Question

Water is filled to a height $H$ behind $a$ dam of width $w$. The resultant force on dam is:

• A. $pgw{H}^2$
• B. $\frac{1}{2}pgw{H}^2$
• C. $2pgw{H}^2$
• D. $4pgw{H}^2$

Answer 1

The correct option is B $\frac{1}{2}pgw{H}^2$

R.E.F image

Let us consider a Strip of

length dx, x distance below

the large

$dp=pgx$

$dF=pgx\left(dxw\right)$

${\int }_0^{F}df={\int }_0^{H}pgxwdx$

$F=pgw\frac{x^2}{2}{|}_0^H$

$=\frac{pgw{H}^2}{2}$

Option (B)