction line of the pump. The system is an already available pipeline in the field or at the working area, to suit the prevailing conditions in the field or working area. It is a fixed system for that particular place. System varies from place to place. Referring to the Fig. 2.2, the pipe 2-d refers to the delivery side and s1 refers to the suction side of the system. For all calculations in a pumping system, the axis of the shaft of the horizontal pump is referred as reference line. For vertical pumps, the inlet edge of the blade of the impeller will be the reference line. Since the difference between the inlet edge of the blade and the centre line of the outlet edge of the blade is usually small, it is neglected and the centre line of the outlet edge of the blade is taken as reference line. Anything above or after the reference line is called delivery side (marked with suffix d) and anything below or before the reference line is called suction side (marked with suffix s) of a pump.

8


Referring to Fig. 2.2, the equation for suction and delivery pipelines of the system can be written as follows. Since no energy is added or subtracted in these lines during the flow through the system, For (2 d) delivery line E2 = Ed + hf (2 d) i.e.,

pd = p2 pd d

p C2 p2 C + Z 2 + 2 = d + Z d + d + h f (2 d ) 2g 2g

hd

hfd

For (s1) suction line Es = E1 + hf (s1)

p C2 i.e., s + Z s + s 2g

p1 C2 + Z1 + 1 + h f ( s 1) = 2g

...(2.3) H X 1

C2

2

G Reference line

The values hf (2 d) and hf (s 1) include major frictional losses and all minor losses. The total head of the pump as per equation 2.2 is

C1 V

p2 C2 p C2 + Z 2 + 2 1 + Z1 + 1 Hp = E2 E1 = 2g 2g = Ed +hf (2 d) Es + hf (s 1)

hs

h fs

ps=p 1 S

pd p C2 C2 + Z d + d + h f (2 d ) s + Z s + s h f ( s 1) Hp = 2g 2g =

Fig. 2.2. Pump in a closed system

C 2 Cs2 pd ps + (Zd Zs) + d + hf (2 d) + hf (s 1) 2g 2 Cd Cs2 =H sy 2g

pd ps = + hs + hd + hf (d) + hf (s) + H

...(2.4)

H syst = f(Q) H O Operating point (H sy = H p)

pd p s

H p = f(Q) + h s + hd Q

Fig 2.3. Head of pump and system

PUMP PARAMETERS

9

Equation 2.4 shows that, if a pump is connected to a system, the pump and the system will operate only at a point where Hp = Hsy. Fig. 2.3 shows graphically this condition.

C2 = KQ2,where K is the For both major and minor losses combined together hf = constant 2g pd ps sum of all constants (major and minor). The system head Hsy= + hs + hd + (Kd + Ks) Q2. If a curve Hsyst= f (Q) is drawn, it will be a parabola moving upwards, i.e., increase of head when the flowQ increases. (Fig. 2.3). If this curve is superimposed with HQ curve of the pump, the meeting point will be (Hp = Hsyst) the operating point of the pump for that system. Different Hsy curves can be drawn by changing hs or hd or pd or ps as well as by changing pipe size Dp, pipe length lp, in suction and delivery, or by adding or removing or changing bends. Tee, crossjoints or by changing the valves in the system. Change of every individual parts mentioned above changes the HsystQ curve. If these curves are superimposed on pump HQ curve, the operating point for each system can be determined (Fig. 2.4).H P1, P2, P3,P4 Operating points Hsyst 4 Q P4 P3 P2 P1 H syst 2 Q H syst 1 Q H syst 3 Q

H st = hs + h d +

pd p s

Head m.

Q4 Q3 Q2 Q1 Quantity m3/sec, Lt/sec.

(H p Q) Q

Fig. 2.4. Different systems operating on one pump

Referring to equation 2.4, if suction and delivery chamber pressures are very high, when compared to the potential and kinetic energies, then the pump is called process pump. If the suction and delivery chambers are open type, then pd = ps = patm and if hd, hs are very high, then these pumps are called domestic or agricultural or circulating pumps. If velocity C2 is very large, when compared to other parameters and pd = ps = patm and hs and hd may be positive or zero, then these pumps are called fire fighting pumps, sprayer pumps. Rearranging equation 2.22 2 pd p2 Cd C2 = + (Zd Z2) + + hf (2 d) 2g

10

ROTODYNAMIC PUMPS (CENTRIFUGAL AND AXIAL)2 2 pd Cd C2 + hd + hfd + ...(2.5) 2g If a pressure gauge is connected very close to the delivery side of the pump at point 2, it will read

=

p the delivery chamber pressure d , static delivery height (hd) delivery line frictional losses (hf) (both major and minor losses) and the difference between the velocity head or kinetic energy at delivery C2 chamber d and immediately after the delivery of liquid from pump i.e., at the outlet of the volute 2g

C2 p casing 2 . If the delivery chamber is a closed one, then d will be real and normally above 2g atmosphere2 Cd will be equal to zero. The pressure gauge P2 will read 2g

pd p2 C2 = + hd + hfd 2 2g

...(2.6)

2 C2 where C2 is the velocity at the delivery pipe, and will be the kinetic energy at the delivery pipe. 2g

2 patm pd Cd In case the delivery chamber is open to atmosphere then = and will be real. The 2g

velocity Cd = C2 and the velocity head at the delivery pipe is will read

Cd2 C22 = 0. The pressure gauge (P2) 2g

p2 = hd + hfd (gauge pressure) p = atm + hd + hfd (absolute pressure) ...(2.7) If a pressure gauge is connected at the end of suction pipe and very near to the pump inlet at point 1, it will read p1 ps = + (Zs Z1) + Cs2 C12 2 g hf (s 1) ...(2.8)

C 2 C12 ps hs hfs + s = 2g Cs2 ps If the suction chamber is closed, will be read and Cs = 0, = 0. Then 2g p1 C2 ps hs + h fs + 1 = 2g where C1 is the fluid velocity at suction pipe.

...(2.9)

PUMP PARAMETERS

11

patm ps p = . The pressure 1 will be negative i.e., under vacuum. A vacuum gauge (V) instead of pressure gauge P1 must be connected at point 1. The velocity Cs = 0 and soIf the suction chamber is open to atmosphere then

C2 p1 pat hs + h fs + 1 absolute 2g = or

C12 hs + h fs + = 2 g vacuum Vacuum gauge will read only vacuum. The same condition will exist if

...(2.10)

ps , the suction chamber pressure is not sufficiently higher than the vacuum in the suction side of the pump. In this case also only vacuum gauge must be connected at point 1. Thats why if the suction chamber is closed, a pressure cum vacuum gauge and if suction chamber is open to atmosphere a vacuum gauge is connected at point 1 i.e., at the end of suction pipe or immediately before the inlet of the pump. Since total head of the pump (Hp) = Total head of the system (Hsyst)Hp = Hsyst = P2 + V + X + 2 Cd

...(2.11) where X is the difference in height between delivery pressure gauge (P2) and suction gauge (P1 or V). If P2 is at a higher level than P1, X is positive. If P2 is at a lower level than P1 then X1 is negative. If P2 and P1 are at the same level X = 0.

