The pressure at the bottom of a water tank is | vedclass

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Question

(C) Let the initial height of water in the tank be $h$. The pressure at the bottom is the sum of atmospheric pressure and gauge pressure.$P_{	ext{bot

Vedclass · Accepted Answer

$\frac{11 P}{5}$

Vedclass · Answer

(C) Let the initial height of water in the tank be $h$. The pressure at the bottom is the sum of atmospheric pressure and gauge pressure.$P_{	ext{bottom}} = P + ho_w g h = 4 P$Therefore,the gauge pressure due to the water column is $ho_w g h = 3 P$ ... $(1)$When water is drawn out such that the level decreases by $\frac{3}{5}$ of its initial height,the remaining height of the water is $h' = h - \frac{3}{5} h = \frac{2}{5} h$.The new pressure at the bottom is $P' = P + ho_w g h'$.Substituting $h' = \frac{2}{5} h$ into the equation:$P' = P + ho_w g (\frac{2}{5} h) = P + \frac{2}{5} (ho_w g h)$.Using equation $(1)$,substitute $ho_w g h = 3 P$:$P' = P + \frac{2}{5} (3 P) = P + \frac{6 P}{5} = \frac{5 P + 6 P}{5} = \frac{11 P}{5}$.

The pressure at the bottom of a water tank is $4 P$,where $P$ is atmospheric pressure. If water is drawn out until the water level decreases by $\frac{3}{5}$ of its initial height,then the pressure at the bottom of the tank is .........

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