Design of A Dowtherm A Pumping · PDF fileDesign of A Dowtherm A Pumping System ......

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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 1 (2016) pp 265-272 © Research India Publications. http://www.ripublication.com 265 Design of A Dowtherm A Pumping System 1 Karthik Silaipillayarputhur, 2 Khalad Al-Muhaysh, 3 Othman Abdullatif Al Yahya 1-3 Department of Mechanical Engineering King Faisal University, Saudi Arabia. Abstract A pumping system from a chemical plant in Chattanooga, TN, USA, is considered in this paper. A pumping system is designed to transfer Dowtherm A (heat transfer fluid) chemical at saturated liquid state, operating at 650°F between two storage tanks. Emphasis is given to pump selection, the various steps in determining the pump specifications, material selection, pipefittings and insulation selection. The importance of net positive suction head (NPSH) calculation is described in the analysis. DuPont Process Safety Management (PSM) Engineering standards are employed in selecting the appropriate materials. A MATLAB model and an Excel model are developed to simulate the required head for various flow rates, pipe dimensions and tank pressures. The steps outlined herein can be used as a reference for designing pumping system for any application. Keywords : Design of Pumping System, Modeling Pumping System Introduction Pumping system is commonly encountered in process industries, power plants, residential units, commercial units, etc. In critical pumping systems, understanding the system and proper equipment and material selection is very important for safe and reliable operation of the system. An improper choice of equipment or material can create a significant safety incident that can harm the environment or mankind. In this project, a pumping system from a chemical plant in Chattanooga is considered. Therein, Dowtherm A, a heat transfer fluid is the pumping medium. Heat transfer fluids are commonly encountered in process plants as they provide very high temperatures at very low pressures as compared to steam. In this work, Dowtherm A chemical at saturated liquid state operating at a temperature of 650°F has to be pumped between two storage tanks. Refer to Figure 1 for details. Herein, emphasis is given to pump selection and to the various steps in determining the pump characteristics. Importance of NPSH calculation is discussed in this study. Occupational Safety and Health Administration (OSHA) standards and DuPont PSM standards are employed in selecting appropriate materials and insulation for the pumping system. Pumps and piping systems have been widely discussed in the literature. Several textbooks and pump manufacturers have described them and only pertinent references are discussed herein. Janna [1] discusses pump and piping systems that includes types of pumps, pump testing methods, piping system design practices, pipe and tubing standards, etc. Tuzson [2] discusses the centrifugal pump design that includes pump specifications, system modeling, pump types, pump configurations, cavitation, performance calculations, system modeling, etc. Jones [3] discusses the design of a pumping station that includes the selection of piping, valves, pump types, pump selection, installation, etc. Chen [4] came up with a single explicit equation for Newtonian fluid correlating the friction factor, pipe roughness, diameter, and Reynolds number for transition and turbulent flow regions that has the same accuracy as that of the implicit Colebrook equation. Engineering Data Book [5] from Hydraulic Institute describes pipe sizes, pressures, relative roughness and friction factors for pipes, the importance of NPSH, etc. DuPont PSM standards [6], a starting point for the OSHA regulations is employed in this project. DuPont PSM standards have been widely accepted and implement across the globe and is considered as one of the best safety standards in the world. The material selection by using the DuPont PSM standards for pipe, fittings, valves, gaskets, insulation, studs and nuts have been discussed in this paper. List of symbols D Diameter of pipe Ɛ – Pipe roughness f Friction factor g Acceleration due to gravity hL Head loss in piping system; cumulative of major and minor losses K Loss coefficient for fittings L Length of piping NPSH Net positive suction head ΔP – Pressure developed by the pump (Pump discharge pressure Pump inlet pressure) Re Reynolds number V Velocity of flow υ – Kinematic viscosity of the fluid Proposed System Pumping system A pumping system consists of storage tanks, pump(s), piping, fittings (such as elbows, valves, tees, etc.), pipe fittings, pressure gages, relief devices for the tanks, controls etc. Proper design and selection of materials/equipment are required for safe and reliable operation of the pumping system. Consider Figure 1

Transcript of Design of A Dowtherm A Pumping · PDF fileDesign of A Dowtherm A Pumping System ......

