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

10 m
B

20 m
C

60 m
D

30 m

Solution

Pressure at bottom of the lake = $P_{0} + hρg$
Pressure at half the depth of a lake $= P_{0} + \frac{h}{2} ρg$
According to given condition
$\begin{array}{l} P_{0} + \frac{1}{2} hρg = \frac{2}{3} (P_{0} + hρg) \Rightarrow \frac{1}{3} P_{0} = \frac{1}{6} hρg \\ \Rightarrow h = \frac{2 P_{0}}{ρg} = \frac{2 \times 10^{5}}{10^{3} \times 10} = 20 m \end{array}$

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