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The water level in a tank is 20 m above the ground. A hose is connected to the bottom of the tank, and the nozzle at the end of the house is pointed straight up. The tank is at sea level, and the water surface is open to the atmosphere. In the line leading from the tank to the nozzle is a pump, which increases the pressure of water. If the water jet rises to a height of 27 m from the ground, determine the minimum pressure rise supplied by the pump to the water line.

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Answer:

[tex]P_{pump}= 68600Pa[/tex]

Explanation:

We understand that the sum of the pressures in the tank and the pump is equal to that of the Nozzle,

In this way,

[tex]P_{tank} + P_{pump} = P_{nozzle}[/tex]

For the pressure we also know that it is given by

[tex]P=\rho gh[/tex]

[tex]\rho gh_1 + P_{pump} = \rho gh_2[/tex]

So,

[tex]P_{pump} = \rho g(h2 - h1)[/tex]

[tex]P_{pump}= 1000*9.8(27-20)[/tex]

[tex]P_{pump}= 68600Pa[/tex]

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