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A closed rectangular vessel is completely filled with a liquid of density rho. The vessel accelerates horizontally with acceleration a = g. Points P1 and P2 are on the rear and front vertical walls of the vessel respectively at the same height, separated by a horizontal distance b. The pressure difference (P1 - P2) is:

1. rho*g*b
2. rho*g*(b + h) / 2
3. rho*(a*b - g*h)
4. rho*g*h

Correct answer: rho*g*b

Solution

For a liquid undergoing horizontal acceleration a, the pressure gradient along the direction of acceleration is -rho*a. The pressure at a point on the rear wall (opposite to acceleration direction) is higher. With a = g and horizontal separation b, P1 - P2 = rho*a*b = rho*g*b.

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