Written by 7:47 am Science

If This Volume Of Water Is In A Cubic Tank, What Is The Pressure At The Bottom ?

The pressure at the bottom of the tank will be equal to the atmospheric pressure.

The volume of water is equal to V = πr^2h, where r is the radius of the base and h is the height.

Atmospheric pressure is equal to P = ρgh, where ρ is the density of air (∼1.29 kg/m^3) and g is the acceleration due to gravity (9.8 m/s^2).

Using these equations, we get

P = ρgh = ρg(4πr^2h) = ρg(πr^3).

The pressure at any point in a fluid is equal to the weight of the fluid above that point. The weight of water depends on its depth (the deeper it is, the greater its weight) and on its density (its weight per unit volume).

The density of fresh water is about 0.998 g/cm3. The density of salt water varies with salinity and temperature, but for our purposes we can assume it’s about 1.025 g/cm3 at 20°C.

At 1000 meters depth, there is approximately 1 atmosphere of pressure (1 bar). So there will be 1000 meters x 1 bar = 1000 N/m2 = 1000 kgf/m2 = 1000 lbf/ft2 = 103 kPa = 103 Pascal = 10 N/mm2.

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Last modified: August 16, 2022