PipeFriction-v9 - MEC616 PF – Pipe Friction Lab...

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Unformatted text preview: MEC616 PF – Pipe Friction Lab 2011-JAN-15 1. Objective To determine the experimental pipe friction factor, f, for a range of pipe flow rates using four dif­ ferent diameter smooth copper pipes and compare the experimental values to theoretical results. 2. Introduction 2.1 Measuring the pipe frictional headloss, hf The Bernoulli energy equation for steady, incompressible flow of a real fluid in a pipe between two points 1 and 2 (see Figure 1) may be written as: p1 1 V 2 p V2 1 z 1= 2 2 2 z 2 h f 2g 2g where p = pressure, = g = fluid weight density, = fluid density, = kinetic energy cor­ rection factor, g = gravity, V = average flow velocity, z = elevation, and h f = head loss due to fluid friction. Rearranging and solving for h f yields: h f= p1 p V 2 − 2 V 2 2 z1 − 2 z 2 1 1 2g For a constant diameter pipe, D1 = D2, therefore V1 = V2 and 1 = 2 . Thus the head loss is giv­ en by: hf= p1 p z1 − 2 z2 Note that neither V or are required in the above formula. For some applications may be required. Typical values are: =1 for uniform flow, = 2 for laminar flow, and =1.06 for turbulent flow. For most turbulent flow engineering applications use ≈ 1 . The term p / z represents piezometric head which can be read by a simple piezometric tube or piezometer (see Figure 2). Two piezometers may be combined together to form an inver­ ted U-tube manometer which reads the difference in piezometric head between points 1 and 2 (see Figure 3). Thus: h m= p1 p z1 − 2 z2 = h f h m≡ h f This means that the head loss, hf, can be read directly from the U-tube manometer. PF - 1 MEC616 PF – Pipe Friction Lab 2011-JAN-15 2.2 Experimental equation for the friction factor, f The head loss between points 1 and 2 may be predicted by the Darcy-Weisbach equation: f L V2 h f= D 2g where f = friction factor (dimensionless), L = pipe length between points 1 and 2, D = internal pipe diameter, and V = average pipe velocity. Note that V =Q / A where Q = measured flow rate, and A= D / 2 2 for a circular pipe. Rearranging and solving for f yields the experi­ mental value (obtained as a result of experimental measurements): f= 2g Dhf LV2 The friction factor, f, is a function of the pipe surface relative roughness, / D , and Reynolds V D number, Re D = where = absolute surface roughness, = fluid density, and = fluid absolute viscosity, which is a function of the fluid temperature. 2.3 Theoretical equations for the friction factor, f For laminar flows, where Re D 2300, use f =64 / Re D . For turbulent flows, where Re D 2300, use the Blasius smooth pipe = 0 equation given 0.316 by f = 0.25 which is valid over the range 4000 Re D 105 . It is also possible to use the ReD Haaland formula given by { −2 [ ]} 6.9 f = −0.782 ln Re D 3.7 D 1.11 with =0 . 2.4 The Moody chart and variation of f versus ReD Examine the supplied Moody chart which contains the friction factor, f , on the vertical axis and the Reynolds number, ReD ,on the horizontal axis. The chart scales are presented in log-log format meaning that both scales are in log format. This is so a large range of data can be plotted, particularly on the horizontal ReD axis. Note that there is a single straight line in the laminar re­ gion as a result of using log-log scales. For turbulent smooth pipe flows there is a single curved line. In this experiment we expect the experimental (calculated) friction factor, f , to follow the same theoretical smooth pipe curves as presented on the Moody chart. PF - 2 MEC616 PF – Pipe Friction Lab 2011-JAN-15 Figure 1. Pipe Head Loss and Bernoulli Energy Equation Figure 2. Piezometric Tubes and Head Loss Figure 3. Inverted U-tube Manometer PF - 3 MEC616 PF – Pipe Friction Lab 2011-JAN-15 3. Apparatus The apparatus consists of four smooth copper pipes which can be selected one-at-a-time using flow control valves at the discharge end of the pipe. The available pipe diameters are: 25.81 mm, 19.46 mm, 13.11 mm, and 6.96 mm. An inverted U-tube manometer is used to measure the pres­ sure drop across the pipe length which is 2.438 m and paired rotary valves are used to switch the manometer across the desired pipe of interest. A small centrifugal pump draws water out of a small supply tank and then discharges the water through two selectable flow rotameters where only one is used at any one time. The largest sized rotameter is used to measure high flows while the smaller rotameter is used for low flows. For very low flows it may be necessary