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Experiment Instructions

HM 284 Series and Parallel

Connected Pumps

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HM 284 SERIES AND PARALLEL CONNECTED PUMPS

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This manual must be kept by the unit.

Before operating the unit:

- Read this manual.

- All participants must be instructed on

handling of the unit and, where appropriate,

on the necessary safety precautions.

Version 1.4 Subject to technical alterations

Experiment Instructions

Dipl.-Ing. (FH) Dipl.-Ing.-Pd. Michael Schaller

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Table of Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Didactic notes for teachers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Safety. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 Intended use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Structure of safety instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3 Safety instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.4 Ambient conditions for the operating and storage location . . . . . . . . . 7

3 Description of the HM 284 device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1 Fluid energy machines range and introduction to HM284. . . . . . . . . . 9

3.2 Process schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.3 Device design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.4 Device function and components . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.5 Operation and measurement data acquisition. . . . . . . . . . . . . . . . . . 13

3.5.1 Program installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.5.2 Program operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.6 Commissioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.7 Operating modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.7.1 Pump in standalone operation . . . . . . . . . . . . . . . . . . . . . . . 18

3.7.2 Pumps in series operation . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.7.3 Pumps in parallel operation . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.8 Decommissioning, storage and disposal . . . . . . . . . . . . . . . . . . . . . . 21

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4 Basic principles for GUNT Labline fluid energy machines . . . . . . . . . . . . . 234.1 Classification of fluid energy machines . . . . . . . . . . . . . . . . . . . . . . . 23

4.1.1 Power machines / work machines . . . . . . . . . . . . . . . . . . . . 24

4.1.2 Turbomachines / positive displacement machines . . . . . . . . 24

4.2 Fundamental physical principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2.1 Laws of conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.2.1.1 Continuity equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.2.1.2 Conservation of momentum . . . . . . . . . . . . . . . . . . . . . . . . . 284.2.1.3 Conservation of energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.2.1.4 Bernoulli's principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.2.2 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.2.2.1 Specific work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2.3 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2.4 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.2.5 Energy conversion in the motion of fluid. . . . . . . . . . . . . . . . 41

5 Further basic principles for HM 284 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.1 Converting pressure energy into velocity . . . . . . . . . . . . . . . . . . . . . 455.1.1 Supply pressure and head of centrifugal pumps . . . . . . . . . 45

5.2 Pump characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.3 System characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.4 Operating point: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.5 Pumps in series and parallel connection . . . . . . . . . . . . . . . . . . . . . . 51

5.5.1 Parallel connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.5.2 Series connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.5.3 Selecting the type of connection. . . . . . . . . . . . . . . . . . . . . . 55

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6 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.1 Experiment 1: Recording a system characteristic curve . . . . . . . . . . 60

6.1.1 Objectives of the experiment . . . . . . . . . . . . . . . . . . . . . . . . 60

6.1.2 Conducting the experiment. . . . . . . . . . . . . . . . . . . . . . . . . . 60

6.1.3 Measured values with calculations of the analysis . . . . . . . . 61

6.1.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.1.5 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.2 Experiment 2: Determining the reference speed. . . . . . . . . . . . . . . . 67

6.2.1 Objective of the experiment: . . . . . . . . . . . . . . . . . . . . . . . . . 67


6.3 Experiment 3: Determining the pump characteristic curve . . . . . . . . 68



6.3.3 Measured values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6.3.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.3.4.1 Pump characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6.3.4.2 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.3.5 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

6.4 Experiment 4: Pumps in series operation . . . . . . . . . . . . . . . . . . . . . 76



6.4.3 Measured values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.4.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.4.5 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.5 Experiment 5: Pumps in parallel operation . . . . . . . . . . . . . . . . . . . . 81



6.5.3 Measured values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

6.5.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

6.5.5 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

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6.6 Final analysis of the experimentsand proposal for further experiments. . . . . . . . . . . . . . . . . . . . . . . . . 85

7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

7.1 Technical data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

7.2 List of formula symbols and units . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

7.3 Tables and graphs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

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1 Introduction 1

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1 Introduction

The HM 284 "Series and Parallel Connected

Pumps"device is part of the GUNT Labline fluid

energy machines series.

The GUNT Labline fluid energy machinesallow

experiments on power engines and machines

such as pumps, fans and water turbines.

All devices in the GUNT Labline fluid energy

machines range are equipped with electronicsensors for PC-based measurement data

acquisition and are operated from a PC.

Measurements can be represented graphically

and characteristics can be recorded using the

measurement data acquisition software provided.

The GUNT Lablineseries of devices puts the HSI

"Hardware-Software Integration" product

approach into effect.

The experimental unit is designed as a tabletopdevice. The measurement data acquisition

software supplied and a PC provided by the

customer are required to operate the HM 284

device.

Centrifugal pumps belong to the group of dynamic

pumps. They are the most widely used type of

pump in the world. The advantages are mainly:

simple design

no oscillating masses

few parts

little wear

reliable

suitable for different media

direct coupling to electric motor without

gearing.

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2 1 Introduction

If necessary, different operating ranges can becovered by connecting two or more pumps.

The centrifugal pumps in HM 284 pump water.

HM 284 essentially consists of the centrifugal

pump with drive motor, the throttle valve, the flow

meter and the water tank. These components are

connected to the water circuit by pipes.

Characteristic curves and operating points can berecorded by:

Using the throttle valve to vary the flow

resistance.

Variable speed at pump 1 and optionally

switchable pump 2.

Varying the pump circuit

(series and parallel connection).

Learning objectives for the centrifugal pump

are:

Principle of operation of a centrifugal pump

Recording a system characteristic curve

Recording a pump characteristic curve

Identifying characteristic data

Investigation of typical dependencies (flow rateand the supply pressure dependent on the

speed).

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1 Introduction 3

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1.1 Didactic notes for teachers

HM 284can be employed both in the training of

skilled workers and in academic engineering

education.

Areas where the HM 284experimental unit can

be employed include:

Demonstration experiments

The demonstrator operates the previously

prepared experimental unit while a small group

of five to eight students observe. Key effects

can be demonstrated over an operating time of

half an hour.

Practical experiments

Small groups of two or three students can carry

out experiments for themselves. The time

required to record measurements and some

characteristic curves can be estimated at aboutone hour.

Project work

HM 284 is particularly well suited to carrying

out project work. In addition to detailed studies

using HM 284, it is possible to conduct a wide

range of comparative experiments using the

separate HM 283 centrifugal pump and

comparisons to the HM 285 and HM 286

positive-displacement pumps.

In this case a single, experienced student can

operate the experimental unit.

