User Guide: Flow Meter Calibration

H40 Flow Meter Calibration

User Guide

© TecQuipment Ltd 2015 Do not reproduce or transmit this document in any form or by any means, electronic or mechanical, including photocopy, recording or any information storage and retrieval system without the express permission of TecQuipment Limited. TecQuipment has taken care to make the contents of this manual accurate and up to date. However, if you find any errors, please let us know so we can rectify the problem. TecQuipment supplies a Packing Contents List (PCL) with the equipment. Carefully check the contents of the package(s) against the list. If any items are missing or damaged, contact TecQuipment or the local agent.

DB/MB/bs/0315

H40 Flow Meter Calibration

Contents Introduction Description

.................................................................. 1

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The Flow Meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

Nozzle (Supplied as standard) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pitot Tube (H40a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Venturi (H40b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sharp-edged Orifice (H40C). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Straight Test Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Key Features of Each Flow Meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 6 7 8 9 9

Technical Details

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Base Unit (H40) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Flow Meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Noise Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Installation and Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Assembly. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . To Connect and Check the Base Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . To Remove and Fit a Flow Meter or Test Pipe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . To Bleed Trapped Air from the Pipes and Prepare the Manometers . . . . . . . . . . . . . . . . . .

13 13 14 15 16

Useful Equations and Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Bernoulli Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coefficient of Discharge (CD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flow Rate (Venturi, Orifice and Nozzle) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calculation of Discharge Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flow Rate - Pitot Tube. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pressure Losses and ‘k’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17 18 19 19 19 19 20 21 21

Experiment 1 - Accuracy, Coefficient of Discharge and Losses . .

23

Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results Analysis - Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results Analysis - Coefficient of Discharge (not the Pitot Tube). . . . . . . . . . . . . . . . . . . . . .

23 23 24 24

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User Guide

H40 Flow Meter Calibration

Results Analysis - Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Experiment 2 - Velocity Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Results Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

Experiment 1 - Accuracy, Coefficient of Discharge and Losses . . . . . . . . . . . . . . . . . . 31 Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Coefficient of Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Experiment 2 - Velocity Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Useful Textbooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Maintenance, Spare Parts and Customer Care . . . . . . . . . . . . . . . . . . . . . . . 41 Pitot Tube (H40a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Spare Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Customer Care . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

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User Guide

H40 Flow Meter Calibration

User Guide Introduction

Figure 1 The H40 Base Unit (shown fitted with the Pitot Tube - H40A) All engineers that work with fluids need to know the best device to measure fluid flow for any particular application. This applies to civil engineers (for flow in rivers, pipes and canals), mechanical engineers (for flow in pipes and conduits) and marine and aerospace engineers. Different devices may be easier or cheaper to build and fit than another. One device may be more accurate than another at a certain range of flow, or the losses created by one device may be too much for the application. The Flow Meter Calibration equipment is a set of parts for use with TecQuipment’s H1 or H1d Hydraulic Benches (available separately) or a suitable water supply and drain. The equipment shows the use, losses and accuracy of common flow meters, including: • • • •

A Nozzle (supplied as standard) A Pitot tube (H40A) A Venturi (H40B) A Sharp-edged Orifice (H40C)

Each flow meter fits onto the Base Unit (H40), and connects to a piezometer (manometer). Water passes from a Hydraulic Bench (not supplied) or a suitable water supply through the flow meter. The manometer measures the pressure changes caused by the flow meter. The student uses the pressure readings and the given dimensions of the flow meter to calculate the flow. The students compare their results with the actual flow (from a Hydraulic Bench or external calibrated flow meter) to show the accuracy of the flow meter at the given range of flow rate. A straight pipe is included for comparison to allow the student to find the true losses caused by the flow meters.

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H40 Flow Meter Calibration

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H40 Flow Meter Calibration

Description Manifold with air valve

Air valve Manometer 3

Manometer 2 Manometer 4 Manometer 1 Hand Pump Back Plate Outlet adaptor Inlet Adaptor Outlet connection Inlet Connection

Flow Control Valve

Stand

Figure 2 H40 Base Unit The Base Unit (H40) consists of a back plate and stand. Fitted to the back plate is a set of four manometer tubes. At the top of the manometers is a small manifold with an air valve. The student can use the hand pump (supplied) to increase the air pressure in the manifold and offset the measurement of the manometers. The stand includes water inlet and outlet connections to connect to one of TecQuipment’s Hydraulic Benches (H1 or H1d) or other external water source and drain. The inlet and outlet adaptors include sockets and seals for the ends of the flow meters. The inlet adaptor slides to allow easy removal and fitting of the flow meters. The internal shape of the inlet and outlet adaptors is a gradual expansion and contraction respectively. This reduces any unwanted flow disturbances. At the outlet is a gate type flow control valve that controls the flow downstream of the flow meters. For this apparatus, downstream (outlet) flow control is better than upstream (inlet) flow control. This is because the valve itself could produce flow disturbances, if it were mounted upstream.

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H40 Flow Meter Calibration

CAUTION

Do not use the flow control valve as a stop valve. It stops water downstream, so you will get wet if you try to change a flow meter (upstream) when the water supply is still connected. When you change flow meters or complete your experiments, always isolate the water supply at the Hydraulic Bench or your water supply.

Each flow meter (and the straight pipe) slides into the inlet and outlet adaptors of the Base Unit. The pressure measurement connections at manometers 2 and 3 are self-sealing push-fit ‘quick connectors’ and will not leak when they are not in use.

