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Water is pumped from a very large pressurized tank. After passing through the pump, the water exits through a short nozzle pointing upward and enters the atmosphere as a free jet. The jet of water reaches a height of 40 m above the top of the tank.

If the pump power is 10.0 kW and the flow rate is 0.030 m\(^3\)/s, what is the pressure inside the tank at its top (in kPa)? Neglect friction.

[P = 59.1 kPa]

Answer :

Final answer:

The pressure inside the tank at its top can be found using the equation PT - PA = ρgH which is 59.1 kPa.

Explanation:

To find the pressure inside the tank at its top, we can use Bernoulli's equation, which states that the sum of the pressure, kinetic energy, and potential energy per unit volume is constant along a streamline.

Since we are neglecting friction, the kinetic energy and potential energy terms can be dropped.

The pressure inside the tank can be found using the equation: PT - PA = ρgH, where PT is the pressure inside the tank, PA is atmospheric pressure, ρ is the density of water, g is the acceleration due to gravity, and H is the height the water reaches above the top of the tank.

Plugging in the given values, we have: PT - 101,325 Pa = (1000 kg/m3)(9.8 m/s2)(40 m).

Solving for PT, we find that the pressure inside the tank is approximately 59.1 kPa.

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