These materials are intended to be used to help

you prepare your lessons. You can compose

parts of the material as information for students

and use it in class.

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4 1 Introduction

We also provide these experiment instructions inpdf format on a CD to support your lessons. We

grant you unlimited reproduction rights for use

within the context of your teaching duties.

We hope that you enjoy using this

experimental unit from the GUNT Labline

range and wish you success in your important

task of introducing students to the

fundamentals of technology.

Should you have any comments about this

device, please do not hesitate to contact us.

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2 Safety

2.1 Intended use

The unit is to be used only for teaching purposes.

2.2 Structure of safety instructions

The signal words DANGER, WARNING or

CAUTION indicate the probability and potentialseverity of injury.

An additional symbol indicates the nature of the

hazard or a required action.

Signal word Explanation

Indicates a situation which, if not avoided, willresult in

death or serious injury.

Indicates a situation which, if not avoided, mayresult indeath or serious injury.

Indicates a situation which, if not avoided, may result inminor or moderately serious injury.

NOTICEIndicates a situation which may result in damage toequipment, or provides instructions on operation of

the equipment.

DANGER

WARNING

CAUTION

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6 2 Safety

Symbol Explanation

Electrical voltage

Hazard area (general)

Note

Wear ear defenders

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2.3 Safety instructions

WARNING

Electrical connections are exposed when theswitch cabinet is open.

Risk of electrical shock.

Disconnect the plug from the power supplybefore opening the switch cabinet.

All work must be performed by trainedelectricians only.

Protect the switch cabinet from humidity.

WARNING

Noise emission > 80dB(A).

Risk of hearing damage.

Wear ear defenders.

NOTICE

To prevent algae growth and sludge formation:

Only operate the device with water of potablequality.

2.4 Ambient conditions for the operating and storage location

Enclosed space

Free from dust and humidity.

Tabletop.

Frost-free.

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8 2 Safety

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3 Description of the HM 284 device 9

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3 Description of the HM 284 device

3.1 Fluid energy machines range and introduction to HM284

The fluid energy machines range allows

experiments on power engines and machines

such as pumps, fans and water turbines.

The HM 284 "Series and Parallel Connected

Pumps" device is part of the fluid energymachines series. HM284 allows experiments on

interconnected centrifugal pumps and is a fully

functional stand-alone experimental unit.

The range of devices includes the other

experimental unit that covers a similar topic:

HM 283, Experiments with a Centrifugal

PumpComparative experiments across devices can be

used to achieve additional learning goals.

Comparative measurements across devices

using the pumps and fan/compressor in this range

are recommended and offer additional benefits.

The following chapters provide a detailed

description of the HM284supply unit.

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10 3 Description of the HM 284 device

3.2 Process schematic

Fig. 3.1 shows the process schematic of the

experimental unit with all measuring points and

essential components.

Fig. 3.1 HM284: Process schematic

Measuring points Components

Pump 1Pump 2Three-way valve for selecting operating modeValve for pump 2Valve for volume flow quantityOutlet valve

Energy input Pelof pump 1Volume flow V

Pressure p1upstream of pump 1Pressure p2downstream of pump 1Pressure p3downstream of pump 2
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3.3 Device design

The practical implementation of the process

schematic can be seen in Fig. 3.2. The measuring

points and components listed above can be seen

in the diagram.

Fig. 3.2 HM 284: Main components

1 Pump P2 7 Volume flow sensor, FI12 Pump P1 8 Valve for flow rate , V3

3 Pressure p1upstream of pump P1 9 Water tank

4 Pressure p2downstream of pump P1 10 Shut-off valve for pump P2, V2

5 Pressure p3downstream of pump P2 11 Outlet valve, V4

6 Three-way valve for operating mode, V1 12 Housing

V

1 2

9

7

11

10

6

8

12

4

3

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3.4 Device function and components

The experimental unit consists of the controllable

pump P1 (2) and the optionally switchable

constant-speed pump P2(1). Water is sucked in

from the water tank(9) and pumped through the

piping in the circuit. The experimental unit can be

operated in a variety of different operating modes

using the 3-way valve for the operating mode

(6) and the shut-off valve for pump P2(10). The

valve for flow rate (8) is used to adjust the

system's flow resistance. In this way, it is possible

to analyse the behaviour of the pressures p1, p2and p3(3, 4, 5) and the flow rate(7) of the system

and the pumps.

Relatively small cross-sections of the suction

lines affect the system characteristics in operation

and can be used to evaluate the flow configuration

and to expand knowledge of fluid mechanics.

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3.5 Operation and measurement data acquisition

The main switch(16 in Fig. 3.3) is used to turn

the power supply on and off. It uses a I/0 rocker

switch design.

The connection sockets are located next to the

main switch (power supply no. 13, USB no. 14).

The fuse holder(15) holds the two microfuses.

The integrated microcontroller boardis used to

control the device and for measurement dataacquisition.

The measurement data acquisition program

provided is used both to operate the experimental

unit and to detect and display the measurement

data. The measurement data acquisition program

(referred to simply as the program below) is

installed on a PC provided by the customer (cf.

Chapter 3.5.1, Page 15).

The experimental unit and the PC are connected

via the USB port.

The program is used to operate the radial fan

(switch on, change speed and switch off). The

program offers the following options for displaying

the current measured values and calculated

values:

System diagram

Graphical presentation of the measured

values.

The available measured values and calculated

values are recorded in measurements files.

These measurements files can be imported

into a spreadsheet program (e.g. MS Excel)

for further processing.

Fig. 3.3 Rear of the device, with mainswitch and connection sockets

13 14

16 15

Fig. 3.4 Rear of the device, with cablesconnected
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The program's help feature explains how to usethe program (see also Chapter 3.5.2, Page 16).

It should also be pointed out that the measured

values and calculated values are measured

continuously in rapid succession. These values

are averaged before they are displayed and

written to the data file. This mostly compensates

for fluctuations.

"Taring"the values at standstill sets the applied

pressures to zero at the moment of taring. The

effect of taring can be clearly seen while the

program is running.

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3.5.1 Program installation

Required for installation:

A ready-to-use PC with USB port (for minimum

requirements see Chapter 7, Page 87).

G.U.N.T. CD-ROM

NOTICE! All components required to install and

operate the program are included on the CD-

ROM provided by GUNT with HM 284. No other

tools are required.

Installation procedure

NOTICE! The device must not be connected to

the PC's USB port while the program is being

installed. The device may only be connected after

the software has been successfully installed.

Start the PC.

Insert GUNT CD-ROM.

In the "Installer" folder, launch the "Setup.exe"

installation program.

Follow the installation procedure on screen.

Installation will run automatically after starting

it. The following program components are

installed onto the PC:

LabVIEW - Runtime software for PC-based data acquisition.