2g = P2 P1 + X for closed system

Cs2 2 g for open system

2.1.4 Power (N)Power is defined as the amount of energy spent to increase the energy of the fluid passingkgf.m N.m or or watts or sec sec kilowatts. If W is the weight of fluid passing through the pump and the energy increase per unit weight of the fluid between inlet and outlet of the pump is H, power N will be

through the pump from inlet to outlet of the pump and is expressed in

WH QH = in kW or watts. constant constant where W = Q, if W is expressed in kgf, the constant will be 102, and if expressed in Newton the constant will be 1000 in order to get the power in kW.

N0 =

2.1.5 Efficiency () The power supplied to the pump will be higher than the energy spent in converting mechanical energy to fluid energy due to various losses, namely, hydraulic, volumetric and mechanical losses. The ratio of actual power utilized to the power supplied is called efficiency ().

12


QH power spent N 0 = QH const (C ) = = C .N power supplied( Nth ) thor Nth =

N0 QH = C.

...(2.12)

2.2 PUMP CONSTRUCTIONAny pump consists of an impeller having specified number of curved blades called vanes, kept in between two shrouds. The impeller is the rotating element responsible for the conversion of mechanical energy into fluid energy. This impeller is connected, through a shaft and coupled, to the prime mover for rotation. The connection may be a direct drive or indirect drive, through belt or gear system. The shaft is supported by one or two fixed bearing supports depending upon the pump duty and one floating sleeve bearing support along with either mechanical seal or asbestos packed stuffing box. This floating support is arranged to take care of liner thermal expansion of shaft, towards the impeller side but not at the prime mover side and at the same time acting as load bearing unit. The mechanical seal material or the packing material is selected according to the type of pumping liquid such as acidic, alkaline, neutral, milk, distilled water, cryogenic liquids like ammonia, hydrogen, oxygen, nitrogen, two phase fluids such as solid-liquid, liquid-gas etc. A gland provided in the stuffing box keeps the packing material or seal in position. The impeller is rotated inside a sealed spiral casing or volute casing. Suction and delivery pipes are connected to the suction side and delivery side of the spiral casing through respective flanges. Since volute casing is a non rotating part and impeller is a rotating element, sufficient clearance should be provided between them. The fluid enters the suction side of the impeller, called eye of the impeller with low energy. Due to conversion of mechanical to fluid energy, the fluid leaving the impeller will be with higher energy, mostly with more kinetic energy. Due to the energy difference between inlet and outlet of impeller and due to the clearance between volute casing and impeller, a part of fluid flows from impeller outlet to the eye of the impeller at the suction side and towards the stuffing box side at the back. In order to control this leakage flow, wearing rings, at the casing and at the impeller at front and back side are provided. The amount of clearance and different forms of wearing rings used depends upon the pumping fluid (temperature, consistency etc.). The mechanical seal and the packing in stuffing box reduces this leakage still further at the rear side. The volute casing and the impeller with shaft are fitted to the bracket which has the bearings to support the shaft. This bracket base is mounted in a common base plate, which has the provision to mount the prime mover. The pump and prime mover will be kept on a common base plate. In Figs. 2.5, 2.6 and 2.7, three types of pump assemblies are given for single suction pumps. However, the construction differs for double suction pumps and multi stage pumps.

PUMP PARAMETERS

132

10 14 9

12 7 16 6

11

4 15

15 3

5 1

8

13

1. 2. 3. 4.

Suction flange Delivery flange Impeller Volute casings

5. 6. 7. 8.

Bearing bed Shaft Deep groove ball bearing Bush

9. Flexible coupling (pump side) 10. Flexible coupling (motor tside) 11. Gland 12. Bearing cap

13. 14. 15. 16.

Impeller nut Coupling nut Air cock Grease cup

Fig. 2.5. Single bearing supported pump with split type volute casing2 1 6 22 29 26 2 18 3 15 14 24 10 21 20 36 40 33 7 27

8 28 32 11 5 44 19 12 31

42 17 43 26 39 30 9 38 13 18 37 34 41 40 25 17. Flat seal 18. Seal ring 19. Radial seal ring 20. Gland 21. Stuffing box ring 22. Bottom ring 23. Block ring 24. Stuffing box 25. Splash ring 4

1. Spiral casing 2. Intermediate casing 3. Cooling room cover 4. Supporting foot 5. Pump shaft 6. Left-hand impeller 7. Radial ball bearing 8. Radial roller bearing (only for bearing bracket)

16 35 9. Bearing bracket 10. Bearing bracket intermediate 11. Bearing cover 12. Flat seal 13. Flat seal 14. Flat seal 15. Flat seal 16. Flat seal

26. Wearing ring 27. Shaft sleeve 28. Disk 29. Pin 30. Oil level regular 31. Hexagon screw 32. Hexagon screw 33. Stud bolt 34. Stud bolt

35. Stud bolt 36. Stud bolt 37. Locking screw 38. Threaded pin 39. Inner hexagon screw 40. Nut 41. Nut 42. Impeller nut 43. Fitting key 44. Fitting key

Fig. 2.6. Back pullout-double bearing type pump with combine volute casing

14


6

1 7 2 8 3 5 10

4

9

Fig. 2.7. Heavy duty pump

Basically pump construction consists of three sub-assemblies namely (1) shaft assembly (2) casing assembly and (3) base assembly or bracket assembly. Shaft assembly, consists of impeller, impeller key, impeller nut, shaft, bushes at stuffing box, bearing inner races, pump coupling, key, and coupling nut, all mounted on a common shaft. The shaft is connected to the prime mover either through belt drive, or direct. This assembly is the only rotating assembly and hence this assembly must be perfectly balanced. But, all components in this assembly are machined components except impeller, viz., inside surface of shrouds and the blade surfaces. These surfaces are normally rough cast surfaces and could not be machined. Hence impeller only is balanced and assembled on the shaft. Casing assembly consists of suction side or front side bracket, rear side or coupling side bracket of the volute casing. However, volute casing construction changes depending upon the pumping fluids. For pumping high consistency liquid, two phase fluids, suction side bracket, coupling side bracket and volute casing are made up of three separate pieces (Fig. 2.7). For ordinary pumping liquids like water, milk, etc. suction side bracket and volute casing are single unit (Fig. 2.6). In agricultural pumps, casing is made into two halves (Fig.2.5). Suction side bracket and one half of the casing become one part. Coupling side bracket and other half the casing become another part. Coupling side bracket will also have stuffing box or mechanical seal chamber. For higher capacity pumps, the base assembly or bracket assembly consists of a bracket with provisions for assembling front and rear bearings, and bearing caps. In agricultural pumps (Fig. 2.5), however, the stuffing box and gland at the front side of the bracket and bearing chamber and bearing cap on the other side of the bracket will be the normal construction. In low capacity pumps, the bracket is fitted on a base plate along with the prime mover. The casing will be connected to the bracket. In such pumps, the entire weight of delivery pipe with fluid, the suction pipe with fluid and all minor fitting like valve, bend etc. will be connected to the casing delivery side and suction side respectively as a overhung unit. In higher and medium capacity pumps, pumps with heavy liquids, two phase fluids will have the base at the casing which is connected to the common base plate. Such assemblies are called back pull out assembly (Fig 2.6). This assembly is a convenient assembly, where in all parts, except casing can be removed by pulling the entire assembly backwards for any repair and maintenance. The pipe system need not be disturbed. However, the prime mover has to be removed from base plate, in order to remove the pump assembly parts.

