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.
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
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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