Question

Example 9.4 A pipeline ABC 180 m long, is laid on an upward slope of 1 in 60. The length of the portion AB is 90 m and its diameter is 0.15 m. At B the pipe section suddenly enlarges to 0.30 m diameter and remains so for the remainder of its length BC, 90 m. A flow of 50 litres per second is pumped into the pipe at its lower end A and is discharged at the upper end C into a closed tank. The pressure at the supply end A is 137.34 kN/m2. Sketch (a) the total energy line, (b) the hydraulic grade line and also find the pressure at the discharge end C. Take f = 0.02.

Answer 1

solution qom length of pipe ABC L=180m slop of 2 1:60 length of AB length of BC 2 gom diameter of pipe das = 0.15m diameter of pipe dbc = 0.30m OA = soxio Pressure at APA 137.34 kN/m2 friction factor f = 0.02 flow rate -3 mis Velocity of pipe in AB V = AI V = soxlox 4 = 2.829umis TX 0.152 velocity of pipe in Be V2 = OIA2 V2 = sox 4x10 IT X 0.80² - 0.707 mis Appley Bernoullis equation between A unde PA 2 VA + ZA Pc + Vez 38 2g + Zet hic eg zy

Total loss from A to C will be loss in AB and BC major loss in friction AB hf. zgd, hfi = 440.02 X 90 X 2.829 4f Liv, 2 - 19.82m 2x 9.81% (0.15) hf = 18.82m = 19.52m major loss in BC hfz = 4 f L₂ V22 zydz nta 4x0.02 X 90 X 0.707 =0.6llum. 2 x 9.81 X 0.30 = hfa = 0.6llum hfi = 19.52m. loss of head due to enlargment of B (V-V2)2 29 he (2.829 -0.707) = = 0.2295m 2x9.81 he = 0.2295m. taking datem at Za zo 3 Zc = x Total length = 1 xX80 = 3m. for

+ substuting all values in Bernoull's egn РА NAZ + ZAZ Pc 39 29 + Zc+ hf, then the sg zej 137.34 t 2 2.824 9.81 2x9.81 + Vez 0.7072 Pc fg + +3+19.57+0.6114 2x9.81 - 14to.4064 Pc + 23.1568 eg PC - 85.84 kN/m2 2

Heydrulic and Energy groolient line. A 0.406m hfi = 19msom B HELL TEL 쨩 0.025 m2 V 2 EA = 14. 406um E ght=0.6llum. 14 Htank c B A Total Energy at A = VA 2 PA я ZA + zeg (T.E)A - 14+0.4064 = 14.4o6um. Total Energy at B = Total Emery A - hfi = 14.4064-19.57 = -5.1636m VC = 0.025mm. zg