Dams at two different locations are needed to form a lake. When the lake is filled, the water level will be at top of both dams. The second dam is twice as high and twice as wide as the first dam. The force of the water on the second dam is how much greater than the force on the first? (Ignore atmospheric pressure since it is pushing on both sides of the dams.)
Physics · Fluid Mechanics
JEE Mains Practice

Question

Dams at two different locations are needed to form a lake. When the lake is filled, the water level will be at top of both dams. The second dam is twice as high and twice as wide as the first dam. The force of the water on the second dam is how much greater than the force on the first? (Ignore atmospheric pressure since it is pushing on both sides of the dams.)

Physics · Fluid Mechanics

G1 Physics · Accepted Answer

Step 1: Use hydrostatic equilibrium, P₂−P₁ = ρgΔh; in an accelerating fluid replace g by the effective acceleration where required. Step 2: Equate pressures at the same horizontal level or integrate pressure over the stated surface. Applying these relations to the given data gives 8. Final answer: 8.