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

Answer 1

Let the point at half depth be x,

P1=P+dgx

Let the depth of lake be 2x,

P2=P+dg2x

P2=3/2×P1

2P2=3P1

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

2P+4dgx=3P + 3dgx

P=dgx

x=P/dg

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

But depth of lake is 2x

2x=2×10=20m