Question

Water is being poured in a vessel at a constant rate α m3/s. There is a small hole of area a at the bottom of the tank. The maximum level of water in the vessel is proportional to​

Answer 1

Answer:

The maximum level of water in the vessel is proportional to​ $h = \frac{r^{2} }{2ga}$

Explanation:

The maximum level of water in the vessel would be when the rate of in flow of water is equal to rate of out flow of water.

Let the maximum level of water in vessel be h

The rate of in flow of water = r m³/s

The rate of out flow of water = area of cross section × speed

                                              = a × v = a × √2gh

(∵K.E. = P.E. of water

          = 0.5 mv²

          = mgh

       v = √2gh

where m is the mass of water)

Rate of in flow of water = Rate of out flow of water.

                      r = a × √2gh

Hence, The maximum level of water in the vessel is proportional to​ $h = \frac{r^{2} }{2ga}$.

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