a cylindrical tank is filled with water at by a pump that produces an absolute p

Question

a cylindrical tank is filled with water at by a pump that produces an absolute pressure of 150kpa at the inlet. at the instant shown below, the air pressure is 100 kPa and H = 25cm. If the air is compressed isothermally, what will H be when the flow ceases?

A cylindrical tank is filled with water at 20degreeC by a pump that produces an absolute pressure of 150 kPa at the inlet. At the instant shown below, the air pressure is 100kPa and H = 25 cm. If the air is compressed isothermally, what will H be when the flow ceases?

Explanation / Answer

The flow will cease when pressure at inlet will become same as water pressure

  

Total height of tank = 75 + 25 = 100 cm = 1m

At H pressure equals

since temprature remains constant

Pi*Vi = Pf*Vf

Pi = initial air pressure

Pf = Final air pressure

Since cross section of tank is constant taking H in meters

=> Pi*0.75 = Pf*(1-H)

=> 100*1000*0.75 = Pf*(1-H) --------- 1

also

at inlet water pressure in final case

=> Pf + pgH = 150 kPa

=> Pf + 1000*9.81*H = 150k

Putting Pf from 1

=> 100*1000*0.75/(1-H) + 1000*9.81*H = 150k

=> DIviding by 1000

=> 75/(1-H) + 9.81*H = 150

=> 75 + 9.81*H - 9.81*H^2 = 150-150H

=> 9.81*H^2 - 159.81*H + 75 = 0

=> H = 15.81 & 0.484

Since Tanks Height is 1m so 15.81 is not possible

so H = 0.484 m = 48.4 cm

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