INSTRUCTIONS FOR LABORATORY EXPERIMENT IN FLUID MECHANICS VT2010 Pipe Flow: General Information: Attendance at the laboratory experiment is required for completion of the course. The experiments will be carried out at the Department of Earth Sciences, Villavägen 16, Room Dl 121. The experiment will mostly be a lab demonstration as there will not be enough time to do all the measurements. We will perform some of the measurements, but a complete set of measurements from a previous year is included below (Tables 1 and 2). Lab reports must be handed in by June 2. Hand in the report to me directly (office Dk 255 in Geocentrum), or to my mailbox outside my office (a few steps to the right), or, if in electronic form, by email to christoph.hieronymus@geo.uu.se. You may work in groups of up to 3 (hand in one report per group with all names written on it). The report should concisely answer the questions below. Please write clearly, or preferably type the report on a computer. Include graphs where appropriate. Experimental Setup: The experiment comprises measurement of the energy distribution in a pipe system and comparison with theory given in chapters 7 (Energy) and 10 (Flow in Conduits) in the course book. Static pressure is measured in manometers (tubes where the liquid is allowed to rise) and discharge is measured using a bucket, watch, and scales. The experimental setup is illustrated in Figure 1, which also indicates the pipe diameters as well as the distances between manometers and other relevant points. First, determine the discharge through the pipe system. Measure the weight of the empty bucket on the scales. Thereafter, let the bucket fill with water at the downstream end of the pipe system for a specific time. By taking the water density as 1000 kg/m 3 you can calculate the discharge. Assuming turbulent flow, you can then also find the average velocities within the three pipes. Measure the static pressure at all the pressure outlets. This is done on the board with the eight manometers using a point meter. The distances between the pressure outlets are given in Figure 1. 1
1 2 3 4 5 6 7 8 Manometer Tubes Reservoir 1 Reservoir 2 Inflow Pipe 1: Diameter = 80 mm Pipe 2: Diameter = 19 mm Pipe 3: Diameter = 40 mm Outflow Distances in mm 150 210 47 50 670 57 48 292 66 FIGURE 1: Water flow through three pipes of different diameter. Pressure is measured as height of water column in manometer tubes. Measurements to be used for Calculations: As indicated earlier, we will not have time in the lab to perform a complete set of measurements. Instead, the necessary measurements are given below: Experiment A Experiment B Discharge Q 0.000350 m 3 /s 0.000212 m 3 /s TABLE 1: Discharge for experiments A and B. Report: 1. Briefly describe the methods and how the experiment was done. Discuss problems and how they were dealt with. 2. From the discharge Q and the pipe diameters, calculate the velocity and the corresponding velocity head at each manometer (the velocity head is the kinetic energy expressed in terms of height; it is the difference between the hydraulic grade line HGL and the energy grade line EGL). 3. Construct a diagram of the energy distribution (EGL) for the whole pipe system using the measured results. You may assume that the EGL changes linearly in between the points where you have data. 2
Experiment A Experiment B Point Pressure Height (cm) Pressure Height (cm) 1 37.50 38.05 2 37.40 38.05 3 37.40 38.05 4 28.15 35.20 5 21.95 33.00 6 21.80 32.95 7 23.90 33.55 8 23.90 33.50 TABLE 2: Height of water column at each manometer for experiments A and B. 4. (a) Calculate the resistance coefficient f for each pipe section. Explain how you chose the points used in your calculations. (b) From the Moody diagram, find the relative roughness k s /D and calculate the equivalent sand grain roughness k s. How do the values for each pipe section compare? Is this different from what is expected? If so, how? 5. (a) What are the head losses h L for the inlet, the contraction, the expansion, and the outlet? Again, how did you choose the locations used in your calculation? (b) The loss for each transition should be given by an equation of the form h L = KV 2 2g (1) The details (e.g., is V the velocity before or after the transition?) are given in table 10.3 in the book. How do your calculations compare with the theory (i.e., how do they compare with the values in table 10.3)? 3
FIGURE 2: Table 10.3 4 from the book.
5 FIGURE 3: Top: Moody diagram; Figure 10.8 from the book. Bottom: Table 10.2 from book.