Two lakes hold water to the same average depth at their dams, but one lake stretches ten times further back from its dam. How do the average pressures on the two dams compare?
AThe larger lake gives ten times the pressure
BThe larger lake gives a slightly lower pressure
CThe two pressures are exactly the same
DThe larger lake gives one tenth the pressure
Answer & Solution
Correct answer: C. The two pressures are exactly the same
1. Pressure due to the weight of a fluid depends only on depth, density and g.
2. Nothing in that relation refers to how far the water extends horizontally.
3. The pressure on a dam is therefore completely independent of the width and length of the lake behind it.
4. Since both lakes have the same average depth at the dam, the two average pressures are exactly the same.
5. The total force can still differ if the dams differ in size, because force is pressure times area, but the pressure itself does not change.
_Source: OpenStax College Physics (CC BY 4.0), Ch 11 "Fluid Statics", section 11.4 Variation of Pressure with Depth in a Fluid_
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