PUMP PARAMETERS

15

2.3 LOSSES IN PUMPS AND EFFICIENCYTheoretically, all the energy supplied to the pump by the prime mover, in the form of mechanical energy, should be converted into fluid energy. Owing to manufacturing inaccuracies and entirely different flow conditions prevailing in pump, entire energy input (mechanical energy) is not converted into fluid energy. Referring to Figs. 2.5, 2.6 and 2.7, 100% mechanical energy supplied at the coupling side of the pump by the prime mover is reduced, due to energy absorption in bearings, stuffing box, disc friction. Hence, the energy input at the impeller will be less than the energy input at the pump coupling. Due to surface roughness inside impeller and due to the leakage flow through clearance, there will be further reduction in the energy input to the impeller. Hence, the energy output from the pump is less than the energy input to the pump. The difference between energy input and energy output of the pump is called losses in pump. The ratio of energy usefully utilized for work to the energy supplied is called efficiency. In other words, efficiency is the ratio of output energy to the input energy of the machine in doing work. Three kinds of losses prevail in fluid machines namely, (1) Hydraulic loss (2) Volumetric loss and (3) Mechanical loss. The sum of all losses will be the total loss. Overall efficiency is the product of hydraulic efficiency, volumetric efficiency and mechanical efficiency.

2.3.1 Hydraulic Loss and Hydraulic Efficiency (h) Due to surface roughness at the inner side of the impeller, through which the fluid passes, losses due to friction and losses due to secondary flow, take place, as a result of which energy loss take place. Actual head developed (Ha) will be less than the theoretical head (Hth) by the amount H = Hth Ha. H is called the hydraulic loss. Hydraulic efficiency (h) is the ratio between, actual head to the theoretical head. Hydraulic loss, H = Hth Ha Ha Hth H Ha H Hydraulic efficiency, h = = = = 1 ...(2.13) Hth Hth Ha + Hth Hth H = (1h) Hth

2.3.2 Volumetric Loss and Volumetric Efficiency (v) In order that the impeller can rotate inside the stationary casing, proper clearance is provided at the front and rear side of the impeller at wearing rings. Due to pressure difference between impeller outlet and impeller inlet at the front side of the impeller as well as the pressure difference between impeller outlet and slightly higher than atmospheric pressure at the stuffing box, part of fluid coming out of the impeller leaks through the clearances on both sides of the impeller. As a result the quantity coming out of the pump, the actual quantity (Qa) will be less than the quantity passing through the impeller, i.e., theoretical quantity (Qth) by the amount of leakage quantity passing through the clearances (Q), i.e., Q = Qth Qa. Volumetric efficiency (v) is the ratio between actual quantity and theoretical quantity Q = Qth Qa

Qa Qa Qth Q Q v = = = =1 Qa + Q Qth Qth Qth Q = (1v) Qth

...(2.14)

16


2.3.3 Mechanical Loss and Mechanical Efficiency (m) Energy loss in ball, roller or thrust bearings (NB), in bush bearings at stuffing box or in mechanical seal portion (Ns), and the disc friction losses (ND ) due to the impeller rotation inside the volute casing, which is filled with fluid are classified as mechanical losses (N ). The energy received at the impeller side of the shaft, i.e., actual power (Ni) for energy conversion into fluid energy will be less than the energy supplied at the coupling side by the prime mover, i.e., theoretical power (Nth), i.e., N = Nth Ni. The ratio between actual power (Ni) and the theoretical power (Nth) is the mechanical efficiency (m) i.e., N = ND + NB + Ns N = Nth Ni m =

N th N Ni Ni N = = =1 N th N th N i + N N th

N = (1 m) . Nth

...(2.15)

2.3.4 Total Losses and Overall Efficiency (h)Total losses = Hydraulic loss + Volumetric loss + Mechanical loss = H + Q + N. Since

Qa v = Q , output energy (N0) = Qa.Ha = Qth.v . Hth .h th

Taking Ni = Qth Hth where Ni = power available at the impeller end of the shaft, Ni = Nth N. Therefore, N0 = Ni v h = Nth m . v . h. Since m =

Ni N th...(2.16)

Overall efficiency, =

N0 = m . v . h N th

2.4 SUCTION CONDITIONSNormal and dependable operation of a pump depends mostly on suction conditions of the pump i.e., pressure at the inlet edge of the impeller blade (Fig. 2.8). Referring to the equations (2.8) and (2.9), the pressure p1 at the impeller inlet is less than the pressure at the suction chamber ps. If the suction chamber pressure ps is low or if the suction chamber is open to atmosphere i.e., ps = patm, the pressure at point 1, the inlet edge of the blade of the impeller will be under vacuum (Equation 2.10). If this pressure, p1 is lower than the local vapour pressure of the pumping fluid, corresponding to the temperature of the liquid at impeller eye (pvp), then the liquid at this point will be boiling. In other words, liquid will not be in liquid form, instead it will be in gaseous form and pumping cannot be done. Hence, the pressure at the inlet of the impeller, i.e., at the eye of the impeller, must be above vapour pressure of the flowing fluid corresponding the temperature of the fluid.

PUMP PARAMETERS

17

h 2 Cs 2 = C 0 2g 2g Xs D1 2

D0 2

C0

B Axial flow

Radial flow

Hs

A

Fig. 2.8. Suction conditions in a pump

or If

pvp p1 Cs2 ps > = hs + h fs + 2g ps pvp p1 pvp Cs2 ...(2.17) = hs + h fs + 2 g > 0 ps patm = i.e., if the suction chamber is open to atmosphere, then

p1 pvp patm pvp C2 hs + h fs + s > 0 = 2g must be greater than zero or in other words, always it should be positive i.e., patm pvp Cs2 > hs + h fs + 2 g patm pvp p1 p vp is termed as Hsv and is called Net Positive Suction Head (NPSH). is called NPSH available. The two terms patm and pvp cannot be altered, since these values patm, the atmospheric pressure at the place where pump is running and pvp is the vapour pressure, which depends upon the

C2 temperature of the pumping liquid, are fixed values. The term hs + h fs + s is called NPSH required 2g which is depending upon, the pump, viz., flow rate, pipe length and size, and the level of suction chamber with respect to the reference line of the pump. All these can be altered during pump erection at site.

18


Hence NPSH (Net) (Hsv) = NPSH (available) NPSH (required) patm pvp C2 Hsv = ...(2.18) hs + h fs + s 2g C2 ( H atm H vp ) hs + h fs + s 2g H sv = = ...(2.19) H H where is called Thomas constant. All pump manufactures give this value i.e., Hsv or by conducting test on water in the laboratory. Depending upon the site conditions, pump erection is carried out so that pump can work without cavitation. In order to have a safe operation, a reserve in the NPSH is introduced and suction lift or suction head is calculated accordingly.

