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Fluid Friction Measurements

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1. Objective: Ø To determine the head loss. Ø To determine the head loss associated with flow of water through standard fittings used in plumbing installations. Ø To determine the relationship between friction coefficient and Reynolds’ number for flow of water through a pipe having a roughened bore. Ø To determine the water velocity by using flow measurement devices. 2. Equipment:

The test pipes and fittings are mounted on a tubular frame carried castors. Water is fed in from the hydraulics bench via the barbed connector (1), and is fed back into the volumetric tank via the exit tube (23). · · · · · · · · · · · · · · An in-line strainer (2) An artificially roughened pipe (7) Smooth bore pipes of 4 different diameter (8), (9), (10) and (11) A long radius 90° bend (6) A short radius 90° bend (15) A 45° “Y” (4) A 45° elbow (5) A 90° “T” (13) A 90° mitre (14) A 90° elbow (22) A sudden contraction (3) A sudden enlargement (16) A pipe section made of clear acrylic with a Pitot static tube (17) A Venturi made of clear acrylic (18)

An orifice meter made of clear acrylic (19) A ball valve (12) A globe valve (20) A gate valve (21)

3. Theory: 3.1 Fluid Friction in a Smooth Bore Pipe Two types of flow may exist in a pipe: 1) Laminar flow at low velocities where h ∝ V 2) Turbulent flow at higher velocities where h ∝ V n where h the head loss due to friction, V the fluid velocity, and 1.7 < n < 2.0. These two types of flow are separated by a transition phase where no definite relationship between h
and V exists. Laminar

Transient

Turbulent

The friction factor, λ , is defined as,

∆h =
where
∆h L D V

λ⋅L V2 ⋅ D 2⋅ g

the head loss [m] the length between the tapping [m] the diameter of the pipe [m] the mean velocity [m/s]

The Reynolds’ number, Re, can be found using the following equation: ρ ⋅V ⋅ D Re = µ where µ dynamic viscosity (1.15 x 10 −3 Ns/m at 15°C) ρ the density (999 kg/m 3 at 15 o C)

For a pipe with a circular cross sectional area; Laminar Flow Re < 2000 Transitional Flow 2000 < Re < 4000 Turbulent Flow Re > 4000 Having established the value of Reynolds’ number for flow in the pipe, the value of f may be determined using a Moody diagram, a simplified version of which is shown below.

3.2 Head Loss Due to Pipe Fittings The local loss can be estimated as follows;

∆h (mH 2 O ) =
where K V g

K ⋅ V2 2⋅g

the fitting “loss factor”, the mean velocity of water through the pipe [m/s] the acceleration due to gravity [m/s2].

The loss factor is dimensionless and is a function of Reynolds number. In the standard literature, the loss factor is not usually correlated with Re and roughness but simply with its geometry and the diameter of the pipe, implicitly assuming that the pipe flow is turbulent.

3.3 Flow Measurement Orifice plate, venturi and a pitot tube will be used to measure the water flow rate. For an orifice plate or Venturi, the flow rate and differential head are related by Bernoulli’s equation with a discharge coefficient added to account for losses; 2 ⋅ g ⋅ ∆h Q = C d ⋅ Ao ⋅ ( Ao A1 )2 − 1 where Q the flow rate [m³/s], Cd the discharge coefficient (Cd = 0.98 for a Venturi, 0.62 for an orifice plate), A0 the area of the throat or orifice in m² (d0 = 14mm for the Venturi, 20mm for the orifice plate), A1 the area of the pipe upstream m² (d1 = 24mm), the differential head of water [m], ∆h g the acceleration due to gravity [m/s²]. For a Pitot tube, the differential head measured between the total and static tappings is equivalent to the velocity head of the fluid; V2 = h1 − h2 2⋅ g

V = 2 ⋅ g ⋅ (h1 − h2 )
where
V (h1 − h2 ) g

the mean velocity of water through the pipe [m/s], the differential head of water [m], the acceleration due to gravity [m/s²].

3.4 Fluid Friction in a Roughened Pipe Use the same theory explained in 3.1.

4. Procedure: 4.1. Fluid Friction in a Smooth Bore Pipe Prime the pipe network with water. Open and close the appropriate valves to obtain flow of water through the required test pipe. View the diagram screen on the PC. Measure the internal diameter of the test pipe sample and enter the result in the appropriate box on the diagram screen. Adjust the control valve on the F1-10 to give the desired flow rate through the apparatus, as displayed on the PC. It is usually best to start the experiment at low flows and work up to higher flows. Use a Moody diagram to estimate the pipe friction factor from the Reynolds’ number. Enter the friction factor on the diagram screen. Note: This stage of the calculations can be carried out after the results have been collected if preferred. When the readings on the PC are stable, click ‘GO’ to take a sample. Repeat this for a range of flow rates between minimum and maximum. In normal operation, the software should be set to record using the electronic sensors.

However, in order to measure very low flow rates it may be necessary to measure the flow rate using a measuring cylinder and stopwatch. In this case the software should be set to record the flow volumetrically, and the volume and time data entered in the appropriate boxes on the diagram screen. 4.2. Head Loss Due to Pipe Fittings Prime the pipe network with water. Open and close the appropriate valves to obtain flow of water through the required test pipe. Connect the pressure sensors to the appropriate tappings for the fitting you wish to investigate. View the diagram screen on the PC. Measure the internal diameter of the largest test pipe sample and enter the result in the appropriate box on the diagram screen. Select the fitting under test from the list. If testing a valve, enter the estimated position of the valve. Adjust the control valve on the F1-10 to give the desired flow rate through the apparatus, as displayed on the PC. It is usually best to start the experiment at low flows and work up to higher flows.

