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Viscous Force

A closed rect...

Question

A closed rectangular vessel completely filled with a liquid of density $ρ$ moves with an acceleration $a = g$ The value of the pressure diffference at point $A$ and $B$ i.e. $(P_{1} - P_{2})$ is

A

ρ g (b - h)

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B

\frac{ρ g h}{2}

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C

\frac{ρ g (b + h)}{2}

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D

ρ g h

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Solution

The correct option is A $ρ g (b - h)$
Given $a_{x} = g$
Let pressure at the opening be $P_{0}$
Then in horizontal direction $P_{1} = P_{0} + ρ g b \dots (i)$
And in vertical direction $P_{2} = P_{0} + ρ g h \dots (i i)$
Subtracting equation $(i)$ and $(i i)$
$P_{1} - P_{2} = ρ g (b - h)$
FINAL ANSWER: (a)

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