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 1 (2016) pp 265-272

© Research India Publications. http://www.ripublication.com

265

Design of A Dowtherm A Pumping System

1Karthik Silaipillayarputhur, 2Khalad Al-Muhaysh, 3Othman Abdullatif Al Yahya

1-3Department of Mechanical Engineering

King Faisal University, Saudi Arabia.

Abstract

A pumping system from a chemical plant in Chattanooga, TN,

USA, is considered in this paper. A pumping system is designed

to transfer Dowtherm A (heat transfer fluid) chemical at saturated

liquid state, operating at 650°F between two storage tanks.

Emphasis is given to pump selection, the various steps in

determining the pump specifications, material selection,

pipefittings and insulation selection. The importance of net

positive suction head (NPSH) calculation is described in the analysis. DuPont Process Safety Management (PSM) Engineering

standards are employed in selecting the appropriate materials. A

MATLAB model and an Excel model are developed to simulate

the required head for various flow rates, pipe dimensions and tank

pressures. The steps outlined herein can be used as a reference for

designing pumping system for any application.

Keywords : Design of Pumping System, Modeling Pumping

System

Introduction Pumping system is commonly encountered in process industries,

power plants, residential units, commercial units, etc. In critical

pumping systems, understanding the system and proper

equipment and material selection is very important for safe and

reliable operation of the system. An improper choice of

equipment or material can create a significant safety incident that

can harm the environment or mankind. In this project, a pumping

system from a chemical plant in Chattanooga is considered. Therein, Dowtherm A, a heat transfer fluid is the pumping

medium. Heat transfer fluids are commonly encountered in

process plants as they provide very high temperatures at very low

pressures as compared to steam. In this work, Dowtherm A

chemical at saturated liquid state operating at a temperature of

650°F has to be pumped between two storage tanks. Refer to

Figure 1 for details. Herein, emphasis is given to pump selection

and to the various steps in determining the pump characteristics.

Importance of NPSH calculation is discussed in this study.

Occupational Safety and Health Administration (OSHA)

standards and DuPont PSM standards are employed in selecting appropriate materials and insulation for the pumping system.

Pumps and piping systems have been widely discussed in the

literature. Several textbooks and pump manufacturers have

described them and only pertinent references are discussed herein.

Janna [1] discusses pump and piping systems that includes types

of pumps, pump testing methods, piping system design practices,

pipe and tubing standards, etc. Tuzson [2] discusses the

centrifugal pump design that includes pump specifications,

system modeling, pump types, pump configurations, cavitation,

performance calculations, system modeling, etc. Jones

[3] discusses the design of a pumping station that

includes the selection of piping, valves, pump types,

pump selection, installation, etc. Chen [4] came up with

a single explicit equation for Newtonian fluid

correlating the friction factor, pipe roughness, diameter,

and Reynolds number for transition and turbulent flow

regions that has the same accuracy as that of the implicit

Colebrook equation. Engineering Data Book [5] from Hydraulic Institute describes pipe sizes, pressures,

relative roughness and friction factors for pipes, the

importance of NPSH, etc. DuPont PSM standards [6], a

starting point for the OSHA regulations is employed in

this project. DuPont PSM standards have been widely

accepted and implement across the globe and is

considered as one of the best safety standards in the

world. The material selection by using the DuPont PSM

standards for pipe, fittings, valves, gaskets, insulation,

studs and nuts have been discussed in this paper.

List of symbols D – Diameter of pipe

Ɛ – Pipe roughness

f – Friction factor

g – Acceleration due to gravity

hL – Head loss in piping system; cumulative of

major

and minor losses

K – Loss coefficient for fittings

L – Length of piping

NPSH – Net positive suction head

ΔP – Pressure developed by the pump

(Pump discharge pressure – Pump inlet

pressure)

Re – Reynolds number

V – Velocity of flow

υ – Kinematic viscosity of the fluid

Proposed System Pumping system

A pumping system consists of storage tanks, pump(s),

piping, fittings (such as elbows, valves, tees, etc.), pipe

fittings, pressure gages, relief devices for the tanks,

controls etc. Proper design and selection of

materials/equipment are required for safe and reliable

operation of the pumping system. Consider Figure 1

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266

describing the pumping system that needs to developed/designed

for the given project. Dowtherm A chemical enters tank A at the

rate of 80 GPM and this chemical must be pumped at a suitable

rate to tank B. Dowtherm A is operating at 650°F and is at

saturated liquid state. The existing pressures of tank A and tank

B, the required piping and the available head are all described in Figure 1.