NOTE

You can only fit and test one flow meter at a time

Clean cold water passes through the flow meter. Manometers 2 and 3 show the pressure drop at the flow meter. For reference, and for tests on losses, Manometers 1 and 4 show the total pressure drop across the inlet and outlet to the Base Unit, measured at the inlet and outlet adaptors. The Base Unit fits onto the top of either of TecQuipment’s Hydraulic Benches (H1 or H1d). The Hydraulic Benches give an accurate external flow measurement and provide a controllable self-contained water supply and drain. Alternatively, the H40 can be used with any other suitable clean water source and drain, with an accurate flow meter or calibrated flow measurement system.

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H40 Flow Meter Calibration

The Flow Meters Nozzle (Supplied as standard)

Pressure at nozzle throat

Downstream pressure at a non-turbulent place (in void).

Small pressure tapping hole at nozzle throat Flow

Inlet Diameter = 34 mm

Nozzle Throat Diameter = 22 mm

484 mm

Figure 3 The Nozzle Nozzles are mainly used to control flow at the outlets of a chamber or flow conduit, for example - at the exhaust of a rocket or jet engine, or at the end of a hosepipe. However, they can also measure flow. When used to measure flow, they work like the Venturi and the Orifice. They constrict the flow, which produces a flow rate increase at the constriction and a pressure drop, that is a function of the flow rate. However, the constriction is formed at the entrance to the nozzle, called its throat. The difference between the pressure at the throat and a non-turbulent ‘static’ place after the nozzle is a function of the flow velocity. A nozzle is similar to a shortened Venturi. The Nozzle is machined into a cylindrical aluminium block. Its shape obeys the ISA (Instrument Society of America) rules to give predictable results. The block includes two pressure tappings, one upstream (at the throat) and one downstream, in the non-turbulent void between the nozzle outlet and the pipe wall.

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User Guide

H40 Flow Meter Calibration

Pitot Tube (H40a)

Wall ‘Static’ Pressure

Micrometer Adjustment

Pitot ‘Total’ Pressure

Flow Internal Diameter = 22 mm Probe

484 mm

Figure 4 The Pitot Tube (H40a) The Pitot tube (named after its original French inventor - Henri Pitot) measures the total or stagnation pressure in the fluid flow. As flow increases, the total pressure increases in proportion. Another French scientist - Henry Darci created the modern design of Pitot tube. The Pitot probe only measures the total pressure, but to find the fluid velocity, you also need the static pressure near to the probe. The Pitot Tube (H40A) also has a pressure tapping on the wall of its pipework in line with the end of the Pitot tube probe, this is the static pressure tapping. The difference between the total and static pressures gives the dynamic pressure, used with Bernoulli’s equation to find the fluid flow. The Pitot tube has a micrometer-type adjustment, for accurate positioning of its probe in the flow. The probe can be moved across the flow to show how the flow velocity varies across the diameter of a pipe (a velocity profile).

NOTE

To give measurable pressures at the probe, the internal pipe diameter of the Pitot tube flow meter is smaller than the other flow meters.

Many types of aircraft use a Pitot tube to measure air speed. It is also used on high speed racing cars and with some types of weather vane for wind speed measurement.

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H40 Flow Meter Calibration

Venturi (H40b)

Upstream Pressure

Throat Pressure

Throat Diameter = 22 mm Flow

Inlet Diameter = 34 mm Outlet diameter = 34 mm

484 mm

Figure 5 Venturi (H40b) The Venturi (named after its Italian inventor - Giovanni Venturi) is a specially machined device that uses the ‘Venturi effect’ to give predictable pressure changes that are related to flow rate. The ‘Venturi effect’ is shown and calculated by Bernoulli’s equation. It shows that fluid flows faster in a constriction, and its pressure drops is a function of the increase in flow velocity. There are two pressure tappings on the Venturi (H40B), one at the inlet and the other at the constriction (throat). As the water passes along the Venturi, it causes a pressure difference between the two tappings which is a function of the water flow rate, the greater the flow rate, the greater the pressure difference. The Venturi effect is used in many places, including river and canal flow measurement and control, combustion engine carburettors, gas burners and spray jets. The gradual expansion after the Venturi gives a good pressure recovery and non-turbulent flow.

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H40 Flow Meter Calibration

Sharp-edged Orifice (H40C)

Upstream Pressure

Flow

Inlet Diameter = 34 mm

Downstream Pressure at the Vena Contracta

Orifice Diameter = 22 mm

484 mm

Figure 6 Sharp-edged Orifice The sharp-edged orifice works in a similar way to the Venturi. It constricts the flow, which produces a velocity increase at the constriction and a pressure drop, which is a function of the flow. However, the constriction is formed just downstream, not in the orifice, as it is in the Venturi. The difference between the upstream and downstream pressure is a function of the flow rate. Just after the orifice, the flow contracts into its smallest diameter before it starts to expand again. This point is called the Vena Contracta. The orifice must have a sharp edge to give a correct Vena Contracta for accurate and predictable readings. The Sharp-edged Orifice (H40C) is machined into a cylindrical aluminium block. The block includes two pressure tappings, one upstream and one downstream. An orifice plate is a simple and cheap flow measurement device.

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H40 Flow Meter Calibration

Straight Test Pipe

Figure 7 The Straight Test Pipe Supplied with the Base Unit is a straight pipe. It has the same internal dimensions and surface finish as the pipe used on the Venturi, the Sharp-edged Orifice and the Nozzle. There are no tappings on this pipe, it is for use in place of the flow meters to give a reference pressure difference for comparison.