C2 KHsv = (Hatm Hvp) hs + h fs + s 2g Normal values of K will be 1.15 to 1.40. Therefore, hs will be C2 hs = (Hatm Hvp) h fs + s KHsv 2g In case the pumping liquid is other than water SL where SL is the specific gravity of the liquid L and w are the specific weights of liquid and water respectively.12 Vapour Pressure ion Metres of Water Column 11 10 9 Additional Suction Head in Metres 8 7 6 5 4 3 2 1 0 10 20 30 40 50 60 70 80 90 100 110 Water Temperature C (a) 8 7 6 5 4 3 2 1 0 100 125 150 175 200 Water Temperature C

...(2.20)

...(2.21)

Hsv (L) =

H sv ( w )

=

w H svw L

...(2.22)

225

(b)

Fig. 2.9. Vapour pressure of water at different temperatures

PUMP PARAMETERS

19

2.5 SIMILARITY LAWS IN PUMPS 2.5.1 Similarity LawsA complete study of fluid flow and the flow pattern in impeller, in casing and in various other elements of pump by theoretical means could not be achieved. Thats why, experimental coefficients are used along with the theoretical equations to solve the problems in pumps. These experimental coefficients are obtained by conducting experiments on different pumps and obtaining results with the help of similarity laws and dimensional analysis. Similarity and dimensional analysis is a process of obtaining the property and characteristics of another similar pump from the available property and characteristics of a pump on which experiment was carried out and the results known. A functional relationship between different parameters of the pump tested and the pump for which the calculations are needed is established by this law. Using dimensional analysis under geometrical similarity, different expressions, connecting pump head (H), quantity (Q), power (N) and speed (n) with the impeller diameter (D), which is the standard reference linear dimension for a pump, and the properties of fluid, such as density (), viscosity () and gravitational acceleration (g) can be established. The following Table 2.1 gives the dimensions and units of different parameters used for non-dimensional analysis. TABLE 2.1: Units and dimensions Parameter 1. 2. 3. 4. 5. 6. 7. 8. Head Quantity Power Speed Diameter Gravitational acceleration Density Viscosity H Q N n D g Dimensions metre (m) m3/second (sec)Newton . m sec 1 sec m

Symbol L L3/t

ML2 t2 1 t LL/t2 M/L3M Lt

m/sec2 kg/m3

kg m sec

As per the laws of dimensional analysis, there are 8 parameters with 3 dimensions. Hence, (8 3) = 5 non-dimensional parameters can be evolved. After solving, we get the following nondimensional parameters. (1) (2)

VL which is Reynolds number Re = n D2 Q V which is Struhauls number Sh = called unit discharge KQ in fluid machines nL nD 3

20


(3) (4)

N called unit power (KN) n3 D 5

V2 which is Froude number Fr = gl n2 D H (5) D g

Multiplying non-dimensional parameters (4) and (5), we get another non-dimensional number H gH . However, since g is a constant, 2 2 is used, in practice which is called unit head (KH) in fluid 2 2 n D n D machines. Based on the above non-dimensional parameters, a functional relationship between unit power (KN) and the unit discharge (KQ) i.e., KN = f (KQ) as well as unit head (KH) and unit discharge (KQ). viz., KH = f (KQ) can be established.Ni n D3 5

Q Q , = f 2 3 = f Re , n D3 nD nD

...(2.23)

Q ...(2.24) Ni = n3D5 f Re , n D3 where, Ni (internal power) or the power input at the impeller unit i.e., the power input at the coupling side minus mechanical losses in bearings, stuffing box, and disc friction.AlsogH = f n2 D2

F GH n D

2

,

Q nD 3

I JK

=f

FG R , Q IJ H nD Ke 3

...(2.25)

Q n2 D2 f Re , or H = ...(2.26) nD3 g Equations (2.24) and (2.26) give the relation between the internal power (Ni) and head (H) with Reynolds number and unit discharge (KQ). The effect of Reynolds number is not considered, since the tests are conducted in auto model region i.e., at high Reynolds number (Re > 105), where the coefficient of friction f remains constant and is independent Reynolds number (Re). This value H will be approximate, since effect due to frictional losses is not considered. Considering two identical pumps viz., prototype (suffix p) and model (suffix m) i.e., pumps of the same series which are geometrically similar, i.e., linear dimensions are proportional and kinematically similar, i.e., flow directions are same within the impeller and in casing, i.e., blade angles are same, velocity triangles are identical.

For Head or

gH p n2 p n2 p2 Dp

= =

gH m2 2 nm Dm

Hp2 Dp

Hm2 nm 2 Dm 2 gn 2 D p p 2 gnm 2 Dm

...(2.27)

Hp Hm

=

=

K2

FG n IJ Hn Kp m

2

where

Dp K= Dm

...(2.28)

PUMP PARAMETERS

21

For Quantity

Qp n p D3 p Qp Qm Np

=

Qm3 nm Dm

or

=

n p D3 p3 nm Dm

= K3

FG n IJ Hn Kp m

...(2.29)

For Power

p n3 D 5 p pNp Nm

=

Nm3 5 m nm Dm

or

=

p n3 D 5 p p3 5 m nm Dm

=

K5

FG n Hn

p

m

IJ FG IJ K H K3 p m 3

...(2.30)

If the pumping liquid is same for both prototype and for model p = m, then = ...(2.31) Nm m Equations (2.28), (2.29) and (2.30) are called similarity equations for pumps, and include the scale and relative Roughness effect effect, i.e., include change in the effect of Reynolds number Re = nD 2 . D However, exact values, which include the change in the corresponding efficiencies between prototype and model, are given below :

Np

K5

FG n IJ Hn Kp

Qp Qm Hp Hm N ip N im

The value

FG IJ H Kvp vm

FG n IJ FG IJ Hn K H K F n I =K G J Hn K Fn I F I =K G J G J Hn K H K = K32p vp m vm 2 p

hp

m p

hm

3

5

p

mp

m

m

mm

U | | | | V | | | | | W

...(2.32)

takes into account the change in volumetric efficiency connected with the

change in the relative values of wearing clearances, balancing holes and usually connected with the hp change in scale K. The value is the change in hydraulic efficiency which is a function of hm mp Reynolds number and scale K. The value is the change in the relative values of mechanical mm losses in bearings, stuffing box and for disc friction. The equations developed under similarity laws for pumps are most important for test result analysis and widely used in pump industries, to analyse the

FG H

IJ K

22


performance of model tested in the laboratory, with the test results obtained from the prototype, tested in industries such as test at different speeds, test at different diameters, tests on liquids other than water etc., and also to develop new pumps.