Figure 1: Pumping system from the chemical facility

Pump selection

Pumps are the heart of any pumping system; they make the fluid

move from one point to another by increasing the flow and by

creating the pressure difference. There are two general types of

pumps: - Centrifugal pumps

- Positive displacement pumps

The centrifugal pumps may further be classified as conventional

centrifugal pumps and special design pumps such as canned

motor pumps. In a centrifugal pump, the impeller is rotating at

high speed and creates lower pressure at the eye of the impeller.

The lower pressure created at the eye of the impeller draws the

liquid into the pump casing. The vanes in the impeller add energy

to the liquid. Two types of energy are added to the liquid and they

are as follows:

1. Kinetic energy, which is seen by the increase in the liquid velocity

2. Potential energy, which is seen by the increase in the

pressure

Centrifugal pumps are used for low viscous fluid applications and

also where the flow rate is not of an absolute concern. Special

design centrifugal pump such as a canned motor pumps are

chosen for high temperature applications where the liquid being

pumped needs to be contained. These are seal less, leak proof pumps usually employed for hazardous conditions. In a canned

motor pump, the pump and the motor serve as one unit. There is

no need for a pump-motor coupling, mechanical seal, bearing

lubrication, etc. There are no alignment issues. However, canned

motor pumps are sensitive to start-up conditions. These pumps

can run neither dry nor cavitate. Failure of these pumps can be

very expensive. However, in process sensitive applications, a

canned motor pump may be preferred over a conventional

centrifugal pump for the following reasons:

1. Seal less; leak proof pump

2. Pump and motor comes are one complete assembly

(unit)

3. There are no alignment issues; nor coupling

issues

4. There is no bearing or coupling lubrication

involved

5. Canned motor pumps do not need external

water cooling for the mechanical seal and bearing housing

6. Pump’s performance can be monitored on the

field and also remotely on the digital control

system (DCS)

7. Very long life

A positive displacement pump traps a fixed amount of

liquid and then discharges the trapped liquid into a pipe.

Positive displacement pumps can be further broadly

classified as reciprocating pumps and gear pumps.

Conventionally, gear pumps are chosen in the following

instances: 1. The liquid being pump has high viscosity

2. Precise amount of liquid needs to be moved

3. Requirement of higher discharge pressures

Consider Table I describing the properties of Dowtherm

A chemical. From Table I, it can be inferred that the

viscosity of Dowtherm A at 650°F is low. Recognize

that it is required to move the chemical from tank A to

tank B and it is not required to maintain the mass flow

rate at high precision. Also, since the operating

temperature of the chemical is high, it very critical to contain the chemical within the pump. Considering all

of the above items, it can be readily seen that the best

choice of pump for the given application is a canned

motor pump.

Material selection

Material selection is as important as the equipment

selection as the material needs to withstand the temperature, pressure and the chemical reactions from

the pumping medium. Improper material selection in a

critical process application is hazardous and can cause a

serious environmental and/or a safety incident. The

Engineering standards from [6] are applied for piping,

fittings, studs/nuts, valves, gaskets and insulation for the

given Dowtherm A chemical. Per [6], the following are

the material selection for the Dowtherm A pumping

system:

Pipe Material: ASTM A587, SCH 40

Pipe Size: 2.5”

Fittings: Std weight, Butt-welding, carbon steel, ASTM A234

Studs/Bolts: ASTM A193 Gr B7. Bolts shall be heavy

hexagon heads, ASME B18.2.1. Studs shall be threaded full length. Thread lubricant: Colloidal copper

Nuts: ASTM A194 Gr 2H

Gasket: G63G4 Flexattalic gasket, refer to Table 2 for

details

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Flanges: Welding Neck; Class 300 forged steel, ASTM A105,

ASME B16.5

Valves: G35B Flanged gate valve; T35W Flanged globe valve,

refer to Table 3 for details

Insulation: 2” insulation; Type B inside cover (material: Two ply glass cloth with a triple aluminum foil laminate) and Type T

outside cover (material: High temperature Teflon coated glass

cloth, code 746.2)

NPSH (Net positive suction head) calculations

Calculation of NPSH is one of the very basic calculation an engineer/designer needs to perform while designing a pumping

system. The available NPSH would indicate whether a selected

pump would cavitate under the given conditions. The available

NPSH or NPSH(A) is given as follows:

