First slide

Fluid statics

Question

The pressure of water at bottom in a lake is $\frac{3}{2}$ times that at 2 half depth where the water barometer reads 10 m. The depth of the lake is:

Moderate

A

15 m
B

infinite
C

20 m
D

10 m

Solution

$(P_{0} + {hρ}_{w} g) = \frac{3}{2} (P_{0} + \frac{h}{2} ρ_{w} g) {hρ}_{w} g (1 - \frac{3}{4}) = \frac{P_{0}}{2} \Rightarrow h = \frac{P_{0} \times 4}{2 \times ρ_{w} g} = \frac{10^{5} \times 4}{2 \times 10^{3} \times 10} = 20 m$

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