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Juli2301 [7.4K]
3 years ago
6

Calculate the time taken to completely empty aswimming pool 15

Engineering
1 answer:
user100 [1]3 years ago
4 0

Answer:

Time needed to empty the pool is 401.35 seconds.

Explanation:

The exit velocity of the water from the orifice is obtained from the Torricelli's law as

V_{exit}=\sqrt{2gh}

where

'h' is the head under which the flow of water occurs

Thus the theoretical discharge through the orifice equals

Q_{th}=A_{orifice}\times \sqrt{2gh}

Now we know that

C_{d}=\frac{Q_{act}}{Q_{th}}

Thus using this relation we obtain

Q_{act}=C_{d}\times A_{orifice}\times \sqrt{2gh}

Now we know by definition of discharge

Q_{act}=\frac{d}{dt}(volume)=\frac{d(lbh)}{dt}=Lb\cdot \frac{dh}{dt}

Using the above relations we obtain

Lb\times \frac{dh}{dt}=AC_{d}\times \sqrt{2gh}\\\\\frac{dh}{\sqrt{h}}=\frac{AC_{d}}{Lb}\times \sqrt{2g}dt\\\\\int_{1.5}^{0}\frac{dh}{\sqrt{h}}=\int_{0}^{t}\frac{0.62\times 0.3}{15\times 9}\times \sqrt{2\times 9.81}\cdot dt\\\\

The limits are put that at time t = 0 height in pool = 1.5 m and at time 't' the height in pool = 0

Solving for 't' we get

\sqrt{6}=6.103\times 10^{-3}\times t\\\\\therefore t=\frac{\sqrt{6}}{6.103\times 10^{3}}=401.35seconds.

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