If the pressure of at half of the lake is equal to 1/3 pressure at the bottom of the lake, what is the depth of the lake
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Answer:
According to the question,
pressure at half depth of lake =
3
2
(Pressure at bottom of lake)
P
0
+ρg
2
h
=
3
2
(ρgh+P
0
)
(P
0
+ρg
2
h
)3=2(ρgh+P
0
) [P
0
=10
5
Pa,ρ=10
3
kg/m
3
]
3P
0
+
2
3
ρgh=2ρgh+2P
0
P
0
=(2−
2
3
)ρgh
P
0
= 2ρgh=
ρg
2P
0 = 10 3 kg/m 3 ×10m/s 22×105 Pa=20m.
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