Driver routines for USB data acquisition.

After the installation has finished, restart the

PC.

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3.5.2 Program operation

Select the program and start via:

Start / Programs / G.U.N.T. / HM 284

When you start the software for the first time

after installation you are prompted to select the

desired language for the program operation.

Notice! The language may be changed at any

time in the "Language" menu.

Afterwards the system diagram for HM 284

appears on the screen.

Various pull-down menus are available for

other functions.

For detailed instructions on use of the program

refer to its Help function. You can get to the

help functionvia the "?"pull-down menu and

selecting "Help".

Fig. 3.5 Language selection

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3.6 Commissioning

Observe the safety instructions (cf. Chapter 2,

Page 5ff.)

Install the measurement data acquisition

program on the PC (cf. Chapter 3.5.1,

Page 15f).

Connect the experimental unit to the PC using

the USB cable provided (USB connection

socket see no. 14 in Fig. 3.3, Page 13).

Fill the water tank with potable water up to the

height of the baffle plate. You may also add

algae retardants to the water.

NOTICE

Evaporation may lead to calcium deposits inthe water tank, therefore GUNT recommendsdraining the water should the device not be in

operation for a long time (> 1 week).

Bleed the transparent pump housings using the

bleed valves.

NOTICE

Risk of damage to the device.

Before connecting to the electrical power

supply:Make sure that the laboratory power supplymeets the specifications on the device's ratingplate.

Connect experimental unit to the mains power

supply.
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Turn main switch (no. 16 in Fig. 3.3, Page 13)to "1".

Turn on PC and launch program for

measurement data acquisition.

Press "Tare"button to calibrate to zero.

Turn on the pump(s) via the program.

Check that each component is functioning

correctly.

Switch off pump.

Main switch to "0".

Disconnect experimental unit from mains

electricity supply.

3.7 Operating modes

3.7.1 Pump in standalone operation

To set the experimental unit to standalone

operation, valve V1 must connect the pump P1

directly to valve V3.

To achieve this, the lever on valve V1 must be

rotated until the symbol assumes the position as

shown in Fig. 3.6.

In this valve position, pump P2 has no function.

Valve V2 must be closed so as to avoid possiblebackflow through pump P2.

Pump P1 draws in water from the tank and pumps

it through valve V1 and V3 back into the tank. By

throttling the volume flow with valve V3, it is

possible to vary the resistance against which the

pump works.

The behaviour of pump P1 can then be analysed.

Fig. 3.6 HM284 in standaloneoperation
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3.7.2 Pumps in series operation

To set the experimental unit to series operation,

valve V1 must connect the pressure side of

pump P1 to the suction side of pump P2.



shown in Fig. 3.7.

Pump P2 is only supplied with water from

pump P1. Valve V2 must be closed so as to avoidflows into or out of the tank.

Pump P1 sucks in water from the tank. The

pressure is increased and the water fed to

pump P2, where a further pressure increase

takes place.

Before the water is pumped back to the tank, the

volume flow can be throttled with valve V3. Thepumps then work against an increased

resistance.

Fig. 3.7 HM284 in series operation
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3.7.3 Pumps in parallel operation

To set the experimental unit to parallel operation,

valve V1 must connect the pressure side of

pump P1 directly to valve V3.



shown in Fig. 3.8.

Pump P2 provides additional volume flow to

pump P1. Pump P2 requires a separate watersupply for this purpose. This is done by opening

valve V2 on the suction side.

Pump P1 and pump P2 suck in the water out of

the tank and compress it together via valve V3

back into the tank.

By throttling the volume flow with valve V3, it is

possible to vary the resistance against which the

pumps work.

Fig. 3.8 HM284 in parallel operation
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3.8 Decommissioning, storage and disposal

Observe the safety instructions (cf. Chapter 2,

Page 5ff.)

If not yet done:

Disconnect experimental unit from mains

electricity supply.

Disconnect connection between PC and

experimental unit (USB cable).

Thoroughly clean the entire experimental unit.

Do not use any aggressive cleaning agents

to clean the device. GUNT recommends a

mild acetic cleaner.

Only soft cloths should be used for cleaning,

in order to avoid chafing on the transparent

water tank.

Store the experimental unit and components

under cover, clean, dry and free of frost.

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4 Basic principles for GUNT Labline fluid energy machines 23

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4 Basic principles for GUNT Labline fluid energy machines

The basic principles set out in the following make

no claim to completeness. For further theoretical

explanations, refer to the specialist literature.

More detailed knowledge is examined in the sub-

sequent section on device-specific basic princi-

ples.

4.1 Classification of fluid energy machines

Fluid energy machines are flowed through by a

fluid; this can be a gas or a liquid. When flowing,

energy is exchanged between the fluid energy

machine and the fluid.

The extensive field of fluid energy machines can

be divided into many subject areas.

This section on the basic principles looks at two

key criteria for differentiation in more detail.

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24 4 Basic principles for GUNT Labline fluid energy machines

4.1.1 Power machines / work machines

The distinguishing characteristic of this classifica-

tion is the direction of the flowing energy.

Power machine:

The fluid's energy is removed by the machine and

converted into the shaft's mechanical energy.

Typical examples include water turbines used in

the provision of electricity.

Work machine:The machine transfers energy to the fluid. The

pressure and/or the flow velocity of the fluid

increases. One typical application is a water

pump.

4.1.2 Turbomachines / positive displacement machines

The distinguishing characteristic is the functional

principle.

Turbomachine:

Energy is continuously added to or removed from

the flow by deflection at stator and rotor blades.

This kinetic energy of the fluid is converted into

pressure energy (work machine) or mechanical

energy (power machine). The fluid is conveyed

continuously. No abrupt change in the energy

transfer can be detected.Positive displacement machine:

A changeable volume drives the fluid or is driven

by the fluid. The pressure difference across the

machine must be big enough to overcome flow

resistances (work machine) or mechanical resist-

ances (power machine). The fluid flow and the

movement of the machine are coupled.

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4.2 Fundamental physical principles

The following section looks at the physical princi-

ples with reference to fluid energy machines.

4.2.1 Laws of conservation

The laws of conservation describe variables that

do not change in the fluid energy machine, in

other words that are preserved.

4.2.1.1 Continuity equation

The continuity equation states that the mass flow

that flows through a system remains constant.

(4.1)

A = Cross-section area in m2

c = Flow velocity in m/s

= Mass flow in kg/s

= Volume flow in m3/s

= Density in kg/m3

In incompressible fluids, the density is not

dependent on the pressure. Gases at low pres-

sure differences can also be considered asincompressible. In this case, the formula can be

reduced to:

(4.2)

Usually two points in the flow are compared to

each other. The path traced by a fluid particle is

referred to as the flow filament. These flow fila-

m V

c A const= = =

m

V

V

c A const= =

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ments are found in the flow conduit as a bundle,which represents the flowed-through shape.

