Consider a strip on gate of dam at a depth of y from free surface of water ofwidth dy. Pressure force acting on this strip is, dF = (P0 + ρgy) dA - P0dA = ρgy × ady Total force , F = ∫ df =
h
∫
0
ρgya dy F =
ρga×h2
2
Torque about 0 due to force on elemental strip is, dτ = dF × (h - y) ⇒ dτ = ρgay dy × (h - y) Total torque τ = ∫ dτ =
h
∫
0
ρga × y (h - y) dy =
ρga×h3
6
If the point of application of force Fis at H above 0, then it produce the sametorque as found. So F × H = τ ⇒ H =