to collect a known volume of water over a short time period and then calculate the flow rate. A measured container is provided for this purpose. After the water passes through the rotameters it enters the pipe assembly. To use the 25.81 mm pipe, for example, it's flow control valve at the far end is opened while all the other valves are closed. A pressure-regulating valve (PRV) is used in the pump discharge side to help control the outlet pressure by averaging out large pressure variations. It attempts to keep the inlet pressure to the pipes constant but does so only approximately. The flow rate through the pipe is adjusted us­ ing the flow control valve located at the discharge end of the pipe. 4. Procedure 1. Turn on the pump and open all four flow control valves for a few moments to clear the air out of the system and all four pipes. 2. Leave the valve for the largest pipe (25.81 mm) open and close all the other three valves. 3. Use the manometer's paired rotary selector valves to switch the manometer across the largest pipe (25.81 mm) and make sure all the other manometer selector valves are closed tightly. Note: The manometer valves are colour coded in pairs of blue, green, yellow, and white. 4. Use the flow control valve at the discharge end of the pipe to adjust the flow rate through the pipe to give the highest differential reading across the manometer. Do not exceed the rotameter's maximum flow rate and do not let the manometer water levels go over the top ends of the manometer tubes near the ceiling. Use the ladder to obtain readings at the top. 5. Record the pipe flow rate and manometer readings using inch readings on the supplied ruler. Note: For low flow rates use the measured container provided for this purpose and collect water at the pipe discharge end over a known time period. 6. Adjust the flow control valve to give about ½ the the maximum manometer differential. Repeat step 5. 7. Adjust the flow control valve to give about a one inch reading on the manometer. Repeat step 5. 8. Close the pipe's manometer valves and open the next smaller pipe's manometer valves. 9. Close the pipe's flow valve and open the next smaller pipe's flow valve. PF - 4 MEC616 PF – Pipe Friction Lab 2011-JAN-15 10. Repeat steps 4 to 9 for the 19.46-mm-diameter pipe. 11. Repeat steps 4 to 9 for the 13.11-mm-diameter pipe. 12. Repeat steps 4 to 7 for the 6.96-mm-diameter pipe. 13. To shutdown the apparatus, close all the manometer valves, and all the flow control valves. Finally shutdown the pump. 5. Report The repetitive calculations for this lab should be done on a spreadsheet and the results plotted on a spreadsheet graph. A sample spreadsheet demonstrating how to setup a log-log graph is avail­ able on the course web site. 1. Show a complete set of sample calculations for the largest pipe diameter and highest flow rate. Place all the other results in a summary table. 2. For each pipe, calculate the experimental friction factor, f, (see Section 2.2) and prepare a spreadsheet graph of f versus the pipe Reynolds number, ReD (f on y-axis and ReD on xaxis). This graph must use log-log scales (see the sample Moody chart and sample spreadsheet on course web site). Use different symbols to help identify curves based on pipe diameter. NOTE: It is highly recommended that you first plot your results by hand on the sample Moody chart just to get an idea of what the graph should look like. Then you can prepare a spreadsheet graph version. 3. On the same graph, include plots of theoretical friction factor, f, (see Section 2.3) versus ReD. 4. Indicate laminar and turbulent regions on the graph. 5. Discuss your graphical results. Comment on why some of the plotted points are above the smooth pipe curve. Are the pipes smooth as claimed? What can be said of points be­ low the smooth pipe curve? PF - 5 MEC616 PF – Pipe Friction Lab Lab Group: Date: Barometer: 2011-JAN-15 Time: Room Temperature: Pipe Material: smooth copper Pipe Length: 2.438 m Pipe Condition: corroded Water Temperature: Water Density, : Water Viscosity, : OBSERVATIONS A B C D E F Flow Measurement G H Head loss Pipe Dia­ meter Rotameter D Q Volume Time Q left, h1 right, h2 hm=h1-h2 (mm) (L/min) (L) (sec) (L/sec) (inches) (inches) (inches) Collection Method 25.81 19.46 13.11 6.96 PF - 6 U-tube Manometer Readings PF - 7 ...
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This note was uploaded on 02/20/2011 for the course MEC 411 taught by Professor Shudong during the Winter '11 term at Ryerson.

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