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You have been tasked to design a large water tank that has the following characteristics:

You have been tasked to design a large water tank that has the following characteristics: 1) open to the atmosphere at the top, 2) an inlet pipe is located near the top, 3) an outlet pipe is located near the bottom, which leads to a pump, and 3) a drain hole is provided at the bottom. The drain hole is a simple open hole that allows water to flow out into a ditch when the drain valve is open. The purpose of the drain hole is to prevent the water tank from overflowing when the inflow from the inlet pipe is greater than the outflow through the outlet pipe. If the design conditions are a steady inflow that is larger than the steady outflow to the pump, derive an equation that allows you to compute the diameter of the drain hole for a desired steady water height in the tank for the design condition inflow and pumping rates.
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Solution:
Let the inflow rate through the inlet pipe = Q1
Outflow rate through the outlet pipe = Q2
Now overflow will happen when Q1>Q2.
Let the flow rate through the drain hole = Q3
Now...

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