Question

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

• A. $15$ m
• B. infinite
• C. $20$ m
• D. $10$ m

Answer 1

Answer: (C)

$20$ m

Let the point at half depth be $x,$

$P_1=P+dgx$

Let the depth of lake be $2x$,

$P_2=P+dg2x$

$P_2=3/2\times P1$

$2P_2=3P1$

$2(P+dg2x)=3(P+dgx)$

$2P+4dgx=3P+3dgx$

$P=dgx$

$x=P/dg$

$x={10}^5/10000(d={10}^{3}kg/m^3)(P={10}^{5}pa)$

But depth of lake is $2x$

$2x=2\times 10=20m$