For a fluid of average density rho, the pressure caused by the fluid's own weight at a depth h below its surface is given by which expression?
APressure equals rho divided by h times g
BPressure equals h divided by rho times g
CPressure equals h times rho divided by g
DPressure equals h times rho times g
Answer & Solution
Correct answer: D. Pressure equals h times rho times g
1. The pressure on the bottom of a container is the weight of the fluid, mg, divided by the supporting area A.
2. The mass of the fluid is its density times its volume, and the volume is the area times the depth, so m = rho A h.
3. Substituting gives pressure = (rho A h)g / A, and the area cancels.
4. What remains is pressure = h rho g, so pressure grows in direct proportion to depth, density and g.
5. Dividing by g or by rho or by h would make the pressure fall as that quantity rose, which contradicts the fact that deeper water presses harder.
_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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