First slide

Fluid statics

Question

If pressure at half the depth of a lake is equal to $\frac{2}{3}$ pressure at the bottom of the lake, then the depth of lake is (Atmospheric pressure = $10^{5} N / m^{2})$

Moderate

A

10 m
B

20 m
C

60 m
D

30 m

Solution

(2)
$\begin{array}{l} \frac{2}{3} (P_{a} + ρ g h) = P_{a} + ρ . g . \frac{h}{2} \\ \Rightarrow \frac{1}{6} ρ g h = \frac{1}{3} P_{a} \\ \Rightarrow h = \frac{2 P_{a}}{ρ g} = \frac{2 \times 10^{5}}{10^{3} \times 10} m = 20 m \end{array}$

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