# Physics question about 2 Dams?

Dams at 2 different locations are needed to form a lake. When the lake is filled, the water level will be at the top of both dams. The Dam #2 is twice as high and twice as wide as Dam #1. How much greater is the force of the water on Dam #2 than the force on Dam #1? (Ignore atmospheric pressure; it is pushing on both sides of the dams)

Relevance
• Anonymous

Depth of Dam #1 = h Depth Dam#2 = 2h

Area of Dam #1 = 1 Area of Dam#2 = 4 (twice as wide and twice as deep)

Ave Pressure Dam #1 = rho x g x h/2 = 1000 x 10 x h/2 = 5000h Pa

Ave Pressure Dam #2 = rho x g x 2h/2 = 1000 x 10 x h = 10,000h Pa

Force on Dam#1 = pressure x area = 5000h x 1 = 5000h N

Force on Dam#2 = pressure x area = 10,000h x 4 = 40,000h N

F #2 / F #1 = 8

force on Dam#2 is 8 times greater than Dam#1

• The pressure of the water on the dam varies with the depth h and is proportional to h

p = a.h (a = constant)

If the dam is W meter wide and H meter high, the force exerted on its surface will be the integral taken on interval (0, H) of

dF = p.dA = p W.dh = a.hW.dh = a.W h dh

. . . .H . . . . . . . .H

F = ∫ p dA = aW ∫h.dh = (1/2)a W H²

. . . .0 . . . . . . . . 0

If F is the force acting on the dam #1, F' the force acting on the dam #2, then

F' / F = (W'/W)(H'/H)² = 2×2² = 8

The force of the water on Dam #2 is 8 times greater than the force on Dam #1