NPSH(A) = Inlet pump pressure – vapor pressure of the fluid

being pumped (1)

The inlet pressure is the summation of the available tank A

pressure and the head pressure at the pump’s inlet. Thus:

Inlet pump pressure = Tank A pressure + available head at the

pump’s inlet (2)

The vapor pressure of the fluid is described in Table 1. Upon calculation for the given conditions, as described in Table 4, it

can be clearly seen that the available NPSH is negative. This

means that the saturated Dowtherm A liquid shall flash off super

heated vapor at the pump’s inlet. Since pumps are not designed to

handle vapor, the pump will most certainly cavitate. In-addition, it

must be noted that the centrifugal pumps are designed such that

the fluid is drawn into the pump by the virtue of low pressure

created at the eye of the impeller. Thus, to compensate for the low

pressure created at the eye of the impeller, the manufacturers of

canned motor pumps usually demand a NPSH(A) of at least 25

psig at the pump’s inlet. In this project, this can be accomplished by adding Nitrogen gas to tank A. Nitrogen being an inert gas,

doesn’t react with Dowtherm A chemical. Therefore, it is safe to

add Nitrogen to tank A to obtain the required NPSH. It should be

noted that both the tanks A and B are designed for a maximum

tank pressure of 150 psig. Thus, it is important to add a relief

valve to tank A, to protect the tank under accidental high

pressures.

Pump’s size & flow rate calculation

From Figure 1, it can be seen that the inlet flow rate to tank A is

80 GPM (gallons per minute). Per the industry standards, pumps

are usually selected to handle more than the required flow rate. This is typically done to address any future expansions in the

company’s processes. Thus, keeping future in mind, the pump is

sized at 1.5X, which means that the pump shall develop 120

GPM. Since the inlet flow rate to tank A is at 80 GPM, the chosen

pump will run dry and begin to cavitate if it is sized at 120 GPM.

Therefore, to circumvent this issue, a certain amount of fluid

being pumped shall be recirculated back to the same tank.

For continuous process applications, the pump’s size is dictated

by the available piping. However, if modifications are feasible,

such as the current scenario, the pump size is chosen per the

optimum pipe diameter and/or by the best available options. Recognize that the larger the pipe size, the greater would be the

initial cost. On the other hand, the larger the pipe size,

the lower is the operating cost. Therefore, in general,

there exists an optimum diameter that minimizes the

initial cost of the pump, the pipe, and the fittings. This

diameter is termed as the optimum diameter. Several

studies have been reported on the optimum pipe size for a given application and the results are reported through

empirical relations such as in [1] or through tables that

are available on the internet. From [6], the optimum

pipe size required for 120 GPM is 2.5 inches and the

existing inlet and discharge connections were at 3

inches and 2.5 inches respectively. Hence, the existing

piping connections were retained and the pump size

shall be 2.5*3.0 (discharge size*inlet size).

For an optimal suction and for uniform velocity

distribution at the pump’s inlet (fully developed flow), it

is essential to maintain a straight run of pipe of at least

10 times the pipe diameter before the pump’s inlet. For the given application, such an ideal condition is difficult

to accomplish.

Head loss calculation

Determining the head loss in the piping system is an

important aspect in determining the pressure that the

pump needs to develop.

Friction factor can be determined by using

Moody chart or by using Colebrook-White equation [7].

The Colebrook-White equation may be given as

(3)

where Ɛ is the roughness of the pipe and Re is the Reynolds number. Reynolds number based on hydraulic

diameter is given by

(4)

The roughness for steel pipes [7] can be approximated

as 0.046 mm.

The head loss due to friction may be given as [7]

(5)

Where corresponds to the major losses in the piping

system and refers to the losses from

elbows, tees, valves, etc., and these are popularly referred as minor losses.

The total head loss is a summation of major losses,

minor losses, and head loss due to vertical piping. Thus:

Total head loss =

+ Head loss due to vertical piping

(6)

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Pump ΔP Calculation Pump is specified by its kind, size, the flow and the pressure it

needs to develop. For the given application, a canned motor pump

having a flow rate of 120 GPM is required. In order to determine

the pump’s ΔP, it is necessary to determine the required discharge pressure of the pump.