2.5.2 Specific Speed (ns)Specific speed (ns) is defined as the speed of a geometrically similar pump which consumes 1 (metric) hp and develops 1 m of total head, the pumping liquid being water under normal temperature of 4C and at atmospheric pressure of 1.0336 kgf/cm2, and = 1000 kgf/m3 viscosity = 1 centipoise or = 1 centistoke i.e., n = ns, when N = 1 hp and H = 1 m. Since, N (hp) =QH . 75 = 1000 kgf/m3

Substituting the values

N (hp) = 1 hp, H = 1 m

1 75 = 0.075 m3/sec. 1000 1 Referring to equation for unit power, KN and substituting the values. N 1 = 3 5 n 3 D 5 ns DsQ = N =n3 D 53 5 ns Ds

=

K5

FG n IJ Hn Ks

3

...(2.33)

gH g .1 2 2 = 2 n D ns Ds2

or

F nI F DI H = G J .G J Hn K HD K2 s s 6

2

=

K2

FG n IJ Hn Ks

2

...(2.34)

Combining equations 2.33 and 2.34 N2

H5 N2

FG n IJ and H = K FG n IJ = Hn K Hn K F n I or n = n N = G J Hn K HK105 10s s 4

10

4

2

s

4 s

5

ns = Since

n N

H5 4 QH N = 75

...(2.35)

ns = Since

= 75

n Q 1000 3.65 3 / 4 75 H

= 1000 kgf/m3

PUMP PARAMETERS

23

H H 3/ 4 Equation (2.35) is used for turbines and equation (2.36) is adopted for pumps.

Hence

ns =

n

N5/ 4

= 3.65

n Q

...(2.36)

2.5.3 Unit Specific Speed (nsq)Unit Specific Speed (nsq) is defined as the speed of a geometrically similar pump delivering 1 m3/sec of discharge and develops 1 m head i.e., n = nsq where Q = 1 m3/s and H = 1 m, i.e., ns =

n Q H 3/ 4

.gH Q and into one by removing D 2 2 n D nD 3

Combining

Q nD3 gH n2D2 Therefore,

or or

D3 D2

Q n gH n2

or or or

D6 = D6 =

Q2 n2 g3H 3 n6

Q2 g3H 3 2 n n6 n 4 Q2 = Constant g3H 3

n 6Q2 = Constant n2 g 3 H 3 n Q

or

= Constant (nsn) ...(2.37) ( gH ) 3/ 4 Equation (2.37) is called non-dimensional specific speed (nsn). Since g is a constant, it can be taken to the right hand side. Unit specific speed, nsq = Similarly, combiningn Q H 3/ 4

or

.

gH N and into one and by removing D in both expressions n2 D2 n 3 D 5 gH n2 N n3

gH n2 D2 or D2 N n3D5

or

D10

g5H 5 n10

or

D5

or

D10

N2 2 6 n

So

N2 g5 H 5 2 6 n n10 n10 N 2 = Constant 2 g 5 H 5

or

n10 N 2 = Constant g 5 H 5 2 n 6

or

24


or

n

N

g 5/ 4 H 5/ 4

= Constant = nsn

...(2.38)

where nsn is the non-dimensional specific speed. Since N = QH = g QH, substituting this value in the above equation

n

g5/ 4

Q H5/ 4

H= Constant

gor

n Q

= Constant = nsn ( gH )3/4 which is the same nsn as defined earlier. While calculating the specific speed, all efficiencies i.e., volumetric, hydraulic, mechanical and overall efficiencies are assumed to remain same for one value of ns i.e., for one series, independent of size, capacity, head of the pump, of same ns. This is not correct since larger size and capacity pumps will have higher efficiency than smaller capacity units of same ns. This is the only drawback in the calculation of specific speed. Referring to the specific speed equation, it can be said that each value of specific speed, ns refers to one particular series of geometrically similar pumps i.e., a number of pumps with different H, Q, n can be developed, all having same (ns) specific speed. From the above it can be concluded that each value of ns refers one particular series of geometrically and kinematically similar pump, each pump in this series will be identical to the other. It can also be said that for the same value of head and discharge (H Q) different types of pumps in different series can be obtained with different specific speed, by changing the speed n. Each pump will be different in type and construction. But due to limited suction conditions and due to cavitation and subsequent vibration, noise and damage of pump parts at higher speeds, high speeds are not recommended unless otherwise needed. Moreover, maximum efficiency can be obtained only at a particular speed for the given head (H) and discharge (Q) i.e., for given ns only at one particular speed. In fact, the specific speed, ns is calculated at the maximum efficiency point only. Normally pumps are driven by electric motor (speed will be 720, 960, 1450, 2990 rpm) or by I.C. Engines (750 or 1000 rpm) or by Turbines (25000 to 50000 rpm). Hence, pumps are always selected or developed to give maximum efficiency at these speeds. The value of specific speed, the type of pump will be always selected for the given H Q of pumps and from the speed, n of the prime mover coupled to the pump.

2.6 CLASSIFICATION OF IMPELLER TYPES ACCORDING TO SPECIFIC SPEED (nS)The shape and type of impeller depends upon the specific speed ns. For the same head and discharge, the specific speed (ns) is directly proportional to the speed (n). ns increases when the speed is increased. When the speed increases, the shape and type of impeller change. In first approximation the pump head (H) is directly proportional to the peripheral velocity or blade velocity (u). This is evident from the non-dimensional equation H n2 D2 u2. When speed (n) decreases the diameter (D) increases.

PUMP PARAMETERS

25

Outer diameter (D2) of the impeller is the characteristic linear dimension or the reference diameter D. So increase in speed n decreases the diameter D2 and correspondingly the size and weight of the pump is reduced which is naturally most advantageous, provided suction conditions do not have any limitations. The eye diameter (D0) or the inlet diameter (D1) is determined from the quantity of flow (Q). D0 or D1 D D and slightly reduces when speed is increased. So the ratio 2 or 2 reduces with the increase of ns. D0 D1 b Also for the given quantity, the diameter D2 reduces, the breadth b2 increases. So 2 increases with the D2 increase of ns. When ns the specific speed increases, the flow rate (Q) increases and total head (H) decreases. High head-low discharge pumps have low specific speed. The pumps have higher value of (D2/D1) and low value of (b2/D2). Impeller blades are in radial direction and of single curvature design. These pumps are called radial flow centrifugal pumps. Medium head-medium discharge pumps have medium specific speed. These pumps have medium D b value of 2 and 2 . At lower range of medium specific speed, the impeller blades have double D1 D2 curvature at inlet and single curvature at outlet. The outlet edge of the blade is parallel to the axis. The inlet edge of the blade extends towards the eye of the impeller in order to reduce blade loading since outer diameter D2 is reduced. When the specific speed increases further the inlet and outlet edges are inclained i.e., neither radial nor axial. The blades have double curvature design. Flow through the impeller is neither radial nor axial, but is in mixed or diagonal direction. These pumps are called mixed flow pumps or diagonal flow pumps. Low head-high discharge pumps have high specific speed. Inlet and outlet edges of impeller blade are almost perpendicular to the flow direction. The blades are of double curvature design. These pumps are called axial flow pumps. Very low head and very high discharge condition gives very high specific speed. The fluid flow direction in impeller is axial. Ship propellers belong to this category. In general, pumps are classified as radial, mixed, diagonal or axial, depending upon the fluid flow through the impeller passage. All positive displacement pumps have very low discharge and very high head and hence very low specific speed. Theoretically, specific speed changes from 0 to i.e., from zero discharge to zero head as well as change in speed. Practically very low speed and very high speeds could not be attained, so also very low head and very high discharge are limited and hence the specific speed.D D1 D2 D C B 80 350 450 800 A ns