Key Features of Each Flow Meter Table 1 shows the typical features of each flow meter for comparison. * The relative cost indicates the relative cost of a full size ‘real world’ flow meter, used in industrial or civil engineering projects. ** The H40A Pitot tube has a micrometer adjustment, but an actual Pitot is usually fixed in position.

Flow meter

Moving Parts

Obstruction to the flow

Relative Cost*

Straight Test Pipe

No

Moderate

Medium

Pitot Tube (H40a)

No**

Minor

Medium

Venturi (H40b)

No

Moderate

High

Sharp-edged Orifice (H40C)

No

Significant

Low

Table 1 Key Features of Each Flow meter

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H40 Flow Meter Calibration

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H40 Flow Meter Calibration

Technical Details Base Unit (H40)

Item

Details

Dimensions

750 mm high x 900 mm long x 300 mm front to back

Weight

9 kg including nozzle flow meter

Manometer range

500 mm water

Maximum Inlet Pressure

2 bar

Maximum Flow through the Flow meters

50 L/min

Nominal water supply flow

60 L/min

Flow Meters

Item Dimensions

Weights

Flow meter

Details

Pitot Tube (H40A)

484 mm long x 230 mm high x 100 mm front to back

Nozzle, Venturi (H40B) and Sharp-edged Orifice (H40C)

484 mm long x 130 mm high x 80 mm diameter

Nozzle

0.6 kg

Pitot Tube (H40A)

0.75 kg

Venturi (H40B)

1.5 kg

Sharp-edged Orifice (H40C)

1 kg

Noise Levels The noise levels recorded at this apparatus are lower than 70 dB (A).

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H40 Flow Meter Calibration

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H40 Flow Meter Calibration

Installation and Assembly The terms left, right, front and rear of the apparatus refer to the operators’ position, facing the unit.

NOTE

• A wax coating may have been applied to parts of this apparatus to prevent corrosion during transport. Remove the wax coating by using paraffin or white spirit, applied with either a soft brush or a cloth. • Follow any regulations that affect the installation, operation and maintenance of this apparatus in the country where it is to be used.

Location Use the Flow Meter Calibration equipment in a clean, well lit laboratory or classroom type area. Put it on the top of a TecQuipment Hydraulic Bench (H1 or H1d), or on a solid, level waterproof workbench.

WARNING

CAUTION

Install and use this apparatus at least 2 m away from any electrical sockets or supplies.

You will spill a small amount of water each time you change a flow meter. This is normal.

The Flow Meter Calibration equipment uses an area of 1 m x 300 mm. It is 750 mm high and will fit onto the top of TecQuipment’s Hydraulic Benches.

Assembly The back plate bolts to the stand for transport. Unbolt the back plate from the stand and refix it to the stand in an upright position, as shown in Figure 2.

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H40 Flow Meter Calibration

To Connect and Check the Base Unit 1. Connect the inlet of the Base Unit to: • the bench supply hose of the TecQuipment Hydraulic Bench or • a source of clean cold water, with an accurate flow measurement device and a stop valve nearby. 2. Connect the outlet of the Base Unit to: • the large hole in the H1 Gravimetric Hydraulic Bench or • the volumetric tank of the H1d Volumetric Hydraulic bench or • a suitable drain

NOTE

To prevent large spills when you change the flow meters, make sure that all parts of the inlet and outlet pipes are below the level of the Base Unit.

3. Fit the straight Test Pipe to the Base Unit (see To Remove and Fit a Flow Meter or Test Pipe). 4. Fully open the outlet valve (turn it fully anticlockwise). 5. Slowly open your water supply (or switch on the Hydraulic Bench and open its gate valve). Check for leaks around the Base Unit and the manometers.

CAUTION

Do not use an inlet water pressure greater than 2 bar

6. Slowly turn the flow control valve to reduce the flow (and increase pressure in the manometers). 7. Carefully press the air valve on the manometer manifold to let the air out of manometers 1 and 4. The water level will rise to the top of the manometers (you may need to shut the flow control valve and get more pressure to the manometers). 8. Use the hand pump to add air to the manometer manifold, so that you can see the water levels in manometers 1 and 4 on the back plate scale. Check for leaks of water and air. 9. Stop your water supply and allow all water to drain out of the Base Unit.

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H40 Flow Meter Calibration

To Remove and Fit a Flow Meter or Test Pipe

CAUTION

The inlet and outlet adaptor seals are ‘O’ shaped rings. They work best when they are lubricated with water or a small amount of silicon grease. Do not force the flow meters into the adaptors, or you will break the seals. A small amount of water will drain out each time you change a flow meter. This is normal.

Figure 8 Unscrew the Locating Screw

Figure 9 Slide the Inlet Adaptor In and Out 1. Shut off the water supply and allow water to drain away from the Base Unit. 2. Disconnect the manometer-to-flow meter pressure tappings.

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H40 Flow Meter Calibration

3. Unscrew the locating screw (see Figure 8). 4. Firmly hold the inlet adaptor and slide it away from the flow meter (see Figure 9). 5. Carefully slide the flow meter out from the outlet adaptor and put it on a clean surface to dry out. 6. Decide which flow meter you need to fit. Add some water or a smear of silicone grease to each end of the flow meter, to help lubricate the seals in the adaptors. 7. Carefully insert the downstream end of the flow meter into the outlet adaptor and turn the flow meter so that its pressure tappings point upwards. 8. Carefully slide the inlet adaptor over the end of upstream end of the flow meter (see Figure 9). 9. Connect Manometer 2 to the upstream pressure tapping and Manometer 3 to the downstream pressure tapping of the flow meter.

