Experiment 2: Flows in Pipe Networks Introduction The purpose of this experiment is to examine the flow characteristics in series and parallel pipe networks. Students will measure the major headloss along each network under different flow rates. Data will be used to determine the friction factor for each flow, and to confirm the power law relationship between flow and headloss given by the Darcy-Weisbach Equation. Each student should analyze the data collected and upload a completed worksheet in Canvas before the deadline. Theory Major headlosses along a pipe, resulting from viscous effects, are a function of the flow and properties of the pipe wall. They can be described by the Darcy-Wiesbach Equation: h₁₂ = f = IV 2 D 2g Which, when substituting flow rate, becomes: h₁ = f 8/Q2 gr²D5 (Equation 1) (Equation 2) f Where is the friction factor, / is the length of the pipe section, D is the pipe diameter, Q is flow rate, and g is the acceleration due to gravity. Often pipes are connected in series or parallel configurations (see page 455 in your book), each of which has a unique flow and headloss characteristics. Consider a system with n number of pipes, the discharge and headloss relationships among the pipes for a parallel system are: Qtotal = [Q i=1 hLTotal = h₁₁ = h₁₁+1 = =h₁₁ (Equation 3a & 3b) And a series system: 1 h L total = Σημ i=1 Qtotal = Q₁ = Qi+1 = ... =Qn (Equation 4a & 4b) Notice that the behavior of each system is unique. For example, measuring the discharge in one pipe is sufficient to characterize the flow through the other pipes in a series system, but the same is not true for a parallel configuration. The latter requires an iterative method using the moody diagram and assumed friction factor values. Apparatus This experiment will be conducted using the Pipe Network Apparatus (Figure 1). Flow rate is controlled with the main valve and the pressure drop along each pipe section is measured using a manometer attached at the ends of each pipe. Recall that for a constant cross section the velocity head is also constant. Therefore, in a horizontal pipe the energy equation equates the measured pressure drop to the headloss: P₁-P₂ γ = h₁ 2 (Equation 5) Reservoir Pump Flow control valve 66" test pipes Figure 1. Pipe Network Apparatus schematic. Blue triangles indicate locations of pressure measurements for each pipe. 3 The pipe network can be configured into a series or parallel flow system as shown in Figure 2. Parallel pipes network Q-Q1+Q2+Q3 HL-HL1-HL2-HL3 Series pipes network HL-HL1 HL2 HL3 Q=Q1=Q2=Q3 d1-0.99" Q1 d1-0.99" Q1-> d2-0.77" d2-0.77" 02->>> Q 02 Q d3-0.54" " 03->>> L=64" Hal Hb pressure head at pressure head at point (a) point (b) d3-0.54" 03->>> L=64" Ha Hb pressure head at pressure head at point (a) point (b) Figure 2. Pipe network apparatus flow patterns for parallel and series pipe configurations. Procedure 1. Record the inner diameter and lengths of the top three pipes using the calipers and tape measure. Turn on the pump. 2. Configure the system for either parallel or series pipe flow. 3. Adjust the flow rate to the maximum flow and record the pressure drop across each pipe length. a. Repeat for a total of 5 flow rates. 4. Reconfigure the system (series, parallel) and repeat step 3. 5. Turn off the pump. Hydraulics Lab 2 Worksheet Name: Please write answers to the following questions in the space below or on separate paper. Attach tables and figures at the end. Turn in the completed packet as a single pdf file uploaded to Canvas by the deadline. 1. Compute the Reynolds number and friction factor, f, for the largest pipe under all flow rates for each configuration (series and parallel) using the Moody diagram (assume an absolute roughness of 0.0015mm). Report calculations in a table and attach it to this worksheet. Is the flow turbulent? 2. Define relative roughness and describe functionally how it relates to major headlosses. 3. Attach two figures that plot the headloss versus flow rate for each configuration and confirm the power law relationship (h₁ cc BQ") between the two given by Equation 2. Use the trendline feature in excel or nlinfit command in MATLAB (i.e. determine m). Do your results match Equation 2? 5