CE440_HW#2_SOLUTION_2024

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California Polytechnic State University, San Luis Obispo *

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440

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Mechanical Engineering

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Feb 20, 2024

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1 CE 440 Hydraulic Systems Engineering H O M E W O R K # 2 Total 250 points Winter 2024 State any assumption made during solution. Use of MS Excel is encouraged. Submit Problems as a Group . F eel free to discuss with others. 1. Mapped below is a pipe network. Use Hardy-Cross method to correct the initial flowrates and show the adjusted discharges after one iteration. Pump curve is given as 100 1 . 0 1 . 2 2 + = Q Q E p . Given f = 0.02 for all pipes. (15+20+15 points) 0.06-200-0.3 0.06-200-0.3
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3 +0.098 +0.098 +0.098 1.959 0.104 -0.008 - - +0.098
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4 2. Diagrammed below is a simple pipe network. Use Hardy-Cross method to correct the initial flowrates/ directions and show the adjusted discharges after one iteration. Use Hazen-Williams method for head loss. (10+10+10 points) Dem A = demand at node A 5 cfs 1.7 cfs = 1.6 cfs
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6 3. Drawn on the next page is a pipeline between a pair of reservoirs with 2 possible pump locations (shown as green and pink, respectively) along the pipeline to move water from the lower to the upper reservoir. The pipe is 8 inch diameter and built in 3 sections. The first section shown in yellow has a roughness diameter of 0.05 inches; the second and third sections (white and orange) have roughness diameters of 0.02 and 0.10 inches, respectively. (5+10+10+5 points) a. If the flow in the pipe is 0.85 cfs, what must be the head input into the flow by the pump? b. Draw the HGL and EGL on the scale drawing for each pump location. c. What are the maximum and minimum pressures in the flow for each pump location? d. Only one pump location will be selected. Which location do you suggest and why? Hint: Please study the extra material posted on PolyLearn on HGL and EGL if you need help with problem #3
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8 (b)
9 I have ignored the velocity head as it is small compared to the other terms, but if you have included that you are correct. (130-150) -20 -1438.5 psf (130-150) +1669.2 psf -20
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10 Submit Problems 4 and 5 as a group . State any assumption made during solution. Use of MS Excel is encouraged. 4. Determine flowrates in each of the pipes in the pipe network shown below. Solve using Hardy-Cross method and Hazen-Williams equation. Assume all pipes are 20- year old Cast Iron with C = 100. Assume the pipe loop is laid horizontally. Use the given initial assumptions for flow rates. (10+20+20 points) Pipe Section Pipe Length (ft) Pipe Diameter (in) BC 4921 18 CD 3281 16 DA 3609 12 AB 2625 10 Also find out the pressures at other nodes given the pressure at C is 20890 psf.
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13 5. Use the Hardy Cross method to analyze pipe flows and head losses in the network shown below. Neglect minor losses and assume that the friction factor f is 0.015 in all the pipes. (15+60+15 points) (a) Compute the coefficient K for the head loss formulation ( h L = KQ 2 ) for each pipe section. (b) Compute the flow rate (in cfs) for each pipe segment using the Hardy Cross method (Note: You do not need to revise the f as you correct initial flowrates). (c) Determine the pressure (in psi) at point A required to maintain a minimum pressure of 50 psi at all other nodes in the network assuming the elevation at each node is the same. Pipe # AB AC BC BD CE DE Initial Q (cfs) 2 1.5 1 1 1.5 0.5 Length (ft) 7500 4500 2000 3000 3000 2000 Diameter (in) 12 10 8 8 8 8 Area (sq.ft) 0.7854 0.5454 0.3491 0.3491 0.3491 0.3491 f 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 K 2.8319 4.2281 5.7347 8.6020 8.6020 5.7347
14 Corrected Qs Iteration # Q1 Q2 AB AC BC BD CE DE 1 0.2128 -0.2976 1.7872 1.7128 0.4896 1.2976 1.2024 0.2024 2 -0.0656 0.0086 1.8528 1.6472 0.5638 1.2890 1.2110 0.2110 3 0.0024 -0.0077 1.8504 1.6496 0.5537 1.2967 1.2033 0.2033 4 -0.0016 0.0003 1.8521 1.6479 0.5556 1.2964 1.2036 0.2036 5 0.0001 -0.0002 1.8520 1.6480 0.5553 1.2966 1.2034 0.2034 Final Discharges Pipe # AB AC BC BD CE DE Headloss (ft) 9.713 11.483 1.769 14.462 12.456 0.237 V (ft/s) 2.358 3.022 1.591 3.715 3.447 0.583