To Bleed Trapped Air from the Pipes and Prepare the Manometers Each time you use the equipment, you must bleed trapped air from its pipes, or your readings will be wrong. To bleed the air: 1. Unplug the flow meter downstream tapping pipe from Manometer 3 and direct it to a drain. 2. Start the water supply and slowly shut the flow control valve to increase the pressure and force water into the manometer tubes. 3. If necessary, press the air valve on the manometer manifold to let some air out. 4. Wait for all air bubbles to leave the pipes. 5. Put your finger over the end of the flow meter downstream tapping pipe and reconnect it to Manometer 3. Wait for the air bubbles to leave this pipe and Manometer 3. 6. At full pressure (no flow), press the air valve to bleed some air or use the hand pump to add some air, so that all the manometer levels are readable and near to the top of the manometers. 7. Fully open the flow control valve to reduce the pressure (full flow) and check that all manometer levels drop to a readable level (not below zero). If the levels drop below zero, you must carefully press the air valve again to let some air out of the manometers.

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H40 Flow Meter Calibration

Useful Equations and Theory This section only gives the basic information needed to do the experiments. For full theory, refer to the textbooks listed in Useful Textbooks on page 39.

Notation

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Coefficient of discharge

CD

Dimensionless

Inlet diameter (upstream pipe diameter)

D

m

Throat or Orifice Diameter

d

m

Diameter Ratio

β

= d/D (m)

Area of Inlet Pipe

Α1

m2

Area of throat or orifice

Α2

m2

Volumetric Flow Rate

Qv

m3.s-1

Mass Flow Rate

Qm

kg.s-1

Height of water

h

m of water

Difference in height between two levels (head)

Δh

m of water

Pressure

p

Pa

Differential pressure

Δp

Pa

Pressure Loss

Δϖ

Pa

Viscosity

μ

Pa.s

Water Density

ρ

kg.m-3

Acceleration due to gravity

g

9.81 m.s-2

Flow velocity

υ

m.s-1

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H40 Flow Meter Calibration

The Bernoulli Principle A Dutch mathematician - Daniel Bernoulli, realized that fluid flow obeys the recognized conservation laws so that: Energy in = Energy out In fluid flow, the total energy in the fluid is a sum of its kinetic energy (flow velocity and pressure), and its potential energy (height or ‘head’). Bernoulli found that an increase in flow velocity (caused by an obstruction or constriction) gives a decrease in pressure at the constriction, so that total energy is conserved. The flow velocity and pressure relationship is shown in aerodynamics, the fast moving air over the surface of a wing reduces pressure above the wing and gives lift. If you stand facing high speed vehicles, the fast flowing air between you is at a lower pressure than the air behind you. You are pushed towards the vehicle.

Inlet Velocity V1

Constriction Velocity V2

Inlet Pressure P1 Height z2

Height z1

Constriction Pressure P2

Figure 10 The Bernoulli Principle As the pressure changes are a function of flow velocity, you can use them to calculate the flow rate through the constriction. Equation 1 and Figure 10 show the relationship between pressure and flow rate in a pipe with a constriction, according to Bernoulli’s Principle. 2 2 P 1 + 1--- ρV 1 + ρgz 1 = P 2 + 1 --- ρV 2 + ρgz 2 2 2

(1)

Note that the heights (z) will cancel out if they are the same.

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Coefficient of Discharge (CD) The coefficient of discharge is a mathematical correction factor used in flow equations. It corrects the equation for a given range of flow velocity through an object of known standard dimensions. You can calculate it from given equations and find it by experiments. An object that gives no resistance to flow has a coefficient of 1. An object that gives a large flow resistance has a coefficient of less than 0.5. From their dimensions and the positions of their pressure tappings, the calculated discharge coefficients (CD) for each flow meter are given in tables of the ISO (International Standards Organisation) 5167.

CD

flow meter Venturi

0.958

Orifice

0.621

Nozzle

0.941

Table 2 ISO Values of Coefficients of Discharge for the flow meters

Flow Rate (Venturi, Orifice and Nozzle) From Bernoulli’s equation and the continuity equation, there is one general equation that works for the Venturi, Orifice and Nozzle flow meters: 2gΔh Q V = C D A 2 ------------------------------------2 [ 1 – ( A2 ⁄ A1 ) ]

(2)

Calculation of Discharge Coefficient Equation 2 is in the form of y = mx, where the CD is the gradient (m). Therefore, a graph of Flow rate (QV) on its vertical axis against equation 3 on the horizontal axis will give a line with a gradient equal to the CD. 2gΔh A 2 ------------------------------------2 [ 1 – ( A2 ⁄ A1 ) ]

(3)

Flow Rate - Pitot Tube A Pitot tube measures flow velocity. So, to find volumetric flow rate, you must first calculate the velocity, then multiply it by the cross-sectional area of the inlet pipe. For the Pitot tube: Dynamic Pressure = 1/2 ρυ2 = Stagnation (Total) pressure - Static (Wall) Pressure = Δp So, 1 2 Δp = --- ρυ 2

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So, when pressure difference is converted to head of water (see Equation 5):

υ =

2gΔh

From this, the volume flow rate is found from: Qv = υ A So, these equations can be combined to give:

(4)

Q v = A 2gΔh

You results will be in m3 per second, so you need to multiply by 1000 to return it to Litres per second.

NOTE

This equation is a general equation that assumes that flow velocity is equal across the pipe, which is not actually correct, as shown in the experiments.