The significance of the continuity equation is par-

ticularly evident when comparing diffuser and

nozzle.

In an incompressible medium it follows:

and from this:

(4.3)



The velocities are inversely proportional to the

flow cross sections.

Nozzle:

The flow velocity is accelerated by the cross sec-

tion becoming smaller.

Fig. 4.1shows an adjustable nozzle, as used in

Pelton turbines. Fig. 4.2is a nozzle in which the

outlet cross section is reduced by means of

blades and deflection.

Fig. 4.1 Schematic change in velocityin the nozzle of a Pelton tur-bine

c2

c1

Nozzle

Inlet Outlet

A1A2

Flow filaments

c1 A1 c2 A2=

c1

c2-----

A2

A1------=

Fig. 4.2 Nozzle: change in velocity bymeans of flow deflectingblades

c1

Inlet

Outlet

A1

A2

Nozzle

c2Flow filaments

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Diffuser:The flow velocity c is decelerated by the flow

cross section becoming larger.

The diffuser in Fig. 4.3is similar in design to the

nozzle (Fig. 4.2). In this case though, the arrange-

ment of the blades results in an increase in the

size of the cross section A.

With a known surface area ratio, it is therefore

possible to calculate the resulting change in

velocity.

Fig. 4.4shows the blades of an axial turbine.

While the first blade row is formed as a nozzle, the

second blade row initially only appears as a

deflection.

Fig. 4.3 Diffuser: change in velocity by

means of flow deflectingblades

c1

Inle

t

Outlet

A1

A2

Diffuser

c2

Flow filaments

Fig. 4.4 The nozzle of an axialturbomachine

DeflectionNozzle
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4.2.1.2 Conservation of momentum

Momentum is a kinetic quantity. The variables of

mass mand velocity care applicable:

(4.4)


I = Momentum in Ns

m= Mass in kg

A change in momentum takes place as a result of

a change in the velocity c. The change in velocity

is caused by an acceleration a . As a result of

this relationship, a force is connected to the term

of the change in momentum:

(4.5)

or for a mass flow:

(4.6)

a = Acceleration in m/s

F = Force in N

= Mass flow in kg/s

t = Time in s

The momentum is a directional quantity. The

quantities I, cand Fall point in the same direction.

I m c=

c

t---=

I m a t F t= =

I m c t F t= =

m

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Looking at these formulae it can be seen that themomentum changes when a force acts.

Fig. 4.5shows how a water jet is deflected at a

blade. While the value of the velocity cremains

constant, the horizontal velocity component

changes its algebraic sign.

A force has to act on the blade so that the deflec-

tion can take place; with Formula (4.6)we get:


F = Force in N

= Mass flow in kg/s

The momentum is transferred from one body to

another when a force acts. Within a system thathas no interaction with its surroundings, the

momentum is constant.

Changes in velocity also occur in the previous

example of diffuser and nozzle. Forces are also

acting here.

Fig. 4.6illustrates this schematically on the blade

of a nozzle.

The force Facting on the blade corresponds to

the force which deflects the fluid.

Fig. 4.5 A water jet is deflected at ablade

c1

c2

F

m c1x

c1y

c2x

c2y

c1y c2y= c1x c 2x=

F m c2x c1x =

F m 2 c1x =

m

Fig. 4.6 Nozzle: retention force to keepthe blade in position.

c1

Nozzlec2

c2x

c2y

Fy

Fx

F

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4.2.1.3 Conservation of energy

Work and energy are similar quantities. Accord-

ingly, energy is also stated in units of joules.

Energy is the capacity to do work.

Energy can be present in various forms (this list

only represents a small selection):

Mechanical energy

Kinetic energy

Potential energy

Spring energy

Thermal energy

Electrical energy

Chemical energy

Hydraulic energy

Hydrostatic energy Potential energy

Hydrodynamic energy

The forms of energy can be converted from one

form to another. In engineering, machines are

used for this purpose. Fig. 4.7shows one exam-

ple.

Fig. 4.7 Energy conversion by a unit consisting of electric motor and pump

Electricmotor

Hydraulicenergy

Mechanicalenergy

Pump

Electricalenergy
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4.2.1.4 Bernoulli's principle

Bernoulli's principle provides essential under-

standing in the consideration of fluid energy

machines. It correlates energies present in a flow.

No energy is added to or removed from the fluid in

this approach.

The important thing to remember when consider-

ing the various energies is the fact that the forms

of energy can be transformed.

The following forms of energy are considered:

Hydraulic energy

(4.7)

Ehyd= Hydraulic energy in J

p = Static pressure in N/m2

V = Volume in m3

Potential energy

(4.8)

Epot=Potential energy in J

g = Gravitational acceleration in m/s2

h = Height in m

m = Mass in kg

Kinetic energy

(4.9)

Ekin= Kinetic energy in J


Ehyd p V=

Epot m g h =

Ekin1

2--- m c

2 =

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Thermal energy can be ignored if the temperatureis constant.

If we consider a fluid particle on its flow path, in

practice we can assume that the total energy of

the particle remains constant.

For this assumption, the formulae can be summa-

rised to form Bernoulli's energy equation.Transposed we get:

(4.10)



h = Height in m


= Density in kg/m3

Strictly speaking this assumption is only valid

for frictionless fluids, since friction leads to

losses.

Usually two points in the flow are compared to

each other. One possible energy conversion is

shown again using the example of nozzle and dif-

fuser.

c12

2--------

p1------ g h1+ +

c22

2--------

p2------ g h2+ +=

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The example of diffuser and nozzle (Fig. 4.8)shows the conversion of velocity and pressure.

Pressure and velocity terms are coupled energet-

ically; if one term falls, the other term rises.

Fig. 4.8 Conversion of pressure energy into velocity kinetic energy and back again

c1

c2

c3

p3

p2

p1p4

Nozzle Diffuser

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4.2.2 Work

Work in the physical sense is performed when a

force acts along a path; in this case force Fand

distance spoint in the same direction.

(4.11)

F = Force in N

W= Physical work in J

s = Active distance of the force in mAn example related to fluid mechanics can be

seen in the axial turbomachine shown previously.

In a turbine, the stationary guide wheel provides

the incident flow to the rotor blade. A force acts on

the rotor blade in the direction of movement.

According to Formula (4.11)work is done in this

process while the Impeller is rotating. This work is

transferred from the fluid to the turbine.