Required Dis. Pressure of Pump = Total head loss + Total

pressure to overcome in tank B + Excess pressure at tank B inlet

(7)

Thus, the pressure that the pump needs to develop is given as

(ΔP)pump = Required Dis. Pressure of the Pump – Inlet

Pressure to the Pump (8)

Recognize that all calculations have been detailed in Table 4.

Based on calculations, it is seen that the canned motor pump

needs to develop 120 GPM at 133 ft of head.

System curve The impact of flow in the piping system can be represented

graphically by means of a system curve. System curve describes

the head required (or the ΔP the pump needs to develop) for

various flow rates. Any pump manufacturer would demand a

system curve from the customer for choosing the right pump for

the given application. The manufacturer would plot the pump

curve on the top of a system curve and the intersection of the two

curves would be the operating point of the pump. It will be hard to choose the right pump in the absence of a system curve. In this

given project, it is desirable to have the operating point

(intersection between the system curve and the pump curve) as

close as possible to the requirement, which is 120 GPM at 133 ft.

of head.

Based on the equations presented a MATLAB model and an

Excel model were developed to study the required head under

various flow rate conditions. Figure 2 describes the system curve

for the given application.

Figure 2: System curve for the project

Final design of the Dowtherm A pumping system As described previously, a pumping system consists of pump,

piping, fittings, insulation, controls, etc. In this project, a 2.5*3.0 canned motor pump is selected to develop a flow rate of 120

GPM at 133 ft of head. It must be recognized that a canned motor

pump is about 3 to 4 times the cost of a regular centrifugal pump;

however, in a canned motor pump, the pumping

medium shall be contained in the event of the pump’s

failure. This aspect is an essential consideration for this

project as the pumping medium is a heat transfer fluid operating at 650°F. The piping, valves, fittings,

insulation are all selected based on [6]. A stand by

pump is also chosen for this project as the second pump

shall serve as a backup in the event of a failure in the

online pump.

It must be noted that both the storage tanks were rated

only for 150 psig and it was essential to pressurize tank A with Nitrogen to have an acceptable NPSH at the

pump’s inlet. Therefore, relief valves were added to the

storage tanks to protect the tanks against any accidental

over pressure. NPSH is a very important concept and is

often ignored or misunderstood in the process industry.

It is very essential to have NPSH(A) greater than

NPSH(R) to protect the pump from cavitation. If

NPSH(A) is lower than NPSH(R), the pumping medium shall flash off super heated vapor at the pump’s inlet,

which would in turn cause the pump to cavitate.

NPSH(R) is provided by the pump manufacturer, and

this parameter is very much a pump specific information

as it takes into account the pressure drop that occurs at

the eye of the impeller.

Though the inlet flow rate to tank A is 80 GPM, keeping future expansions in mind, the new pump was chosen to

develop 120 GPM. To prevent the pump from running

dry, a bypass line was constructed to recirculate some

amount of pumped fluid back to the same tank. In

addition, recirculation kept the heat transfer fluid stirred

in the tank at all times and therefore reduced the

chances of scale formation in the tank walls. A control

valve was chosen such that the level in tank B is maintained at safe limits at all times. In-addition, the

control vale output was adjusted such that the tank A’s

pump did not starve for fluid at any given time.

A system curve was generated depicting the head

required for various flow rates. The system curve was

shared with the pump manufacturer who in turn super

imposed the pump’s curve on the system curve to have the desired operating point. The new pumping layout

describing all of the above is depicted in Figure 3.

Figure 3: Modified layout of the pumping system

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Conclusions A pumping system from a chemical plant in Chattanooga, TN is

considered in this project. A pumping system was designed to

transfer Dowtherm A (saturated liquid) chemical at 650°F from tank A to tank B. Emphasis was given to pump selection and to

the various steps in determining the pump required flow rate and

ΔP. The importance of NPSH calculation was stressed in the

analysis. Likewise, importance was given to material selection

and DuPont PSM Engineering standards were employed in

selecting the appropriate materials. The procedure outlined in this

paper can be used as a reference while developing a pumping

system for any application. An excel model and a MATLAB

model was developed to simulate the required head for various

flow rates, pipe dimensions and tank pressures.

