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  • A tank with a square base of area 1.0 m^2 is divided by a vertical partition in the middle. The bottom of the partition has a small-hinged door of area 20 cm^2 . The tank is filled with water in one compartment, and an acid

Q 10.21 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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Pressure in the waterside at the bottom is

\\P_{w}=\rho _{w}gh\\ P_{w}=10^{3}\times 9.8\times 4\\ P_{w}=3.92\times 10^{4}

Pressure in the acid side at the bottom is

\\P_{a}=\rho _{a}gh\\ P_{w}=1.7\times 10^{3}\times 9.8\times 4\\ P_{w}=6.664\times 10^{4}

The pressure difference across the door is

\\\Delta P=P_{a}-P_{w}\\ \Delta P=6.664\times 10^{4}-3.92\times 10^{4}\\ \Delta P=2.774\times 10^{4}\ Pa

Area of the door, a = 20 cm2 

The force necessary to keep the door closed is

\\F=a\Delta P\\ F=20\times 10^{-4}\times 2.774\times 10^{4}\\ F=54.88\ N

Note: The dimensions of the door are small enough to neglect pressure variations near it.

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