Fig. 2.10. Form and shape of impeller for

D2 D1

26


Figs. (1.3) and (2.10) give different forms or shapes of impellers and their range of specific speeds as well as the range of diameter ratio (D2/D1). TABLE 2.2: Specific speed of pumpsType of impeller3.65 n H 3/ 4 Q

Positive displacement pumps

Centrifugal Radial Mixed Low Normal Higher discharge discharge discharge 4080 80150 150300

Mixed

Axial Ship propellers 12001800 and above

Diagonal 300400

Propeller 400600

Propeller 6001200

ns=

835

D2 D1n H Q3/ 4

2.5

2

1.81.4

1.31.15

1.151.1

0.80.6

0.60.55

nsq =

210

1022

2241

4182

82110

110165

165330

330495

n Qnsq =

( gH ) 3/ 4

0.361.8

1.84.0

4.07.4

7.414.8

14.819.8

19.829.8

29.859.5

59.589.3

2.7 PUMPING LIQUIDS OTHER THAN WATER 2.7.1 Total Head, Flow Rate, Efficiency and Power Determination for Pumps when Pumping, Liquids other than WaterUnlike turbines; pumps are used not only for pumping clear cold water at normal temperatures, but also for pumping liquids with different properties such as different densities, different viscosities and different consistencies, pumping not only at normal temperatures, but also at cold or hot temperatures. Liquids may be corrosive or non-corrosive, two phase fluids such as gas-liquid or solid-liquid mixtures, milk, distilled water, acids, alkaline solutions, cryogenic liquids like liquid hydrogen, liquid oxygen, liquid nitrogen, liquid ammonia, molasses, tar, petrol, diesel, crude-oil etc. It is not possible to design each pump for each liquid and test them in the laboratory with the pumping liquid at the actual field working conditions. Pump design is always carried out for clear water at normal temperature. Water is considered as reference liquid for all the liquids mentioned above. For pumping liquids with viscosity and consistency, correction coefficients KH , KQ and K (or Ke) are used for converting the liquid parameters to equivalent water parameters. These coefficients are taken from standard recommended graphs and tables. These values are the consolidated results from a number of experiments by many authors and recommended by International Hydraulic Institute and Bureau of Indian Standards | 46 |. Suitable pump is then selected from the commercially available water pumps for which performance characteristics are known.

PUMP PARAMETERS

27

2.7.2 Effect of TemperatureIncrease in the temperature of the liquid decreases the density, viscosity and consistency and increases vapor pressure of the liquid. Due to high temperature of pumping liquid, the dimensions of pump parts change at running condition, due to thermal expansion of the material of the pump parts. Extra dimensional allowances in clearances are given depending upon the temperature of the pumping liquid and coefficient of thermal expansion of the material of the pump parts. These pumps are brought to the running temperature by filling with the pumping liquid or by external heating, before starting of the pump for smooth and vibration free operation. These pumps will not be started at normal temperatures and also should not be used for liquids at other than the recommended temperature. Increase in vapor pressure due to increase in temperature of the pumping liquid changes the net NPSH value and also reduction in suction lift. The system at suction side of the pump must be suitably altered for cavitation free operation of the pump. Recommended changes are given in chapter 9 of this book.

2.7.3 Density Correction ( or ) Pumping pressure p and the total head (H) are related by the hydrostatic equation p = H = g H where is the specific weight and is the density of the pumping liquid and g is the gravitational acceleration. For the same pumping pressure, total head of the pump changes according to the specific weight (v) or the density (v) or the specific gravity (Sv) of the pumping liquid i.e., p = w Hw = v Hv = Sv w Hv Since rv = Sv w. Suffix w is for water and suffix v is for the viscous liquid. Hw =v H v = Sv Hv w

Although theoretically density has no influence on flow rate i.e., Qw = Qv, practically Qv changes by 2 to 3% Qw and even up to 5% at higher density of pumping liquid due to the influence of surface tension. For high temperature liquid pumping at tC, the density of pumping liquid (tC) is calculated as (equation 2.39).

1 + t C (t C 15 C ) where (tC) is the coefficient and (15C) is the density at t = 15C.Table 2.3 gives the values of (tC) for different values of (15C). TABLE 2.3: Density correction coefficients 15C tC 0.7 82 1010 0.8 77 105 0.85 72 105 0.9 64 105 0.95 60 105

tC =

15 C...(2.39)

28


2.7.4 Viscosity CorrectionPerformance of centrifugal pump changes when the viscosity of the pumping liquid changes. For higher viscous liquids, total head (Hv), flow rate (Qv) and efficiency (v) reduce considerably. Correspondingly, power consumption (Niv) increases. Head-discharge graph droops down more. Overall efficiency reduces. Optimum efficiency shifts to lower flow rate condition. Power consumption increases considerably especially at high viscous liquid pumping due to higher reduction in efficiency. However, shut off head of viscous liquid remains same as that of water. Fig. 12.27 shows the change in pump parameters when viscosity of the pumping liquid changes. However, up to liquid viscosity 20 C.S., pump performance for viscous liquid pumping does not change with respect to the pump performance pumping with water. Correction is applied only if the pumping liquid viscosity is more than 20 C.S. Figure 2.12 gives the values of coefficient for flow rate (KQ), coefficient for total head KH and coefficient for efficiency (Kn or Ke) for different values of Qv, Hv and v, where v is the viscosity of liquid in (S or SSU). If the temperature of pumping liquid is higher, viscosity (tC) at the temperature (tC) is calculated as 0.01775 ...(2.40) tC(C.S.) = 1 + 0.0337 t + 0.00023 t 2 tC must be taken while referring the Fig. 2.12. However, this graph can be referred only for : (a) Pumps of radial type centrifugal pumps under the normal operating range, having open or closed impellers. It cannot be used for mixed and axial flow pumps or for pumps of special design of impellers such as s-type impellers, single blade or two blade impellers or for nonuniform liquids like, slurries paperstocks etc., since it may produce widely varying results, depending upon the particular characteristics of the liquids. (b) Sufficient NPSH should be available in water parameters in order to avoid cavitation. Relation between viscous and water parameters is expressed as Qv = Hv = v = Niv = KQ . Q W KH . Hw K . w( Sv w Qv H v ) (kW) 1000 v

...(2.41)

2.7.4.1 Determination of Water Parameters for the Given Head, Quantity and Viscosity of the Pumping LiquidFor the given total head (Hv), quantity (Qv), efficiency (v) and specific gravity (Sv) at the pumping temperature (tC) of the viscous liquid to be pumped, equivalent water parameters (Hw, Qw, w, Niw) can be determined referring the graph (Figures 2.11 and 2.12). The procedure is as follows: From the point of given viscous quantity (Qv) (Point A) in X-axis, a vertical line is drawn to meet the given viscous head (Hv) line (Point B). From this meeting point of Hv and Qv (Point B) a horizontal line, either left or right, is drawn to intersect the given viscosity (v) line (Point C). From the point C, a

PUMP PARAMETERS100 90 Water pump peak efficiency %

29

Head

80 70 60 100 90 20 30 40 50 60 90 80 70

Capacity

80 70 60 50 100 90 80 70 20 30 40 50 60 70 80 90 Water pump peak efficiency %

Efficiency

60 50 40 Water pump peak efficiency % 30 20 10 20 30 40 50 60 70 80300 200 150 100 75 50 40 30 20 15 10 5m

90

00 15,0 0 ,00 1 0 00 50 0 0 80 00 40 00 30 0 0 20 0 0 15 00 10 0 90 0 80 0 40 0 30 0 20 0 15 0 10 90 80

Head per stage in m at peak efficiency for water at actual operating r.p.m.