W F s=

Fig. 4.9 Work done within a turbomachine

Rotating

impeller

Stationary

guide

wheel

Direction of force

Direction of movement
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Another example of work done can be shownusing a piston pump.

During the stroke sof the piston pump in Fig. 4.10,fluid is conveyed out of the cylinder. This causes

the pressure p required to overcome the flow

resistances in the downstream system to build up

in the fluid.

The force Fthat has to be applied by the piston

results from the pressure pof the fluid and the sur-

face area A of the piston. Formula (4.11)

becomes:

(4.12)


F = Force in N

p = Pressure in Pa


s = Active distance of the force in m

Fig. 4.10 Transfer of work within a piston pump

Direction of movement

Direction of force

Flowing fluid

p2p1

Fig. 4.11 Variables at a piston pump

s

F

p

A

W F s p A s = =

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This work is transferred from the pump to the fluid.Since the processes within a double stroke are

uneven, it is better to calculate mean values in this

case.

4.2.2.1 Specific work

The work W transferred within a fluid energy

machine can be based on the mass of the fluid.

This corresponds to the specific work:

(4.13)

m= Mass in kg


Y = specific work in J/kg

Because of the possibility of converting energy,

this specific work can also be used to define the

velocity head or pump head:

(4.14)

h = Height in m


The velocity head or pump head is an important

quantity in the design and selection of turbines

and/or pumps.

Y W

m-----=

h Y

g----=

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4.2.3 Power

Power is the work done per unit of time t. As

already explained in Chapter 4.2.1.3, energy is

the ability to perform work. Accordingly, energy

can be used in the same way as work.

Generally speaking, power is defined as:

(4.15)

E = Energy in J

P = Power in watts

t = Time in s


The key power calculations related to this series

of equipment are:

Electrical power:

(4.16)

Pel = Electrical power in W

U = Voltage in V

I = Current in A

Mechanical power

(4.17)

Pmech= Mechanical power in W

M = Torque in Nm

= Angular velocity in 1/s

P W

t-----

E

t----= =

Pel U I=

Pmech M =

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Hydraulic powerin incompressible fluids

Powers can be calculated from all of the energies

listed in Chapter 4.2.1.4, Page 31. Potential

energy has a lesser role in the fluid energy

machines considered here, because it is con-

verted into pressure energy and/or kinetic energy

before it enters the machine.

Hydraulic power of the fluid

(4.18)

Phyd = Hydraulic power in W



Kinetic power of the fluid

(4.19)

Pkin = Kinetic power in W


= Mass flow in kg/s

Note on energy and power:

Energy is the quantity which is preserved. How-

ever, it is often used in calculations since it is eas-ier to calculate from measured values.

Energy is converted in the fluid energy machine.

Similarly, a proportion of energy is stored in each

machine, for example in the rotational energy of

the shafts and impellers.

Phyd p V

=

V

Pkin12--- m c

2 =

m

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The stored energies are relatively small com-pared to the transferred power. If there is a

change in the operating point, either spent power

is stored over a short time or stored work is

released over a short time. The change in speed

to the new operating point happens quickly. This

time response can be explained by

Formula (4.15), Page 37.

The forms of energy in fluid energy machines are

quickly converted into each other. In contrast, lotsof heat transfers with heating up and cooling down

processes take place slowly.
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4.2.4 Efficiency

The efficiency is defined as the ratio of benefit to

effort.

% (4.20)

Pin = Incoming power: the effort in W

Pout = Outgoing power: the benefit in W

= Efficiency in %

Real energy conversions are subject to loss. Fig.

4.12illustrates this using the example of an elec-

trically driven pump. The thickness of the arrows

represents the transferred power.

PoutPin

----------- 100=

Fig. 4.12 Energy conversion by a unit consisting of electric motor and pump

Electricmotor

Hydrauliceffective power

Mechanicalpower

Pump

Electricalinput power

Losses: Losses:

Pin

Pout

Electrical

Mechanical

Hydraulic

Mechanical

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4.2.5 Energy conversion in the motion of fluid

An energy balance can be established between 2

points of a flow conduit.

For the flow conduit from Fig. 4.13we can say,

regardless of the direction of flow, that gravita-

tional potential energy is converted into pressure

energy from cross section 1 to cross section 2.

Since the cross sections of the two points being

considered are the same, we should not expect

any change in velocity. If there is a flow, the flowvelocity will be greatest in the middle between the

points being considered.

The energies of pressure, velocity and vertical

height add up to the total energy. According to the

(lossless) Formula (4.10) this total energy

remains the same.

Nevertheless, it is still possible to act on this

energy by technical means. This is shown in Fig.

4.14by means of an example. According to Ber-

noulli, changes in the velocity kinetic energy

and/or pressure energy are also possible.

Fig. 4.13 2 points of a schematic flowconduit

h1

p1

A1

p2

A2

p1-----

c12

2----- g h1+ +

p2-----

c22

2----- g h2+ +=

m

m

h2

A < A1=A2

1

2
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As shown in the figure, the action can occur on the

fluid energy by means of:

Work machines

(Pumps/ventilators/fans/compressors):

These convert a mechanical rotational move-

ment into the fluid's pressure energy or velocity

kinetic energy. The structural design takes

account of the required pressure ratios and

mass flows as well as the size and direction of

the connections.

Power machines (turbines):

These convert pressure energy or velocity

kinetic energy into mechanical energy. As with

the work machines, pressure ratios and mass

flows are critical variables that determine the

structural design.

Fig. 4.14 Energy conversion at a pump/turbine

Fluid energymachine

Increases

theenergyo

fthe

flu

id

Removes

energy

from

the

flu

id

Power machine

e.g. turbine

Work machine

e.g. pump

Mechanical

work

Mechanical

workEnergy

p1-----

c12

2----- g h1+ +

p2-----

c22

2----- g h2+ +

p1

A1

c1

h1

p2

A2

c2h2

1

2

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The power of the fluid is dependent on the pres-sure and the volume flow. In a lossless machine,

this would correspond to the shaft power on the

machine (cf. Formula (4.17)and Formula (4.18)).

By equating we get the expression:

(4.21)

M = Torque in Nm

p = Pressure in Pa


= Angular velocity in 1/s

Looking at powers is equivalent to looking at the

converted energy differences. In the case of

mechanical power, it can be assumed that the

lower levels of torque and velocity lie at zero.

This is not necessarily the case when it comes to

hydraulic power. While the volume flow canoften be regarded as constant due to incompress-

ible behaviour, under pressure it often has to be

calculated with the pressure difference p2-p1. This

is because the lower pressure level does not have

to correspond to the ambient pressure. The for-

mula becomes:

(4.22)

The shaft power of the machine in this case is

equivalent to the hydraulic power of the fluid. Ini-

tially it does not matter whether the shaft power is

achieved by a large torque or high angular veloc-

ity. Likewise, the power of the fluid may signify a

large volume flow or a high pressure difference.