Unit Conversions Note that some fluid equations are based on mass flow rate. To convert from volume flow rate (L/s) to mass flow rate (kg/s) accurately and back again: Water Density (kg/m^3) Mass Flow (kg/s) = Volume Flow (L/s) × ---------------------------------------------------------------1000 Mass Flow (kg/s) Volume Flow (L/s) = ---------------------------------------------------------------- × 1000 Water Density (kg/m^3)

To convert volume flow rate from m3.s-1 to L.s-1 multiply by 1000. (1 m3.s-1 = 1000 L.s-1) To convert pressure from bars to Pascals, multiply by 100000. (1 bar = 100000 Pa) To convert from mm of water to Pascals, you need the water temperature to find its density, (see Graph 1) so that:

p = hρg

(5)

but generally, at 4°C: 10 mm (0.01 m) of water = 98 Pascals. For most experiments with this equipment at room temperature you can use a water density of 1000 kg/m3. This makes the calculations easier.

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Typical Tap Water Density 1005

Density (kg/m3)

1000 995 990 985 980 0

10

20

30

40

50

60

Temperature (°C)

Graph 1 Tap Water Density

Errors To find the percentage error of your flow rate readings, use equation 6. Actual Flow Rate - Calculated Flow Rate- × 100 --------------------------------------------------------------------------------------------------------Actual Flow Rate

(6)

Pressure Losses and ‘k’ The pressure losses in the Venturi are found from actual experiment, where the losses in a straight pipe are subtracted from the losses caused by the Venturi. British Standard 1042 states that the loss (shown as a percentage) is between 5 and 20%. It also gives suggested values of pressure loss based on a good quality installation, where the pipes align well and have a smooth (low friction) internal finish. To find the actual pressure losses of the flow meters, you must fit the straight pipe and measure its pressure loss* Δp1 between the inlet and outlet adaptors. Then you must fit the flow meter and measure its insertion loss Δp2 between the inlet and outlet adaptors. The total loss due to the flow meter is then simply: Δp2 - Δp1

NOTE

* A long straight pipe would normally give a pressure loss (negative value), but expansions or contractions can cause a positive or negative value.

However, it is difficult to directly compare these losses unless you can set the flow rate to be exactly the same in the straight pipe as it is in the flow meter. For this reason, it is better to plot a curve of the losses of the straight pipe and use it to compare the losses of the flow meters. The head loss caused by any pipe or part fitted in a pipe system (for example - a bend or an elbow) is proportional to the square of the flow velocity (υ). The proportional constant is given the term ‘k’. The equation to link these terms is:

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2 kυ Head loss = --------

2g

(7)

This equation shows that a high value of k indicates a high head loss. Each of the flow meters is a part of a pipe system. Its value of k value can be calculated. A comparison of k for each flow meter shows their relative losses. If the equation is turned around, the value of k is the gradient of a curve of head loss against υ2/2g.

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Experiment 1 - Accuracy, Coefficient of Discharge and Losses The flow meters are fundamental flow meters. Their accuracy depends on the coefficient of discharge. However, the coefficient of discharge varies slightly with the flow rate, due to the viscous properties of the water and its velocity through the flow meter. While you do this experiment, you may also record the overall pressure loss at the inlet and outlet adaptors to calculate the pressure loss caused by the flow meters.

Aims • To demonstrate the effect of flow rate on the accuracy of the flow meters. • To demonstrate the calculation of the coefficient of discharge and how it is affected by flowrate (not the Pitot tube). • To use the straight pipe and overall pressure loss to calculate the loss caused by the flow meters.

Procedure

flow meter flow meter (at Manometers 2 and 3)

flow meter

Δp

Overall Head loss (at Manometers 1 and 4)

(mm)

(Pa)

(mm)

H Actual Flow (L/s)

(kg/s)

Calculated Flow from the flow meter (L/s)

(kg/s)

Table 3 Blank Results Table for the Effect of Flowrate

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1. Create a Table of Results as shown in Table 3. Note that you can use volume flow OR mass flow, depending on your external flow measurement system, but do not mix the two readings. 2. Make sure that the flow meter is fitted as described in To Connect and Check the Base Unit. 3. Bleed the air from the pipes as described in To Bleed Trapped Air from the Pipes and Prepare the Manometers on page 16. 4. Fully open the flow control valve. 5. Turn on your water supply to give a maximum flow rate of between 35 and 45 Litres a minute (0.58 to 0.75 kg.s-1). If necessary you may use the flow control valve to make adjustments to the flow. 6. For the Pitot Tube, adjust it so that its probe is near to the centre line of its pipe (approximately 10 mm up from the bottom of the pipe wall). 7. Allow the flow to stabilize. 8. Record the actual flow rate and the pressure (head) difference between manometers 2 and 3. If you are to calculate losses, also record the overall pressure drop at manometers 1 and 4. 9. Repeat the experiment for at least five more flow rates, until you reach approximately 0.2 kg.s-1 (or 12 Litres a minute). 10. Now fit the straight pipe and record the overall pressure drop (at manometers 1 and 4) for a range of flow rates down to approximately 0.2 kg.s-1 (or 12 Litres a minute).

Results Analysis - Accuracy Use the equations in the ‘Useful Equations and Theory’ section to calculate the volume or mass flow for your flow meter and compare it with the actual flow. What do you think are the main causes of error at the different flow rates? What type of liquids and flow rates do you think will work best with your flow meter?

Results Analysis - Coefficient of Discharge (not the Pitot Tube) Use equation 3 on each line of your results to produce a chart of actual flow rate against the equation. Use the gradient of the chart to calculate the coefficient of discharge for your flow meter. How does your coefficient of discharge value compare with the ISO value given in Table 2?

