First slide

Fluid statics

Question

A cart supports a cubic tank filled with a liquid up to the top. The cart moves with a constant acceleration a in the horizontal direction. The tank is tightly closed. Assume that the lid does not exert any pressure on the liquid when in motion with uniform acceleration. The pressure at a point at a depth h and distance / from the front wall is:

Moderate

A

dgh
B

dla
C

dgh + dla
D

dgh-dla

Solution

The pressure P at point x in the sum of pressure $P_{1}$ and $P_{2}$ where $P_{1}$ is the pressure due to gravity and $P_{2}$ is the pressure necessary to impart an acceleration a to the column of water of length /. Pressure $P_{2}$ acting on a column of length I and area of cross-section A gives it an acieration a in the horizontal direction.
$P_{2} A = Alda$
$P_{2} = lda$
As pressure is a scalar quantity, so
$P = P_{1} + P_{2} = hdg + lda = d (hg + la)$

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