Q. 213.6( 8 Votes )

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.

Answer :

Given,


Base area of the tank = 1 m2


Area of the hinged door = 20 cm2


Height of both water and acid columns, h = 4 m


Density of the water, ρw = 1000 kg/m3


Density of the acid, ρa = 1.7 × ρw = 1700 kg/m3


Pressure, P = ρgh


Where,


ρ = density


g = acceleration due to gravity


h = height of the column


Pressure exerted by water, Pw = 1000 × 9.81 × 4


= 3.92 × 104 pa


Pressure exerted by the acid, Pa = 1700 × 9.81 × 4


= 6.664 × 104 pa


Pressure difference, ΔP = Pa – Pw


= (6.664-3.92) × 104 pa


= 2.744 × 104 pa


Thus, Force exerted on the hinged plate,


= 54.88 N


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