Results Analysis - Losses Each flow meter creates an obstruction to the flow, shown by a lower outlet pressure than the inlet pressure. To find the pressure losses due to the flow meter you must ideally measure the pressure drop directly at its inlet and outlet. However, the flow may be turbulent at these places, so the measurements may be unreliable. For sensible and comparable results, you must measure the pressure drop at less turbulent places at a fixed distance upstream and downstream of the flow meter. Manometer tappings 1 and 4 are connected to the correct places for this measurement. However, you must allow for the small pressure difference caused by the length of pipe that the flow meter is mounted on. For this reason you must find the

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pressure difference caused by the straight Test Pipe and compare it with the losses of your flow meter. The best way is to compare the calculated k values for the straight pipe and the flow meters as shown in Useful Equations and Theory on page 17. To find and compare the k values: For each line of results of your straight pipe and your flow meter, calculate υ2/2g For the straight pipe, create a chart of pressure difference in Pascals (vertical axis) against υ2/2g Find the gradient of the line to find the value of k for the straight pipe For each set of results of your flow meter, multiply the υ2/2g value by the k value of the straight pipe. e) Subtract this new value from the overall pressure drop for the flow meter at each flow rate. This will give an adjusted pressure drop that allows for the straight pipe. a) b) c) d)

NOTE

Be careful and note the (+/-) polarities when you subtract these values

f) Now plot a curve of the adjusted pressure drop against υ2/2g for your flow meter g) Calculate the gradient of your curve to find the actual k value for your flow meter.

Questions If you have more than one flow meter, compare the head losses. Which gives the most losses? If you have more than one flow meter, how do the losses compare with the coefficients of discharge? Compare the losses with the relative costs of the flow meters (Table 1). What do you notice? To give a good resolution, the diameter of the Pitot tube flow meter is smaller than that of the other flow meters. If it were the same diameter, how would this affect the losses? As the flow rate reduces, the measured change in head (Δh) reduces sharply because of the square law relationship. If you needed to measure a much lower flow rate than 0.2 kg/s (12 L/min), how would you modify the flow meter or the manometer to give good results?

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Experiment 2 - Velocity Profile The flow velocity in a pipe is not uniform across the full width of the pipe. The surface of the pipe walls causes the flow nearby to slow down, due to friction. This slower moving layer of flow near to the wall is called the boundary layer. The rougher the surface, the longer the pipe or the faster the flow velocity, the more the boundary layer effect is shown. The flow along the centre of the pipe is less affected by this frictional loss and has a slightly higher flow velocity (see Figure 11). The Pitot probe is an excellent tool to measure this profile. The pipe used with the Pitot tube is smooth and has a low friction, but with high flow rates a boundary layer will form and the Pitot tube will measure a velocity profile. To find the flow rate in the pipe you must find the velocity at different radii to produce a velocity profile curve, as shown in Figure 11. You must then use the trapezium method to calculate the area under the curve.

Trapezium Flow V0

r0

Velocity Curve V1

r1 r2 r3

V2 V3 V4

Figure 11 Flow Velocity in a Pipe

Aim To show the velocity profile in a pipe and demonstrate the effect of the boundary layer.

Procedure 1. Create a blank results table, similar to Table 4. 2. Make sure that the Pitot tube is fitted as described in To Connect and Check the Base Unit. 3. Bleed the air from the pipes as described in To Bleed Trapped Air from the Pipes and Prepare the Manometers on page 16. 4. Carefully adjust the micrometer of the Pitot tube so that its probe just touches the bottom of its pipe. The Pitot probe is 1.6 mm in diameter, so the probe centre will actually be 0.8 mm from the pipe wall (see Figure 12). For ease of use, the micrometer adjustment is calibrated to show 0.8 mm when the probe is at the bottom wall of the pipe.

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Pitot probe 1.6 mm Diameter Clear Pipe

0.8 mm

Figure 12 The Pitot Probe in the Pipe 5. Fully open the flow control valve. 6. Turn on your water supply to give a flow rate of approximately least 20 Litres a minute or 0.3 kg.s-1. If necessary you may use the flow control valve to make adjustments to the flow. 7. Allow the flow to stabilize. 8. Record the pressure difference between manometers 2 and 3 and for reference, record the overall pressure difference between manometers 1 and 4. 9. Move the Pitot tube upwards in steps of 1 mm until the probe reaches the centre of the pipe (11 mm). Record the pressure difference at each step.

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Pitot Position (mm)

Radius (r)

πr

-

11

0.000380

-

0.8

10.2

0.000327

0.000053

1.8

9.2

0.000266

0.000061

2.8

8.2

0.000211

0.000055

3.8

7.2

0.000163

0.000048

4.8

6.2

0.000121

0.000042

5.8

5.2

0.0000849

0.0000361

6.8

4.2

0.0000554

0.0000295

7.8

3.2

0.0000322

0.0000232

8.8

2.2

0.0000152

0.000017

9.8

1.2

0.00000452

0.0000107

10.8

0.2

0.000000126

0.000004394

11

0

0

0.000000126

Area Difference

2

Height difference at flow meter (Δh) (mmH2O)

Overall height difference (mmH2O)

Actual Flow:

Flow Velocity (m.s-1)

Trapezium Rule

Total Flow:

Table 4 Blank Results Table for Velocity Profile

Results Analysis Calculate the flow velocity at each probe position. Plot a chart of the velocity (horizontal axis) against the radius (vertical axis) to see the velocity profile for the bottom half of the pipe. Use the trapezium rule to calculate the area of each trapezium. To do this you must: • Find the difference between each two consecutive areas (already done for you in the results table) • Multiply this by half the sum of two consecutive velocities So that: Trapezium area = (πr21-πr22) x (V1+V2)/2 Now you must add all the trapezium areas together to find the flow rate and compare it with the actual flow rate.

