Three open vessels stand on a bench

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Fluid statics and the continuum picture · Fluid statics and the continuum picture

Fluids and Continuum Physics, Ch The continuum hypothesis, pressure and the stress tensor

Problem

Three open vessels stand on a bench. Each has a flat horizontal base of internal area

0.020\ \mathrm{m^2}

, and each is filled with water to a depth of

0.35\ \mathrm{m}

. Vessel A is a straight cylinder and holds

7.0\ \mathrm{kg}

of water; vessel B widens upwards and holds

11.5\ \mathrm{kg}

; vessel C narrows upwards and holds

4.0\ \mathrm{kg}

. Take the density of water as

1000\ \mathrm{kg\,m^{-3}}

, atmospheric pressure as

1.013\times10^{5}\ \mathrm{Pa}

and

g = 9.8\ \mathrm{m\,s^{-2}}

. ((a)) Find the gauge pressure of the water on the base of vessel B. ((b)) The air below the base pushes up on it with atmospheric pressure. Find the magnitude of the net downward force on the base of vessel B from the water above and the air below. ((c)) State whether your answers to (a) and (b) would be different for vessels A and C, and say in one sentence what carries the difference in weight.

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