M p V

=

V

V

M p2 p1 V

=

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However, the technical implementation can onlydeliver high efficiency for one particular design

case. The types of fluid energy machines differ

depending on the objectives and the environmen-

tal conditions.

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5 Further basic principles for HM 284 45

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5 Further basic principles for HM 284

5.1 Converting pressure energy into velocity

Pressure and velocity are both forms of energy.

Pressure energy can be converted into velocity

kinetic energy.

The pump adds energy to the fluid. This happens

as pressure and/or velocity kinetic energy.

Assuming that all of the pressure is converted intovelocity kinetic energy, we can derive the

following from Formula (4.10), Page 32:

(5.1)


p = Static pressure in Pa

= Density in kg/m3

5.1.1 Supply pressure and head of centrifugal pumps

Centrifugal pumps generate a head which is inde-

pendent of the density of the fluid.

For the same head, a higher pressure is needed

at higher density. The pressure is proportional to

the weight of the fluid:

(5.2)


h = Head in m


= Density in kg/m3

c 2 p

-----------=

p g h =

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46 5 Further basic principles for HM 284

Note:Where the pumped medium is water, theunit is often specified in "mWC". This non-SI com-

pliant unit derives from "metre Water Column".

This pressure results from the conversion of

velocity to pressure. The impeller transfers veloc-

ity kinetic energy to the fluid as it passes through.

From Formula (5.1) and Formula (5.2) we can

transpose:

(5.3)



h = Head in m


= Density in kg/m3

Thus the velocity of the fluid is decisive for the

resulting pressure and/or the head. This is directly

related to the rotational speed of the impeller.Because the pressure is measured, it is this

measured variable that is the focus of the descrip-

tion that follows.

Conversion is possible by Formula (5.2):

(5.4)

Some diagrams show the pressure in bar and also

as a head in m. The factor has been adopted tothe secondary y-axis with 10 for better axis

scaling.

h p

g-----------

c2

2 g-----------= =

h p

g-----------=

m

bar---------

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5.2 Pump characteristic

The pumps used are centrifugal pumps. They

transfer energy to the fluid by accelerating the

fluid on a circular path in the impeller.

The inertia forces cause the water to be thrown

outwards.

The characteristic curves of centrifugal pumps

can be approximated fairly well by parabolas. This

is done in the figure below:

When talking about energy transfer it is possible

to make a qualitative distinction between high

pressures and high flow rates.

The processes can be explained as follows:

Fig. 5.1 Schematic characteristic curve of a centrifugal pump

Volume flow in L/minV

Pressur

ep

inbar

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High pressures:At low flow rates, the fluid particles are moved in

a narrower circular path. If there is no flow, the

pump swirls the fluid in a circle. The centrifugal

force is highest here. This force is seen as

pressure.

High flow rates:

The trajectory of a fluid particle deviates more and

more from the circular path with increasing flow

rates and approaches a straight line that pointsoutwards from the centre. The centrifugal forces

responsible for the pressure build-up become

smaller.

Note:The representation shows the relationships

on a simple level. Detailed knowledge of energy

transfer is dealt with in HM 283 "Experiments

with a Centrifugal Pump".

5.3 System characteristic

Pumps are mainly used to pump fluids through

pipe networks or systems. This requires that a

certain pressure be applied to overcome the flow

resistances.

The following proportionality can be derived from

Formula (5.1)and Formula (4.2), Page 25:

(5.5)




V

c p

V
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Therefore four times the pressure must be appliedto realise double the flow through a system.

If the pressure is plotted against the volume flow,

we get a curve in the shape of a parabola:

5.4 Operating point:

The operating point of a pump/system

combination is located at the intersection of the

system and pump characteristics.

In order that the fluid can flow, it is necessary to

overcome the system resistance. The pump

allows for this by increasing the pressure of the

fluid.

If the system has a variable system resistance

(e.g. by switching between different flow

Fig. 5.2 Schematic system characteristic


Pressurep

inbar

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sections), then the operating point shifts on thepump characteristic.

If the pump's output is varied by the speed, then

the operating point shifts on the system

characteristic.

Fig. 5.3 Schematic characteristics.System characteristic and pump characteristic of a centrifugal pump


Pressurep

inbar Operating point

Moving the operating pointby varying the systemcharacteristic

Moving the operating point

by varying the pump

characteristic

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5.5 Pumps in series and parallel connection

Specific circuits mean that two or more pumps

can be connected to each other. This is useful in

order to achieve operating points above the limit

of a single pump.

Note:

There are analogies to electrical engineering:

Pump vs. energy source (battery)

Pressure vs. voltage

Volume flow vs. current

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5.5.1 Parallel connection

In parallel-connected pumps, the outputs of both

pumps are joined together. The delivered volume

flow is increased. The pressure cannot be

increased above the level of a single pump.

In the ideal case of a (non-existent) completely flat

system characteristic, the volume flows are added

together without losses.

The following diagram indicates schematicallyhow a real system behaves.

Connecting the pumps in parallel increases the

volume flow. However, the steep system

characteristic requires a significantly increased

pressure to further increase the throughput. As a

result, in the assumed case the increase is not as

steep.

Fig. 5.4 Schematic characteristics. Single and parallel centrifugal pumps.


Pressure

p

inbar

Operating point

single

Operating point

2 parallel

Single

pump

2 parallel

pumps

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5.5.2 Series connection

In series-connected pumps, the output of the first

pump is connected to the input of the next pump.

The delivered volume flow remains constant.

The subsequent pump increases the pressure of

the volume flow being passed through.

In the case of very steep system characteristics,

the pressures are approximately added together.

Lossless addition is only possible with the "0"

volume flow.

As described in the Parallel connectionsection,

the use of a series connection leads to the

following result in the system characteristic:

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The system characteristic is relatively flat. There

is not enough resistance against the pumps, so

that there is no increase to the possible pressure.

The achieved increase is very small.

Fig. 5.5 Schematic characteristics. Single and series-connected centrifugal pumps.


Pressurep

inbar

Operating point

single

Operating point

2 in series

Single

pump

2 pumps

in series

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5.5.3 Selecting the type of connection

The single pump characteristic can be extended

by switching to an additional pump, as has

already been discussed:

The characteristic in which the pump is to be used

is crucial for the meaningful use of an additional

pump.

The following diagram provides an overview:

Fig. 5.6 Characteristics of single pump and parallel-connected and series-connectedpumps


Pressurep

inbar

Single

pump

2 pumps

in series

2 pumps

in parallel

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The diagram shows the previous pump

characteristic curves with a boundary line that

divides parallel and series connection into two

regions. This line passes through the intersection

point of the pump characteristic curves from

series and parallel operation.