Table 1: Properties of Dowtherm A Chemical [6]

Table 2: Spiral wound gasket codes [6]

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Table 3a: G35B Gate Valve Details [6]

Table 3b: T35W Globe Valve Details [16]

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Table 4: Dowtherm A Pumping Model

Fluid Dowtherm A

Service Temperature (°F) 650

Supply Tank Pressure (mm of Hg; gage) 400 0.526 bar 7.74 psig

Available Head (ft) 4 1.311 psig

Inlet Flow Rate to Supply Tank (GPM) 80

Total Piping length (ft) 10 3.048 m

Vertical length (ft) 4.5

Discharge Tank Pressure (psi; gage) 95

Head to overcome in Discharge Tank (ft) 1

Density of mercury (kg/m3)

Density of Dowtherm (lb/ft3) 47.25 756.848 kg/m

3

Density of Water (lb/ft3) 62.43

S.G of Dowtherm 0.757

Vapor Pressure at 650°F (psia) 70.73

Vapor Pressure at 650°F (psig) 56.03

Viscosity (cP) 0.17 0.00017 Ns/m2

Pump Type Canned motor; Centrifugal

Selected Pipe Size (OD) 2.5 inches

Pipe Schedule 40

Pipe Thickness 0.203 inches

Surface Roughness for steel pipe (ks; ɛ) 0.046 mm

Number of gate valves anticipated 5

Number of globe valves anticipated 1

Loss coefficient / gate valve 0.15

Loss coefficient / globe valve 10

Excess Pressure for ease of flow in Discharge Tank 20 psig

MODELING PUMPING SYSTEM

NPSH Calculation

Inlet Pump Pressure 9.0 psig

NPSH (available) -47.0 psig

NPSH (required) 25.0 psig

Addition of N2 required (to attain NPSHR) Yes

Tank pressure due to N2 addition 79.7 psig

NPSH (available) after N2 addition 25.0 psig

Inlet Pump Pressure after N2 addition 81.0 psig

Flow Calculation

Required Flow Rate 120.0 GPM 454.249 lit/min

Selected Pipe Size (OD) 2.5 inches 0.0635 m

Pipe Schedule 40.0

Pipe Thickness 0.2 inches

Pipe ID 2.1 inches 0.05319 m

Flow Area 0.002 m2

Velocity of flow 3.4 m/s

Reynolds number of flow 806867.5

ΔP Calculation

Surface Roughness for steel pipe (ks; ɛ) 0.046 mm

Friction factor f - Colebrook equation 0.0195

ɛ/D 0.0009

Friction factor f - Moody chart 0.020

Number of gate valves anticipated 5.0

Number of globe valves anticipated 1.0

Loss coefficient / gate valve 0.15

Loss coefficient / globe valve 10.0

Total Piping length (ft) 10.0 3.048 m

Head loss due to friction (m) 7.0

Head loss due to vertical piping (ft) 4.5 1.3716 m

Total Head Loss (m) 8.4

Total Pressure Loss in Piping (Pa) 62322.9 0.62323 bar

Total Pressure Loss in Piping 9.2 psig

Discharge tank pressure (psig) 95.0

Head to overcome in Discharge Tank (ft) 1.0

Head pressure to overcome in Discharge Tank (psig) 0.3

Total pressure to overcome in Discharge Tank 95.3 psig

Excess Pressure for ease of flow in Discharge Tank 20.0 psig

Pump Discharge Pressure 124 psig

ΔP Requirement for the Pump 43 psig

ΔP Requirement for the Pump 132.6 ft

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The pump must develop 120 GPM @ 133 ft of head

Pump Type

Result

Centrifugal; Canned Motor

Table 5: Loss Coefficients for Pipe Components [7]

References

[1] Janna. S.W., 1998. Design of Fluid Thermal

Systems, 2nd Ed., PWS Publishing, Boston, MA. ISBN 10: 0-534-95319-0

[2] Tuzson. J., 2000. Centrifugal Pump Design, 1st

ED., Wiley Publications, ISBN: 978-0-471-

36100-8

[3] Jones. G.M., & Sanks. R.L., 2008. Pumping

Station Design, 3rd ED., Butterworth-

Heinemann, ISBN: 9780080560052

[4] Chen, N. H., 1979. An Explicit Equation for

Friction Factor in Pipe, American Chemical

Society Communication

[5] Hydraulic Institute, 1979. Engineering Data Book

[6] DuPont Technology Consulting; E.I. du Pont

Nemours Company; Engineering Standards;

2002 revision

[7] Fundamentals of Fluid Mechanics; 6th edition;

Munson, Okiishi and Huebsch; Wiley Inc.,

2009; ISBN 978-0470-26284-9