Question

5) A 6-km cast-iron (new) pipeline conveys 0.32 m/s of water at 30°C. If the pipe diameter is 30 cm, compare the head loss calculated (a) Darcy-Weibach equation (f = 0.0195), (b) the Hazen- William equation (Chw = 130), and (c) the Manning equation (n=0.011). Use Excel. (Max. 15 Points) 6) Pipes AB and CF in figure below have a diameter of 48 in possess a Hazen-Williams coefficient factor of 100 and carry a discharge of 120 ft/s. The length of AB is 2,000 ft and that of CF is 1,800 ft. Branch 1 is 1,800 ft long and has a diameter of 36 in and Chw of 100. Brach 2 has a length of 1,500 ft, a diameter of 24 in, and a Chw of 100. (Max. 60 Points) a) Determine the total head loss resulting from friction between points A and F, and b) Determine the discharge in each of the two branches (1 and 2).

Answer 1

Since there are some equations, I preferred a handwritten note. Results are tabulated in the answer for your easier understanding. Hope that it is clear for you and it really helped you.

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Given Data length or = 6 km = 60oom Discharge, Q = 0.32 m/s Pipe diametes, D= 30 cm = 0. 3m Velocity of flow, va 0:32a T/4x0.32 - 4.53 m)s To find out Head loss He.. . a) Dancy werbach equation - The darcy, weibach formula is H = f2 va He agd Criven f= 0.0195 8-9.81 ml sa il H, 20.01958 6ooox 4.522 2x9.810.3 = 407.9 m Head loss wsing Dascy. Weibach equation = 407.9m. b) lazen-William equation The equation is given by, V=0.8SCHW 20.6360.54 Whose Chw=130, Ryhydraulic mean depth of hydraulic radices 03007519. slope of energy line = He s Substituting, 4.53=0.85x130x(0.015706320.54 S=0.0553 ce Hy0.0553 . Hiz0.0553x6000 = 332.33 m Head loss using Hazen Williams Equation -332.33 mg () Mannings Equation mannings formula is given by Whose, n=0.011, Ranyaaulic radius = 2020.0156 syslope of hydraulic grade line ..075m CO substituting, 4.532 (0.01573% 3* 0.011 S-0.0785 h 0.0785 He = 471.03m Hence Head loss using manning's Equation) =471.03

I didn't do it by using excel as I can not upload the excel worksheet directly. So I preferred this handwritten note.