First slide

Pressure in a fluid-mechanical properties of fluids

Question

If pressure at half the depth of a lake is equal to 2/3 pressure at the bottom of the lake then what is the depth of the lake

Moderate

A

10m
B

20m
C

60m
D

30m

Solution

Pressure at half the depth $= P_{0} + \frac{h}{2} d g$
Pressure at the bottom $= P_{0} + h d g$
According to given condition
$\begin{array}{l} P_{0} + \frac{h}{2} d g = \frac{2}{3} (P_{0} + h d g) \\ \Rightarrow 3 P_{0} + \frac{3 h}{2} d g = 2 P_{0} + 2 h d g \\ \Rightarrow h = \frac{2 P_{0}}{d g} = \frac{2 \times 10^{5}}{10^{3} \times 10} = 20 m \end{array}$

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