40

V is co s ity

1000

1400

10

15

20

30

40 50 60

80 100

150 200

300

400

600 8002000

30

40

50 60 70 80 100

150

200

300

400 500 600 700 800 1000

3000 4000 5000 6000 8000 imp gpm

Fig. 2.11. A viscosity correction nomogram based on that quoted by (from Davidson (3), 1993, Process Pump SelectionA System Approach, Second Edition IMechE, London)

1800 2200

300 200 150 100 75 50 40 30 20 15

m /hr

3

301.0 0.9 0.8


KH0.60 0.80 1.00 1.20

Correction Factors

0.7 0.6 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 KQ

33.4 45.2 60.5 75 114 132 190 223 304 350 436 610 760 915 1217

1670 2280 3190

6.25

11.8 16.5 21.2

Hm200 150 100 80 60 40 30 25 20 15 10 8 6 4

KCentistokes

Engler

1.5

2

2.5 3

4.5

20 25 30 40 50 60

10 15

6

8

160

100

1000

50

130

300

200

400

60

20

30

10

500

600

800

1500

100 120

220

80

2000

300 430Q imp gpm

Fig. 2.12. Performance correction chart for viscous liquids

vertical line is drawn to meet the correction curves K, KQ and KH at peak water efficiency points D, E, F respectively. The values K, KQ and KH are the correction coefficients. By using the equation (2.41), equivalent water parameters QW, HW, W can be calculated. For multistage pumps, the total head (Hv) must be the total head per stage only i.e., Hv = [(HV) multistage/number of stages]. Based on the water parameters (HV and QV), suitable pump can be selected from the commercially available pumps.

2.7.4.2 Determination of Viscous Parameters When Water Parameters are KnownFor the given Hw, Qw, w values of water pump, equivalent viscous parameters Hv, Qv, and v can be determined, referring the graph (Figures 2.11 and 2.12). From the performance characteristics of the available water pump, namely Hw = f (Qw), w= f (Qw) and Niw = f (Qw), where Qw is the quantity at the

PUMP PARAMETERS

31

maximum efficiency condition and Hw, w, Nw are the corresponding values at Qw, the values of Hw, w, Nw for 0.6 Qw, 0.8 Qw, 1.0 Qw and 1.2 Qw are determined. As first approximation, all the above determined water parameters are assumed as viscous liquid parameters, so that graph (Figs. 2.11 and 2.12) can be referred to find KH, KQ, and K for all four capacities, following the same procedure as mentioned. Using the equation (2.41), equivalent values of HV, V, and QV can be calculated for all four Qw capacities. Two graphs Hw, V, NW = f (QW) and Hv, V, NV = f (QV) are drawn taking shut off head is same for water and for viscous liquid pumping. From this curve QV, can be found out for the given value of Qw, and other values. One such graph is given in Figure 2.13.H N H

Q 0, 6

0, 8 Q

1, 0 Q

1, 2 Q N

Water parameters Q

Viscous liquid parameters

Fig. 2.13. Determination of viscous parameters from water parameters of pump

Example: A water pump has the following details as per the performance graph: Optimum efficiency condition W (max)= 80% is at QW = 150 m3/hr. Corresponding Hw = 40 m, Nw= 28 kW. Pumping liquid viscosity is 57 CS. Referring to the performance characteristic of water pump, the values of HW, W, NW, for 0.6 Qw = 90 m3/hr, 0.8 Qw = 120 m3/hr and for 1.2 Qw = 180 m3/hr are found out. Referring the conversion graphs (Figs. 2.11 and 2.12), the values of K,KH, and KQ for all four capacities are determined. Using equation (2.41), HV ,QV, V, and the power required for viscous fluid pumping NV, are calculated. All these values are given in Table 2.4. TABLE 2.4: Viscous parameter determination from water parameters% QW values Parameters Flow rate m3/hr QV = KQ.QW Total head m HV = KH . HW Efficiency % V = KW Input power kW Qw QV HW HV W V NW NV 0.6 90 88.2 44 43.2 70 49 15.7 21.6 0.8 120 117.5 42 40.8 78 54.5 17.9 24.6 1.0 150 147 40 38 80 56 20.9 27.6 1.2 180 176.5 36 33.5 77 54 23.1 29.8

32


Based on the results tabulated in above table (2.4), HV, V, NV = f (QV) are drawn in the same scale and in the same available performance characteristics of water pump, taking shut off head same for both liquids. From this graph (Fig. 2.13), for any value of QW, HW, W, corresponding values of QV, HV, V and NV can be determined.

2.7.5 Effect of Consistency on Pump PerformancePumps in chemical and process industries, handle two phase fluids i.e., liquid with another nonmixing liquid, liquids with solids in suspension, gas particles in liquids. Apparently average specific gravity of such mixtures is different from specific gravity of liquid alone. The problem becomes more difficult, if the liquid is other than water, which is very common in chemical industries. As a result, the net pumping head, flow rate, power, NPSH of the mixture change. So the pump parameters of the mixture is converted into equivalent water parameters by using experimental coefficients called consistency factor. Consistency is defined as the percentage by volume or by weight (or specific gravity) of the solid content or gas content or other liquid present in suspension in the whole pumping mixture. It is the property of material by which, a permanent change of shape is resisted and is also defined by the complete force-flow relationships. As done for viscous fluids, the experimentally determined conversion factors are used to determine the liquid parameters. The following equations are used for such conversion: Pulp (or) stock rating for Q or H ( Qs or H s ) Water Rating (Qw or HW) = Conversion factor for Q or H ( Eq or EH ) ... (2.42) HS = EH , HW , QS = EQ . QW Water efficiency (W) Conversion factor (E) = Pulp or stock efficiency (s) W E = s Table 2.5 gives the conversion factor for pulp or stock pumping at different consistency conditions | 5 |. TABLE 2.5: Consistency conversion coefficient Pulp or stock consistency % 1.0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 EQ 0.99 0.99 0.98 0.97 0.96 0.92 0.87 0.80 0.72 0.62 0.52 0.42 EH 1.00 1.00 1.00 1.00 0.99 0.98 0.97 0.95 0.93 0.90 0.87 0.83 E 0.99 0.99 0.98 0.97 0.95 0.90 0.85 0.76 0.67 0.56 0.45 0.35

PUMP PARAMETERS

33

Such conversion factors are available for different liquid mixtures from the manufactures such as KSB pumps, pump manual or International Hydraulic Institute Standards. Rotodynamic pumps can be used only up to 7% consistency. For consistencies above 7%, positive displacement pumps must be used. Correct design, construction and material of pump parts must be followed especially for impeller blade shape, casing shape and location, sealing arrangement, and cooling arrangements such as external cooling or mother liquid circulation for cooling and sealing to suit the pumping fluid and operating conditions. In this book, water handling pumps and their constructions are only dealt with and discussed in chapter 13. For special pumps, however, handling hydrocarbons and other high consistency liquids, specific manufacturers recommendation must be referred.

