Reservoir A sits at an elevation 50 meters below Reservoir B, with Reservoirs A

Question

Reservoir A sits at an elevation 50 meters below Reservoir B, with Reservoirs A and B both open to the atmosphere. They are connected by a pipeline that is 160 meters long, with entrance and exit of the pipe as square-edged. The pipe is a smooth riveted-steel pipe and 70 centimeters in diameter, with a fully-open lift-type check valve. Determine the overall efficiency of the pump system if the power requirement for the motor is 850 kilowatts, with the discharge design calling for 0.90 cubic meters per second at 20 degrees Celsius.

Explanation / Answer

Overall efiiciency of the pump = Density of water x Discharge x g X H / Total power input to shaft

= 1000 x 0.90 x 9.81 x H / P

Power input = 850 Kw

Applying energy equation between two reservoirs surfaces

P1 / gama + V1^2 / 2 x g + Z1 = P2 /gama + V2^2 /2xg +Z2 + V^2 / 2 x g

Pressusre at atmospheric at A = Presussure at atmospheric at B = 0

P1 = P2 = 0 and Velocity at A V1 = V2 = 0

datum head Z1 - Z2 = 50 mtrs

Total head avilable H = 50 + V^2 /2 x 9.81

V = Q /A

Q = 0.90 m^3 /Sec given in the problem

Area of cross section A = pi /4 X d ^2 = 3.14 /4 x 0.70^2

V = velocity = 2.33m/sec

H = 50 + 2.33^2 / 2x 9.81

   = 50 + 0.279

   = 50.279 m

Overall efficiency = 1000 x 0.90 x 9.81 x 50.279 / 850000

= 52.2 %

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