This results in regions that are better suited for the

single pump, the series-connected pumps or the

parallel-connected pumps.

The applied pressure causes the flow of the fluid

and is thus the cause of the volume flow. In each

operating mode, the operating point appears as

the intersection of the pump and system

characteristics.

Fig. 5.7 Characteristics of single pump and parallel-connected and series-connectedpumps


Pressurep

inbar

Single

pump

2 pumps

in series

2 pumps

in parallel

With 2 pumps

cannot be achieved

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When choosing a pump for an existing system,the required pressure is thus the criterion for

selecting the pump. The system characteristic

curve is also crucial.

The diagram is divided into a region of steep

system characteristic curves, which are

preferably operated with pumps connected in

series, and rather flat curves that bring benefits for

pumps operating in parallel.

If one pump is not sufficient for the real

application, an additional pump may help.

At low pressures, parallel connection has its

advantages in that it can provide a substantially

greater volume flow than pumps operating in

series.

If the required pressures through an existing

system are greater than the pressure of a single

pump, then only series connection can be used.In principle, both types of connection are suitable

for the low pressure region above the intersection

of the pumps in series or parallel connection. This

raises the question of whether we want to hold

more reserves as maximum pressure or in the

maximum volume flow.

In the overall consideration we should not forget

that a single larger pump may certainly be

justified, depending on the procurement situation.

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6 Experiments

The selection of experiments makes no claims of

completeness but is intended to be used as a

stimulus for your own experiments.

The results shown are intended as a guide only.

Depending on the construction of the individual

components, experimental skills and

environmental conditions, deviations may occur in

the experiments. Nevertheless, the laws can be

clearly demonstrated.

The measured values of the moving fluid are

subject to constant fluctuations. This means that

the measured values are always varying around

the value of the operating point. Filtering is used

to smooth the measured values before they are

presented to the user.

Since GUNT wants to use this device to

demonstrate the physical relationships in practicaloperation, the interpretation of the measured

values follows these relationships.

When operating points are saved, so are all

measured values and the derived calculation

variables. The values listed in the tables below

only represent a selection for a better overview.

The measurements file created by the

measurement data acquisition program is further

processed in this instruction manual with MS

Excel.

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60 6 Experiments

6.1 Experiment 1: Recording a system characteristic curve

6.1.1 Objectives of the experiment

The system characteristic has to be recorded with

pump P1 on the experimental unit.

The objective is to be able to interpret this

characteristic curve. The result shall be an

awareness of the interaction of the flow rate and

the pressure difference in a flow-through system.

6.1.2 Conducting the experiment

To record the system characteristic curve we shall

proceed according to the following points:

1. Bleed the experimental unit

2. Set the experimental unit for standalone

operation of pump P1. See Fig. 6.1 inChapter 3.7.1, Page 18.

3. Open valve V3 fully

4. Use the Tarebutton to calibrate to zero

5. Leave pump P1 to run to 3300 1/min

6. Measured values for the suction pressure p1,

the pump outlet pressure p2 and the volume

flow should now be recorded

7. Reduce the volume flow bit by bit by gradually

slowing the pump speed and take the

measurements according to point 6

8. Repeat steps 6 and 7 until the volume flow is

completely throttled

Fig. 6.1 Circuit for standaloneoperation of pump P1

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6.1.3 Measured values with calculations of the analysis

6.1.4 Analysis

If we plot the measured values of pressure over

volume flow in the diagram, we can clearly see a

quadratic dependence. The following diagram

shows quadratic trend lines assigned to themeasurements:

Speed of

pump P1

nin 1/min

Volume flow

in L/min

Pressure p1

in bar

Pressure p2in mbar in

3300 47,5 -0,28 0,16 -0,081

3000 43,3 -0,23 0,13 -0,082

2700 38,6 -0,18 0,11 -0,081

2400 34,4 -0,15 0,09 -0,082

2100 29,8 -0,11 0,07 -0,080

1800 25,4 -0,08 0,05 -0,081

1500 21,1 -0,06 0,04 -0,081

1200 16,7 -0,04 0,03 -0,080

900 12,4 -0,02 0,01 -0,077

600 7,7 -0,01 0,01 -0,074

300 3,4 0,00 0,01 -0,058

0 0 0,00 0,00

Tab. 6.1 Volume flows and pressures in the unthrottled system at various speeds

V

V

p1-----------

kg

m2

N--------------------

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62 6 Experiments

The dependency concerns the section upstream

of the pump that is flowed through (suction side,piping from tank to p1) and downstream of the

pump (pressure side, from p2to tank).

Pressure changes into velocity. This can be

demonstrated particularly well on the suction

side.

The dependency can be attributed to Bernoulli's

energy equation Formula (4.10), Page 32:

(6.1)


g = Gravitational acceleration in m/s

h = Height of the liquid column in m


= Density in kg/m

Fig. 6.2 Characteristics of the system in operation with pump P1

Volume flow in L/min

Head

inm

Suction side

Pressure sidePres

sure

inbar

c02

2--------

p0------ g h0+ +

c12

2--------

p1------ g h1+ +

=

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While the pump is being operated the pressurelevel on the pump suction side falls, so that the

higher pressure in the water tank leads to the flow

of the fluid.

Formula (6.1)is used in the following to compare

the "water tank" location (= index "0") with the

pressure measuring point p1location (= index "1")

in terms of energy.

Since the height difference of the pressure

measuring points is eliminated during zero

calibration, this part of the formula can be ignored.

Velocity components c0 in the relatively large

water tank are negligible.

The pressure in the water tank is greater than the

location of the pressure measurement by the

amount of p1( ).

(6.2)

Thank to the constant density of water, we can

derive from Formula (6.2)that the flow velocity is

proportional to the square root of the pressure:

(6.3)



= Density in kg/m

p0 1 p1=

p1

---------c12

2--------=

c1 p1

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64 6 Experiments

In the experiment, this proportionality isdemonstrated by the volume flow. This is also

proportional to the flow velocity:

thus: (6.4)

and also: (6.5)

(6.6)

A = Flowed through cross-sectional area in mc = Flow velocity in m/s

p = Pressure in Pa

= Volume flow in m/s

The results are listed in the table of measurement

results. The unit in is given by

Formula (6.6).

The values oscillate rapidly around the value of -0,08 .

Flow resistances were ignored in this calculation.

This simplification can be made on the suction

side due to the relatively undisturbed flow. A more

precise consideration of flow resistances is

outside the scope of this manual, which is why

there is no analysis of the pressure side.