2.7.6 Special Consideration in Pump SelectionNormally pumps are manufactured as per the manufacturers standard of production range. Any customer selects pump for his requirement from the available standard ranges. Sometimes, pumps are selected according to space availability in the field such as in ships, rigs, railways, in general for transport systems and sometimes to replace the existing pump with the new pump especially in mechanical and process industries. In such cases, efficiency is not considered as a major factor, instead functional applications such as fitting the pump in the space available, non-stop or continuous operation even at emergency conditions are considered as important. Such conditions change from field to field and installation to installation. Pumps must be designed and constructed and must work as per the requirement of prevailing conditions at the fluid.

3THEORY OF ROTODYNAMIC PUMPS3.1 ENERGY EQUATION USING MOMENT OF MOMENTUM EQUATION FOR FLUID FLOW THROUGH IMPELLEREnergy transfer from the impeller blade to the fluid, per unit mass (or weight) of fluid flow, when fluid passes through the impeller, can be developed by using momentum equation between point O, just before the impeller blade and point 3 just after the blade. The cylindrical contour surface passing through point O and point 3 are shown in figure (3.1). The contour circles drawn with radius r1 passing through the point O and with radius r2 passing through point 3 are connected to the front and rear shrouds (Fig. 3.1). Pressure and velocity forces, on both sides of the shrouds, are equal and opposite and hence get cancelled. Only two forces, due to absolute velocities, one acting on the outer cylindrical surface 3 and another on the inner cylindrical surface O are responsible for energy transfer. Taking moment of this momentum at inlet and at outlet i.e., moment of tangential component of these forces with respect to the centre of the circle and since l0= r0 cos 0, r0= r1, C0 cos 0 = Cu0= Cu1 and l3 = r3 cos 3, r3= r2, C3 cos 3 = Cu3 = Cu2, the reactive moment due to the tangential forces acting on the cylindrical surfaces 3 and 0 will beC3 Contour C0 0 3 Contour line 3 C u3 3

r3=r2

r0=r1

l3

C u0 l0 0 r 1

0

r20

II

I

Fig. 3.1. Moment of momentum equation as applied to impeller

Moment M 0 = C0 l0 = C0 r0 cos 0 = Cu1r0 = Cu1r1 Moment M 3 = C3l3 = C3 r3 cos 3 = Cu 3 r3 = Cu 2 r2 ...(3.1) Taking into account, moment Mf due to friction, created due to the fluid passing through blade passages, total moment M will be M = M3 + M 0 + M f34

THEORY OF ROTODYNAMIC PUMPS

35

rQ (Cu 2 r2 Cu1 r1 ) + M f ...(3.2) g For ideal fluid flow, Mf = 0. Energy transfer per unit weight of fluid flow through the impeller of a pump i.e., the theoretical head developed under infinite number of blades, with infinitesimally smaller vane thickness, will be= Hth = where M = N, Q = W and u = r. Equation 3.3 is the Eulars equation for the head developed by a pump.

M Cu 2 Cu1 = Q g

...(3.3)

3.2 BERNOULLIS EQUATION FOR THE FLOW THROUGH IMPELLEREulars equation for an elementary flow along a streamline (S) is given by

1 p dC C C s C C C C 2 . = = = + + C= + Fs t s t s dt t s t s 2 where, Fs = Resolved component unit of mass along the direction of the streamline S p = pressure C = velocity (absolute) = density For an elementary length ds on the streamline the equation (3.4) can be written asFs ds For steady flow condition Therefore,

...(3.4)

C2 C 1 p ds ds = ds s s 2 t

...(3.5)

C = 0. tFs ds

...(3.6) ds = 0. mg The force due to unit mass is the gravitational force g = which is directed downwards. m Fg = g.Taking vertically upward direction of Z-axis as +ve direction anddZ ds Substituting this value of Fs in equation 3.6 and changing the sign Fs Fg ( cos Z , ds ) = g

C2 1 p ds s s 2

...(3.7)

+g

dZ 1 p C2 ds + ds + ds = 0 ds s s 2 gdZ + dp C2 +d = 0 2

...(3.8)

or

36


For compressible flow, density is a function of the pressure p i.e., = f ( p). Integrating the equation (3.8) with respect to ds

dp C 2 + = Constant ...(3.9) gZ + 2 For incompressible fluid, the density is constant. The specific weight = g. Hence, the equation (3.9) can be written for unit weight of fluid as,p C2 +Z + = Constant 2g

...(3.10)

Equations (3.8), (3.9) and (3.10) are called Bernoullis equation derived from fundamental Eulars equation of motion under steady absolute flow condition along a streamline. It is evident that, this equation cannot be applied for the change of energy of ideal fluid under unsteady absolute motion of fluid in impellers. Perhaps this equation can be applied for other elements like approach pipe with or without inlet blades, volute casing, diffuser, return passage of multistage pumps, which are non-moving or stationary elements, where steady flow prevails under optimum conditions. For impellers, however, steady flow condition can be applied for relative velocity of flow of fluid since this velocity is actual velocity flowing past the blades. Referring the equation (3.7) the force Fs in impeller blades consists of the gravitational force Fg and inertia force (since blade is moving) namely centrifugal force FCF and Coriolis force Fc . Fs = Fg + FCF + Fc ...(3.11) For unit mass flow along the streamline S, the gravitational force Fg = g towards downward direction. The centrifugal force FCFdZ and is directed ds = 2 r, where is the angular velocity and

r is the radius, and is directed towards radial direction. Coriolis force, Fc = w sin ( w) , is directed normal to the direction of relative velocity, vector w and angular velocity . Since ds = w dt along the streamline, the resolved component of the total mass force Fs will be Fs = fg cos (Fg.ds) + FCF cos (r.ds) + Fc cos (Fc.ds)

Wu W. sin (,w)

Fc F cu Fcr acu u a cr

W

Wr

Wz

Fig. 3.2. Vector diagram for Coriolis component Fa determination of Mz

THEORY OF ROTODYNAMIC PUMPS

37

Taking axis of rotation vertically upwards as +ve direction the resolved component of the mass force in relative motion along a streamline will be Fs = gdz dr + 2 ds ds

...(3.12)

substituting the value of Fc in equation (3.6) and since, Fcs = Fc cos (Fc.ds) = 0, because of the direction of Fc normal to the direction of w on the elemental strip ds where the relative velocity w is tangential to the streamline g

dr w2 1 p dZ ds ds ds = 0 ds + 2 r ds s s 2 ds2 w2 dp 2 r +d gdZ d + =0 2 2

...(3.13)

Simplifying

...(3.14)

Integrating the above equation (3.14) and since u = r

dp w2 u 2 + = Constant ...(3.15) 2 For an incompressible fluid flow, the density is constant and independent of pressure p. Hence, the above equation can be written asgZ + for unit mass flow for unit weight flow

gZ +

p w2 u 2 + = Constant 2

...(3.16) ...(3.17)

w2 u 2 +Z + = Constant 2g

Th

Rotodynamic Pumps

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