Question

The pressure $P_1$ at the top of a dam and $P_2$ at a depth $h$ from the top are related as:

• A. $P_1>P_2$
• B. $P_1=P_2$
• C. $P_1-P_2=\rho gh$
• D. $P_2-P_1=\rho gh$

Answer 1

The correct option is D

$P_2-P_1=\rho gh$

The pressure at a point at a depth h from the top of the surface of the dam is due to the weight of the liquid acting on the point.
So, $P=\rho gh$
where, $\rho$ = density of the liquid
and, g = acceleration due to gravity
Also, depth h for $P_1$ = 0 (top of the dam)
and, depth h for $P_2$ = h
Or, $P_1$ = $\rho \times g\times 0$ = 0
And, $P_2$ = $\rho gh$
So, $P_1$ and $P_2$ are related as:
$P_2$ - $P_1$ =$\rho gh$