However, pressure is also converted into velocity,

which corresponds to a quadratic function.

V

A c=

V

p1

V

p1

------------- const=

V

kg

m2

N--------------------

kg

m2

N--------------------
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6.1.5 Evaluation

The system characteristic curve indicates what

flow resistance a system has at a certain volume

flow.

Flowing through the system with a volume flow

requires a certain pressure differential. This

pressure differential is applied by the pump. The

pressure differential is the same as the pump's

supply pressure. This is the pressure differentialthat the pump applies between the suction side

and pressure side. The calculation is as follows:

(6.7)

pP1 = Pressure differential or supply pressure

over pump P1 in Pa

p1 = Pressure upstream of P1 in Pa

p2 = Pressure downstream of P1 in Pa

pP1 p2 p1=

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66 6 Experiments

A portion of this energy is used up in flow

resistances. This occurs particularly in bends andabrupt changes in cross section.

The system's flow resistance can be altered by

valve V3. The next experiment shall address this

in more detail.

From the proportionality of Formula (6.3)

( ) we can further deduce that four times

the pressure is needed to double the volume flow

(the velocity).

Fig. 6.3 System characteristic with pump P1 from the suction and pressure side (p2-p1)


System characteristic

He

adinm

Supp

lypressure

inbar

c1 p1
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6.2 Experiment 2: Determining the reference speed

6.2.1 Objective of the experiment:

This experiment is used to improve the results of

the following experiments.

The reference speed of the two pumps is

determined. This is the speed at which the pumps

have the same delivery characteristics.

Deviations from the theoretically equal speed arepossible due to manufacturing tolerances.

The reference speed is roughly in the range of

2850 1/min.


To find the reference speed we shall proceed

according to the following points:1. Bleed the experimental unit.

2. Set up the experimental unit for series

operation. See Fig. 6.4 in Chapter 3.7.2,

Page 19.

3. Close valve V3 fully.


5. Switch on pump P2.

6. Switch to pump P1 and gradually increase the

speed until the ratio of the two pressures p3/p2is equal to 2.

7. Note down the reference speed:

___________________ 1/min.

Fig. 6.4 Circuit for operating thepumps in series
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68 6 Experiments

6.3 Experiment 3: Determining the pump characteristic curve

6.3.1 Objectives of the experiment

The objective of the experiment is to create a

pump characteristic curve for pump P1.

By using valve V3 we can influence the system

characteristic. In doing so, it is possible to operate

the pump at different system resistances and to

plot the relationship between pressure differential

over the pump and volume flow.


To record the pump characteristic curve we shall

proceed according to the following points:

1. Bleed the experimental unit

2. Set the experimental unit for standalone

operation of pump P1. See Fig. 6.5 in

Chapter 3.7.1.

3. Open valve V3 fully


5. Leave pump P1 to run to reference speed (see:

Chapter 6.2).

(The characteristic at this speed allows a direct

comparison with the subsequent experiments).

6. Measured values for the suction pressure p1,

the pump outlet pressure p2 and the volume

flow should now be recorded.

7. Reduce the volume flow bit by bit by gradually

closing valve V3 and take the measurements

according to point 6.

8. Repeat steps 6 and 7 until the volume flow is

completely throttled

Fig. 6.5 Circuit for standaloneoperation of pump P1

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6.3.3 Measured values

6.3.4 Analysis

6.3.4.1 Pump characteristic

The pressure difference compared to the volume

flow produced with one pump is the interesting

factor.

The pressure difference, or the supply pressure,

can be calculated according to Formula (6.7):

Speed of

pump P1nin 1/min

Volume flow

in L/min

Pressure p1

in bar

Pressure p2

in bar

Hydraulic

power Phyd

in W

Electrical

power Pelin W

Efficiency

in %

2760 39,5 -0,2 0,11 20 221 9

2760 32,3 -0,13 0,42 30 214 14

2760 27,1 -0,09 0,58 30 211 14

2760 22,6 -0,07 0,72 29 206 14

2760 18,7 -0,04 0,81 27 196 14

2760 14,1 -0,03 0,88 21 187 11

2760 9,3 -0,01 0,93 15 181 8

2760 4,9 0,00 1,01 8 173 5

2760 0 0,00 1,09 0 169 0

Tab. 6.2 Volume flows and pressures of the device at different throttling

V

pP1 p2 p1=
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70 6 Experiments

This results in the following diagram for the pumpcharacteristic curve:

The result is a profile of the measured points

which can be closely approximated by a parabola.

The maximum pressure is applied when the pump

is not producing any volume flow. According to the

measurements taken by GUNT this was

1,090 bar (at reference speed).

When valve V3 is opened, the maximum possibleflow rate is 39,5 L/min. With a lower system

pressure loss, a higher volume flow could be

implemented.

Fig. 6.6 Pressure differential over volume flow of pump 1 generated at 2760 1/min


Pump

Hea

dinm

Supp

lypressu

reinbar

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Fig. 6.7 shows the measuring points from the

measured pump and system characteristiccurves. We can see that the pump characteristic

curve is limited at the bottom due to the lowest

possible system curve (valve V3 open).

Each operating point is an intersection point of the

pump characteristic and system characteristic. To

illustrate this point, the system characteristic

curves from which the operating points result are

inserted mathematically as a parabola.

6.3.4.2 Efficiency

The experimental unit also offers the possibility of

studying pump P1 in standalone operation in

more detail.

Fig. 6.7 Pump and system characteristic curves, pump at 2760 1/min


Pump

System

Head

inm

Supplypressure

inbar
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72 6 Experiments

In terms of energy, the interesting factor is theefficiency which arises from the pump

characteristic curve.

The efficiency is the ratio of benefit to effort. The

effort corresponds to the electrical power that the

pump motor requires at the respective operating

point. It is measured and displayed directly by the

experimental unit .

The benefit of a pump is defined as the hydraulic

output. This can be calculated from pressure and

volume flow, see Formula (4.18), Page 38. For

the pump in standalone operation, this

corresponds to:

(6.8)

Phyd = Hydraulic power in W

To calculate the pump efficiency, we need theshaft power at the pump. In contrast to the input

power of the electric motor, this is relatively

difficult to determine, which is why the total

system efficiency at the coupling of the electric

motor and pump is often used.

The system efficiency can be calculated as

follows:

(6.9)

= Efficiency in %

Phyd pP1 V

=

PhydPel------------ 100

=

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This calculation results in the followingrelationship:

The efficiency increases with increasing volume

flow until it reaches a maximum point and then

falls off again. This is due to the value of the

hydraulic power. At the axis intersection points

this is zero, because here either pressure or

volume flow is equal to zero.

The incoming electrical power is converted into

hydraulic power by the pump

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