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Results Note: These results are sample results only, actual results may be slightly different.

Experiment 1 - Accuracy, Coefficient of Discharge and Losses Accuracy

flow meter - Orifice flow meter (at Manometers 2 and 3)

flow meter

Δp

Overall Head loss (at Manometers 1 and 4)

(kg/s)

(mm)

(Pa)

(mm)

0.625

290

2842

130

0.620

0.556

224

2195.2

104

0.545

0.5

184

1803.2

84

0.494

0.4

118

1156.4

52

0.396

0.297

64

627.2

30

0.291

0.233

42

411.6

20

0.236

0.174

22

215.6

12

0.171

Δh

Actual Flow (L/s)

Calculated Flow from the flow meter (L/s)

(kg/s)

Table 5 Results for the Orifice

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flow meter - Nozzle flow meter (at Manometers 2 and 3)

flow meter

Δp

Overall Head loss (at Manometers 1 and 4)

(kg/s)

(mm)

(Pa)

(mm)

0.625

134

1313.2

31

0.639

0.566

103

1009.4

24

0.560

0.5

80

784

20

0.493

0.429

58

568.4

16

0.420

0.297

30

294

10

0.302

0.214

15

147

4

0.214

0.13

5

49

2

0.123

Δh

Actual Flow (L/s)

Calculated Flow from the flow meter (L/s)

(kg/s)

Table 6 Results for the Nozzle

flow meter - Venturi flow meter (at Manometers 2 and 3)

flow meter

Δp

Overall Head loss (at Manometers 1 and 4)

(kg/s)

(mm)

(Pa)

(mm)

0.645

132

1293.6

5

0.645

0.6

110

1078

5

0.589

0.455

66

646.8

0

0.456

0.417

56

548.8

0

0.420

0.361

40

392

0

0.355

0.3

29

284.2

0

0.302

0.244

20

196

0

0.251

0.211

15

147

0

0.218

0.158

8

78.4

0

0.159

Δh

Actual Flow (L/s)

Calculated Flow from the flow meter (L/s)

(kg/s)

Table 7 Results for the Venturi

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flow meter - Pitot tube flow meter (at Manometers 2 and 3)

flow meter

Δp

Overall Head loss (at Manometers 1 and 4)

(kg/s)

(mm)

(Pa)

(mm)

0.638

226

not needed

108

0.800

0.53

141

not needed

70

0.632

0.44

95

not needed

49

0.519

0.323

57

not needed

33

0.402

0.2

23

not needed

13

0.255

Δh

Actual Flow (L/s)

Calculated Flow from the flow meter (L/s)

(kg/s)

Table 8 Results for the Pitot Tube The calculated flow rates for the Nozzle, Orifice and Venturi should be very close to the actual flow rates. The calculated flow rates for the Pitot tube will be higher than the actual flow rates (up to 25%). This is due to the velocity profile of the flow in the tube. The effect is shown and explained in Experiment 2 - Velocity Profile.

Coefficient of Discharge

Actual flow rate (kg.s -1)

Orifice 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

y = 0.6286x

0

0.2

0.4

0.6

0.8

1

1.2

f(h) (kg.s-1)

Graph 2 Coefficient of Discharge for the Orifice

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Actual flow rate (kg.s -1)

Nozzle 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

y = 0.9542x

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.7

0.8

f(h) (kg.s-1)

Graph 3 Coefficient of Discharge for the Nozzle

Venturi Actual flow rate (kg.s -1)

0.7 y = 0.9593x

0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5

0.6

f(h) (kg.s-1)

Graph 4 Coefficient of Discharge for the Venturi Graphs 2, 3 and 4 show that the experiments give coefficients of discharge that are very close to the ISO values for the range of flow rates used in the experiments.

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Losses

Straight pipe 0.025 y = 0.8894x Δ h (Pa)

0.020 0.015 0.010 0.005 0.000 0.000

0.005

0.010

0.015

0.020

0.025

0.030

2

υ /2g

Figure 13 k Value for the Straight Pipe

k Value for the Flowmeters 0.000

0.005

0.010

0.015

0.020

0.025

0.030

Adjusted Pressure Drop (Pa)

0.000 -0.020 y = -1.0601x

-0.040 y = -2.1302x

-0.060 -0.080 ORIFICE

-0.100

NOZZLE

y = -5.1212x

VENTURI

-0.120

PITOT y = -6.2982x

-0.140 -0.160 2

υ /2g Graph 5 k Value for the flow meters The results show that the orifice produces the biggest losses and the Venturi gives the lowest losses.

