The height of water at two identical dams is the same, but dam A holds back a lake containing 2

step 1 we have problem number 16 question says the height of water at two identical dams is same but da

The height of water at two identical dams is the same, but...

The height of water at two identical dams is the same, but dam $\mathrm{A}$ holds back a lake containing 2 cubic kilometres of water while dam B holds back a lake containing 4 cubic kilometres of water. The ratio of the total force exerted on dam $\mathrm{A}$ to that exerted on dam $\mathrm{B}$ is: (a) 2 (b) 4 (c) 1 (d) $\frac{1}{2}$

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Key Concepts

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. It is directly proportional to the depth of the fluid and is determined using the relation p = ?gh, where ? is the fluid density, g is the acceleration due to gravity, and h is the height of the fluid column. This concept shows that the pressure at a given depth is independent of the total amount of fluid present.

Force on a Submerged Surface

The force exerted by a fluid on a submerged surface, such as a dam, is obtained by integrating the hydrostatic pressure over the area of the surface. This force depends on the shape and size of the surface and the fluid depth, not on the overall volume of fluid behind the structure.

Volume Independence in Hydrostatic Force Calculations

Even when reservoirs have different volumes, if the water height—or the depth of the fluid—is the same, the hydrostatic pressure profile remains unchanged. Hence, the total force acting on the dam, which is a function of this pressure, will be identical despite differences in the total water volume.

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