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NOMENCLATURE

 Units Nom. Type Description Length of m L Given Length of pipe test section. The test pipe Test Pipe length is measured in mm. Convert to metres for the calculation. Diameter of m d Given Diameter of pipe test .  The test Test Pipe pipe diameter is measured in mm. Convert to metres for the calculation. Volume m3 V Measured Volume of water collected in a known Collected time.  The volume is measured in ml. Convert to cubic metres for the calculation. (divide reading by 1,000,000) Time to s t Measured Time taken to collect the known Collect volume of water, V. Temp of °C Measured The temperature of the water collected. Water Kinematic m2/s υ Measured See Table Viscosity Manometer m h1 Measured Head at inlet to test section of the pipe. The head is measured in mm. Convert to metres for the calculation. Manometer m h2 Measured Head at outlet to test section of the pipe. The head is measured in mm. Convert to metres for the calculation. Head Loss m h1 -h2 Calculated Head loss over the test section of the pipe. Flow Rate m3/s Qt Calculated Volume Collected Time to Collect Velocity mls v Calculated Fluid velocity through the pipe

Friction Factor                          f

Reynolds Number                     Re

EXPERIMENTAL PROCEDURE

Objective

To investigate the head loss due to friction in the flow of water through a pipe and to determine the associated friction factor.  Both variables are to be determined over a range of flow rates and their characteristics identified for both laminar and turbulent flows.

Method

By measurement of the pressure difference between two fixed points in a long (length = many diameters) straight tube of circular cross-section for steady flows. The range of flow rates will cover both laminar and turbulent flow regimes.

Equipment

In order to complete the demonstration we need a number of pieces of equipment.

 The F1-1O Hydraulics Bench which allows you to measure flow by timed volume collection. The F1-18 Pipe Friction Apparatus. A stopwatch to allow you to determine the flow rate of water. A thermometer. A spirit level for setting up the equipment. A measuring cylinder for measuring very low flow rates.

Technical Data

The following dimensions from the equipment are used in the appropriate calculations.  If required these values may be checked as part of the experimental procedure and replaced with your own measurements.

Length of test pipe                           L = 0.500                   m

Diameter of test pipe                       d = 0.003                   m

Theory

A basic momentum analysis of fully developed flow in a straight tube of unifom cross­ section shows that the pressure difference (Pl - P2) between two points in the tube is due to the effects of viscosity (fluid friction).  The head-loss Δh is directly proportional to the pressure difference (loss) and is given by

Δh = (Pl -P2)
ρg

and the friction factor, f, is related to the head-loss by the equation

Δh = 4fLv2
2gd

where d is the pipe diameter and, in this experiment, Δh is measured directly by a manometer which connects to two pressure tappings a distance L apart; v is the mean velocity given in terms of the volume flow rate Qt by

v = 4Qt
πd2

The theoretical result for laminar flow is

f = 16
Re

where Re = Reynolds number and is given by

Re = vd
υ

and υ is the kinematic viscosity.

Procedure - Equipment Set Up

Mount the test rig on the hydraulic bench and, with a spirit level, adjust the feet to ensure that the base plate is horizontal and, hence, the manometers are vertical.

Check with your tutor that the mercury (Hg) manometer is correctly filled;

this should not be attempted by students because Hg is a hazardous substance. Attach a Hoffman clamp to each of the two manometer connecting tubes and close them off.

Setting-up for high flow rates

The test rig outlet tube must be held by a clamp to ensure that the outflow point is firmly fixed. This should be above the bench collection tank and should allow enough space for insertion of the measuring cylinder.

Hoffman Clamp (white)                    Measuring Cylinder next to outlet pipe

Join the test rig inlet pipe to the hydraulic bench flow connector with the pump turned off.

Close the bench gate-valve, open the test rig flow control valve fully and start the pump.

Flow control valve (blue top)

Now open the gate valve, on the work bench, progressively and run the system until all air is purged.

Open the Hoffman clamps and purge any air from the two bleed points at the top of the Hg manometer.

Setting up for low flow rates (using the header tank)

Attach a Hoffman clamp to each of the two manometer connecting tubes and close them off.

With the system fully purged of air, close the bench valve, stop the pump, close the outflow valve and remove Hoffman clamps from the water manometer connections.

Water manometer

Disconnect test section supply tube and hold high to keep it filled with liquid.

Connect the bench supply tube to the header tank inflow, run the pump and open the bench valve to allow flow.  When outflow occurs from the header tank snap connector, attach the test section supply tube to it, ensuring no air is entrapped.

When outflow occurs from header tank overflow, fully open the outflow control valve.

Slowly open air vents at top of water manometer and allow air to enter until manometer levels reach a convenient height, then close the air vent.  If required, further control of levels can be achieved by use of the hand-pump to raise the manometer air pressure.

Procedure - Taking a Set of Results

Running high flow rate tests

Apply a Hoffman clamp to each of the water manometer connection tubes (essential to prevent a flow path parallel to the test section).

Close the test rig flow control valve and take a zero flow reading from the Hg manometer.

With the flow control valve fully open, measure the head loss h Hg shown by the manometer.

Determine the flow rate by timed collection and measure the temperature of the collected fluid.

The Kinematic Viscosity of Water at Atmospheric Pressure can then be determined from the table provided further on this page.

Repeat this procedure to give at least nine flow rates; the lowest to give h Hg = 30mm Hg, approximately.

Running low flow rate tests

Repeat procedure given above but using water manometer throughout.

With the flow control valve fully open, measure the head loss h shown by the manometer.

Determine the flow rate by timed collection and measure the temperature of the collected fluid.

The Kinematic Viscosity of Water at Atmospheric Pressure can then be determined from the table provided.

Obtain data for at least eight flow rates, the lowest to give h = 30mm, approximately.

Plot graphs for log f against log Re and compare with the Moody diagram.

and

Plot log i against log v to determine the relationship between head loss and velocity

This is what your results should look like

 Kinematic Viscosity of Water at Atmospheric Pressure Temperature Kinematic Viscosity       υ Temperature Kinematic Viscosity     υ (degrees C) (x10-6  m2/s) (degrees C) (x10-6  m2/s) 0 1.793 25 0.893 1 1.732 26 0.873 2 1.674 27 0.854 3 1.619 28 0.836 4 1.568 29 0.818 5 1.520 30 0.802 6 1.474 31 0.785 7 1.429 32 0.769 8 1.386 33 0.753 9 1.346 34 0.738 10 1.307 35 0.724 11 1.270 36 0.711 12 1.235 37 0.697 13 1.201 38 0.684 14 1.169 39 0.671 15 1.138 40 0.658 16 1.108 45 0.602 17 1.080 50 0.554 18 1.053 55 0.511 19 1.027 60 0.476 20 1.002 65 0.443 21 0.978 70 0.413 22 0.955 75 0.386 23 0.933 80 0.363 24 0.911 85 0.342

Eg. At 20°C the kinematic viscosity of water is 1.002 x 10-6m2/s.

 Last Edited :  30 June 2011 14:00:11