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Problem on pressure rise of a water tank

The water level in a tank is about 20 m above the ground. A hose is joined to the bottom of the tank, and the nozzle in the end of the hose is pointed to straight up. The tank is at sea level, and the water surface is open to the environment. In the line leading from the tank to the nozzle is a pump, that rises the pressure of water. If the water jet increases to a height of 27 m from the ground, then find out the minimum pressure rise that is supplied by the pump to the water line.

828_pressure rise.jpg

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Entry and exit losses at the pump and nozzle are neglected since no data is given

The Bernoulli’s equation

P1/δg + V12/2g +z1 = P2/δg + V22/2g +z2 + Losses (L) – (i) 
P1/δg =  pressure head V2/2g =velocity head Z=  height

Assuming an air  density of 1.225 Kg/m3

Pressure at (2) = δa gh
                      = 1.225 x 9.81x 7
                      = 84.12 Pa ( below  atmosphere

P2 =Absolute pressure at (2)  = Atmospheric  pressure – 84.12
                    = 101.325 x 103 – 84.12
                    = 101240.88 Pa
                    = δa g h + PP ( PP = pump pressure , SW= Water density)
                    =1000 x 9.81 x 20x+PP
                    =196200 + PP Pa

P1=Absolute pressure at (1)  = Patm  +  PP + 196200
                                           = 297525 +PP Pa
V1=V2 =0 a very negligible

Substituting  is (1) where δ =δw  = 1000 Kg/ m3 in the density of water
297525 +PP/ 1000g = 101240.88/ 1000g + 27
Solving for PP , it  comes out to be

PP = 68585.88Pa

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