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Experiment 2 - Velocity Profile Velocity profile Velocity (m .s -1)

0

0.5

1

1.5

2

2.5

Radius (mm)

0 2 4 6 8 10 12

Graph 6 Velocity Profile

πr 2

Area Difference

Height difference at flow meter (Δh) (mmH2O)

11

0.000380

-

-

0.8

10.2

0.000327

0.000053

1.8

9.2

0.000266

2.8

8.2

3.8

Pitot Position (mm)

Radius (r)

-

Overall height difference (mmH2O)

Trapezium Rule

0

0.0000428

132

1.61

0.0001021

0.000061

155

1.74

0.0000975

0.000211

0.000055

170

1.83

0.0000898

7.2

0.000163

0.000048

182

1.89

0.0000816

4.8

6.2

0.000121

0.000042

202

1.99

0.0000718

5.8

5.2

0.0000849

0.0000361

208

2.02

0.0000597

6.8

4.2

0.0000554

0.0000295

210

2.02

0.0000474

7.8

3.2

0.0000322

0.0000232

214

2.05

0.0000349

8.8

2.2

0.0000152

0.000017

218

2.07

0.0000221

9.8

1.2

0.00000452

0.0000107

222

2.09

0.0000922

10.8

0.2

0.000000126

0.000004394

226

2.11

0.0000264

11

0

0

0

227

2.11

0

Actual Flow: 0.638 kg.s-1

0

Flow Velocity (m.s-1)

Total Flow:

0.00065984

Table 9 Results for Velocity Profile The chart shows the difference in flow velocity between the centre of the pipe (highest velocity) and the pipe wall (lowest velocity). The lower velocity at the wall is due to the boundary effect.

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The trapezium rule method produces a flow rate of 0.660 kg.s-1, which is very similar to the actual flow of 0.638 kg.s-1.

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Useful Textbooks The following textbooks are good for more study of flow measurement.

Mechanics of Fluids by B.S Massey Sixth edition Published by Chapman and Hall ISBN 0 412 34280 4

Understanding Hydraulics by L.Hamill Published by Macmillan Press Ltd ISBN: 0 333 59910 1

Measurement of Fluid Flow in Closed Circuits British Standards Institute BS1042 Section 1.1/ ISO 5167 Part 1

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Maintenance, Spare Parts and Customer Care After use, drain any water from the equipment and dry it down with a clean cloth. Store it in a dry and dust free area suitably covered. To clean the apparatus, wipe clean with a damp cloth - do not use abrasive cleaners.

Pitot Tube (H40a) The Pitot Tube has a precision movement which may become stuck if you do not keep it clean and free from the deposits that may be present in your water - especially if your water has a high mineral content. To prevent this, TecQuipment recommend that you dry the assembly after use and lubricate its guide rods using a water repellent lubricant or light mineral oil.

Spare Parts Check the Packing Contents List to see what spare parts we send with the apparatus. If you need technical help or spares, please contact your local TecQuipment Agent, or contact TecQuipment direct. When you ask for spares, please tell us: • Your Name • The full name and address of your college, company or institution • Your email address • The TecQuipment product name and product reference • The TecQuipment part number (if you know it) • The serial number • The year it was bought (if you know it) Please give us as much detail as possible about the parts you need and check the details carefully before you contact us. If the product is out of warranty, TecQuipment will let you know the price of the spare parts.

Customer Care We hope you like our products and manuals. If you have any questions, please contact our Customer Care department: Telephone: +44 115 954 0155 Fax: +44 115 973 1520 email: [email protected] For information about all TecQuipment products visit:

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Air Valves TecQuipment’s Fluid Mechanics Products

Instruction Sheets

Figure 14 Typical Air Valves on Some of TecQuipment’s Products Many of the products in TecQuipment’s Fluid Mechanics range use air valves at the tops of manometers or piezometers. The valves keep the air in the manometer tubes to allow you to offset the pressure range of the manometer or piezometer. The valves are similar to valves used in vehicle tyres and include a special cap. The hand pump supplied with the equipment is similar to those used for bicycle tyres, except that TecQuipment remove the crossshape part of the flexible pipe.



TecQuipment take this part out



Figure 15 TecQuipment Remove the Cross-shape Part of the Flexible Pipe

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Instruction Sheets

Air Valves on TecQuipments Fluid Mechanics Products

Normally, when you connect the flexible pipe to an air valve, the cross-shape piece in the flexible pipe pushes open the valve as you pump air with the hand pump. With TecQuipment fluid mechanics products, this could allow water back out through the valve. For this reason TecQuipment remove the cross-shape piece. Without the cross-shape piece, only pressurised air can go through the valve in one direction, and no water can come back out.

Figure 16 The Hand Pump and Flexible Pipe When you first use the hand pump with the air valve, you may find it hard to push air through the valve. This is because the valve is new and you do not have the cross-shape piece to help push it open. The valve will open more easily after you have pumped air through it a few times. You may need some practice to use the air valve. To do it correctly: 1. Unscrew the cap from the valve.

Figure 17 Unscrew the Cap and Fit the Pipe 2. Connect the flexible pipe to the valve. 3. Connect the hand pump to the flexible pipe. 4. Using complete strokes, slowly and firmly pump the hand pump to force air into the manometer or piezometer. 5. Unscrew the hand pump and flexible pipe and refit the valve cover. 6. To let air back out through the air valve, use the end of the special cap to press on the inner part of the valve (see Figure 18).

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Air Valves on TecQuipments Fluid Mechanics Products

Figure 18 To Let Air Out - Use the End of the Special Cap to Press the Inner Part of the Valve

WARNING

Take care when you let air back out from the air valve. Water may come out! Clean up any water spills immediately.

If using the hand pump is too difficult, the valve may be stuck. If you need to check the valve is working, use the special cap to unscrew the valve, then gently press the end of the valve. It should move easily and return back to its original position (see Figure 19).

Figure 19 Unscrew the Valve and Check it If the valve does not move easily, then contact TecQuipment Customer Services for help. Telephone: +44 115 9722611 Fax: +44 115 973 1520 Email: [email protected]

TecQuipment 0809 DB

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Instruction Sheets