A horizontal pipe line 40m long is connected to a water tank at one end and discharges freely into the atmosphere at the other end. For the first 25m of its length from the tank, the pipe is 150mm diameter and its diameter is suddenly enlarged to 300mm. The height of water level in the tank is 8m above the center of the pipe. Considering all losses of head which occur, determine the rate of flow. Take f = .01 for both sections of the pipe
Answers
The rate of flow is 78.67 litres/s.
Explanation:
Length of pipe = 40 m
Length of 1st pipe = 25 m
Diameter of 1st pipe = 150 mm = 0.15 m
Length of second pipe = 40 - 25 = 15 m
Diameter of second pipe = 300 mm = 0.3 m
Height pf water = 8 m
Co-efficient of friction = 0.01
Hf2 = head loss due to friction in pipe 2 = 4 x f x l2 x V2^2/ d2 x 2 g
BY using equation of continuity:
A1 V1 = A2 V2
V1 = A2V2 / A1 = π/4 d2^2 x V2/ π/4 d1^2 = (d2^2 / d1^2) x V2 = 4V2
Substituting the value of v in losses we get.
Hf2 = 4 x 0.01 x 15 x V2^2 / 0.3 x 2g = 2.0 x V2^2 / 2g
Now substituting the value of these losses in equation we get:
V2 = √ 8.0 x 2 x g / 126.67 = √1.2391 = 1.113 m/s
Rate of flow = A2 x V2 = π/4 (0.3)^2 x 1.113 = 0.07867 m^3/s = 78.67 litres / s.
Thus the rate of flow is 78.67 litres/s.
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