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Pressure

A tank with a...

Question

A tank with a square base of area 1.0 m² is divided by a vertical partition in the middle. The bottom of the partition has a small-hinged door of area 20 cm². The tank is filled with water in one compartment, and an acid (of relative density 1.7) in the other, both to a height of 4.0 m. compute the force necessary to keep the door close.

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Solution

Given, area of the square base is 1.0 m 2 , area of the small hinged door is 20 cm 2 , relative density of the acid is 1.7 , and the tank is filled with water and acid up to a height of 4.0 m .

When the liquids is filled into the tank then the pressure difference across the door is,

P d =( ρ 1 gh− ρ 2 gh )

Here, ρ 1 is density of the acid ( ρ 1 =1.7× 10 3 kgm -3 ) and ρ 2 is the density of the water.

Substitute the values in the above equation.

P d =( 1700×4×9.8−1000×4×9.8 ) =2.744× 10 4 Pa

Now the force exerted by the acid and liquid is,

Force exerted by the acid and the liquid=pressure difference×area of the door F d = P d × A d =2.744× 10 4 ×20× 10 −4 ≈55 N

Hence, the force necessary to keep the door close is 55 N .

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