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  4. A completely filled hemispherical tank of radius R has an orifice of small area a at its bottom. Time required to completely empty the tank is (p √2 ⋅ π R5 / 2/q a √g). Find (p+q). (Assume that the top surface area of the liquid is always much greater than the orifice area)

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Q. A completely filled hemispherical tank of radius $R$ has an orifice of small area $a$ at its bottom. Time required to completely empty the tank is $\frac{p \sqrt{2} \cdot \pi R^{5 / 2}}{q a \sqrt{g}}$. Find $(p+q)$.
(Assume that the top surface area of the liquid is always much greater than the orifice area)

Mechanical Properties of Fluids

Solution:

image
$Q=a v=\pi x^{2}\left(-\frac{d h}{d t}\right)$
$a \sqrt{2 g h} \,d t=-\pi x^{2} d h$
$x^{2}=R^{2}-(R-h)^{2}$