When the readings on the PC are stable, click ‘GO’ to take a sample. Repeat this for a range of flow rates between minimum and maximum In normal operation, the software should be set to record using the electronic sensors. However, in order to measure very low flow rates it may be necessary to measure the flow rate using a measuring cylinder and stopwatch. In this case the software should be set to record the flow volumetrically, and the volume and time data entered in the appropriate boxes on the diagram screen. 4.3 Flow Measurement 4.3.1. Venturi and Orifice Plate: Prime the pipe network with water. Open the appropriate valves to obtain flow of water through the flow meters. View the diagram screen on the PC. Adjust the control valve on the F1-10 to give the desired flow rate through the apparatus, as displayed on the PC. It is usually best to start the experiment at low flows and work up to higher flows. When the readings on the PC are stable, click ‘GO’ to take a sample. Repeat this for a range of flow rates between minimum and maximum.

In normal operation the software should be set to record using the electronic sensors. However, in order to measure very low flow rates it may be necessary to measure the flow rate using a measuring cylinder and stopwatch. In this case the software should be set to record the flow volumetrically, and the volume and time data entered in the appropriate boxes on the diagram screen. Note: To measure the differential head developed by the orifice plate or Venturi (for the purpose of flow measurement) connect the probes to the two tappings on the flow meter body, upstream and at the throat (do not use the downstream tapping in the pipe). To measure the head loss across the orifice plate or Venturi connect the probes to the upstream tapping on the flow meter body and the tapping in the pipe downstream of the device (do not use the throat tapping).

4.3.2. Pitot Tube: Ensure that the nose of the Pitot tube is directly facing the direction of flow and located on the centre line of the pipe. Adjust the control valve on the F1-10 to give the desired flow rate through the apparatus, as displayed on the PC. It is usually best to start the experiment at low flows and work up to higher flows. When the readings on the PC are stable, click ‘GO’ to take a sample. Repeat this for a range of flow rates between minimum and maximum. In normal operation the software should be set to record using the electronic sensors. However, in order to measure very low flow rates it may be necessary to measure the flow rate using a measuring cylinder and stopwatch. In this case the software should be set to record the flow volumetrically, and the volume and time data entered in the appropriate boxes on the diagram screen.

At the maximum flow setting unscrew the sealing gland sufficiently to allow the Pitot tube to move. Traverse the tube across the diameter of the pipe and observe the change in differential head. Estimate the average reading obtained and compare this with the maximum reading at the centre of the pipe. Note: The Pitot tube is included for the purpose of demonstration only. The small differential head produced by the Pitot tube means that it should only be used in applications where high velocity is to be measured. Accuracy of measurement on the C6 will be poor because of the low water velocity. 4.4 Fluid in a Roughened Pipe Prime the pipe network with water. Open and close the appropriate valves to obtain flow of water through the roughened pipe. Estimate the nominal internal diameter of the test pipe sample using a Vernier caliper (not supplied). Estimate the roughness factor k/d. Enter the result in the appropriate box on the diagram screen. Load the C6-304 software on the PC and view the diagram screen.

Adjust the control valve on the F1-10 to give the desired flow rate through the apparatus, as displayed on the PC. It is usually best to start the experiment at low flows and work up to higher flows. When the readings on the PC are stable, click ‘GO’ to take a sample. Repeat this for a range of flow rates between minimum and maximum. In normal operation the software should be set to record using the electronic sensors. However, in order to measure very low flow rates it may be necessary to measure the flow rate using a measuring cylinder and stopwatch. In this case the software should be set to record the flow volumetrically, and the volume and time data entered in the appropriate boxes on the diagram screen.

5. Analysis and Discussion For 4.1: • All readings will be stored by the software and can be viewed in tabular or graphical formats. • Plot a graph of h versus V for each size of pipe. Identify the laminar, transition and turbulent zones on the graphs. • Confirm that the graph is a straight line for the zone of laminar flow h ∝ V . • Plot a graph of log h versus log u for each size of pipe. Confirm that the graph is a straight line for the zone of turbulent flow h ∝ V n . Determine the slope of the straight line to find n. • Compare the values of head loss determined by calculation with those measured using the manometer. • Confirm that the head loss can be predicted using the pipe friction equation provided the velocity of the fluid and the pipe dimensions are known.

For 4.2: • Confirm that K is a constant for each fitting over the range of test flow rates. • Plot a graph of K factor against valve opening for each test valve. Note the differences in characteristic. For 4.3: 4.3.1: • Compare each calculated flow rate with the actual flow rate measured. • Compare the head loss across the Venturi and orifice at the same flow rate. • Compare the differential head across the Venturi and orifice plate at the same flow rate. • Comment on the differences in the two devices and their suitability for flow measurement. • Use the theory covered by 3.1 to determine the K factor for the two flow meters. 4.3.2: • Compare each calculated velocity with the measured velocity (determined from the volume flow rate and cross sectional area of the pipe). • What is the effect of the velocity profile on the results obtained? For 4.4: • • Plot a graph of pipe friction coefficient versus Reynolds’ number (log scale). Note the difference from the smooth pipe curve on the Moody diagram when the flow is turbulent.

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