What is the diameter of the hole for a flow rate of 4.17x10-5 m3/s?

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To determine the diameter of a hole allowing a flow rate of 4.17x10-5 m3/s from a tank 15 m below the water level, Bernoulli's theorem is applied. The pressure inside the tank is calculated using the total pressure equation, factoring in atmospheric pressure and hydrostatic pressure. The velocity of the liquid exiting the hole is derived from the pressure difference, leading to the calculation of the hole's cross-sectional area. Finally, the diameter of the hole is computed from the area, providing the required measurement in millimeters. This approach effectively combines fluid dynamics principles to solve the problem.
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Homework Statement


A large tank is filled with water and open to the atmosphere has a small hole in its side at a point 15 m below the water level. If the rate of flow from the hole is 4.17x10-5 m 3/s .
What is the diameter off the hole (in mm)

Homework Equations


R=A*V, where R is the rate flow
 
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In side the tank at the depth h the total pressure = Pa + ρgh. Velocity of the the liquid is zero.
Out side the hole the pressure = Pa.
Using Bernoulli theorem find the velocity of liquid flowing out of the hole, From that find the area of the hole.
 
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