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7/25/2019 HM284_e - V1.5
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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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G.U.N.T.
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tebau,
Bars
btte
l,Germany
09/2013
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
6.2.2 Conducting the experiment. . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.3 Experiment 3: Determining the pump characteristic curve . . . . . . . . 68
6.3.1 Objectives of the experiment . . . . . . . . . . . . . . . . . . . . . . . . 68
6.3.2 Conducting the experiment. . . . . . . . . . . . . . . . . . . . . . . . . . 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
6.4.1 Objectives of the experiment . . . . . . . . . . . . . . . . . . . . . . . . 76
6.4.2 Conducting the experiment. . . . . . . . . . . . . . . . . . . . . . . . . . 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
6.5.1 Objectives of the experiment . . . . . . . . . . . . . . . . . . . . . . . . 81
6.5.2 Conducting the experiment. . . . . . . . . . . . . . . . . . . . . . . . . . 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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HM 284 SERIES AND PARALLEL CONNECTED PUMPS
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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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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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 5
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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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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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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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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
5
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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 Description of the HM 284 device 13
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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.
To achieve this, the lever on valve V1 must be
rotated until the symbol assumes the position as
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.
To achieve this, the lever on valve V1 must be
rotated until the symbol assumes the position as
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
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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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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26 4 Basic principles for GUNT Labline fluid energy machines
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)
A = Cross-section area in m2
c = Flow velocity in m/s
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)
c = Flow velocity in m/s
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:
c = Flow velocity in m/s
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
c = Flow velocity in m/s
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)
c = Flow velocity in m/s
g = Gravitational acceleration in m/s2
h = Height in m
p = Static pressure in N/m2
= 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)
A = Cross-section area in m2
F = Force in N
p = Pressure in Pa
W= Physical work in J
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
W= Physical work in J
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
g = Gravitational acceleration in m/s2
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
W= Physical work in J
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
p = Static pressure in N/m2
= Volume flow in m3/s
Kinetic power of the fluid
(4.19)
Pkin = Kinetic power in W
c = Flow velocity in m/s
= 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
= Volume flow in m3/s
= 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
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)
c = Flow velocity in m/s
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)
g = Gravitational acceleration in m/s2
h = Head in m
p = Static pressure in Pa
= Density in kg/m3
c 2 p
-----------=
p g h =
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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)
c = Flow velocity in m/s
g = Gravitational acceleration in m/s2
h = Head in m
p = Static pressure in Pa
= 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)
c = Flow velocity in m/s
p = Static pressure in N/m2
= Volume flow in m3/s
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
Volume flow in L/minV
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
Volume flow in L/minV
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.
Volume flow in L/minV
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.
Volume flow in L/minV
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
Volume flow in L/minV
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
Volume flow in L/minV
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
V
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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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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)
c = Flow velocity in m/s
g = Gravitational acceleration in m/s
h = Height of the liquid column in m
p = Static pressure in Pa
= 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)
c = Flow velocity in m/s
p = Static pressure in Pa
= Density in kg/m
p0 1 p1=
p1
---------c12
2--------=
c1 p1
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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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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)
Volume flow in L/min
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.
6.2.2 Conducting the experiment
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.
4. Use the Tarebutton to calibrate to zero
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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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.
6.3.2 Conducting the experiment
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
4. Use the Tarebutton to calibrate to zero
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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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
Volume flow in L/min
Pump
Hea
dinm
Supp
lypressu
reinbar
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htsreserve
d,
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Ger
tebau,
Bars
btte
l,Germany
09/2013
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
Volume flow in L/min
Pump
System
Head
inm
Supplypressure
inbar
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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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Ger
tebau,
Bars
btte
l,Germany
09/2013
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