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A geothermal pump is used to pump brine whose density is 1050 kg/m3 at a rate of 0.3 m3/s from a depth of 200 m. For a pump efficiency of 90 percent, determine the required power input to the pump. Disregard frictional losses in the pipes, and assume the geothermal water at 200 m depth to be exposed to the atmosphere.

Answer :

Answer:

Input power of the geothermal power will be 686000 J

Explanation:

We have given density of brine [tex]\rho =1050kg/m^3[/tex]

Rate at which brine is pumped [tex]V=0.3m^3/sec[/tex]

So mass of the pumped per second

Mass = volume × density = [tex]1050\times 0.3=315[/tex] kg/sec

Acceleration due to gravity [tex]g=9.8m/sec^2[/tex]

Depth h = 200 m

So work done [tex]W=mgh=315\times 9.8\times 200=617400J[/tex]

Efficiency is given [tex]\eta =0.9[/tex]

We have to fond the input power

So input power [tex]=\frac{617400}{0.9}=686000J[/tex]

So input power of the geothermal power will be 686000 J

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