Pressure Equation
In a liquid of density ρ, the pressure at a depth h, due to the liquid, is given by p = hρg.
Exercise. Find the pressure from water, at a depth of 10 m. Density of water is 1000 kg/m3. Assume that acceleration of free fall is 10 m/s2. Answer. Depth h = 10 m, density &rho = 1000 kg/m3. So pressure p = hρg = 10 x 1000 x 10 = 100000 Pa.
Exercise. The water pressure at 10 m depth is 100000 Pa. Air pressure is 100000 Pa. Find the total pressure 10 m below the water surface. Answer. The pressure at 10 m comes from the water and the air. So total is 100000 + 100000 = 200000 Pa.
Exercise. The top of a 1 m cube is 10 m below the water surface. Find the pressures on the top and bottom faces of the cube. Then find the forces and the resultant. Density of water is 1000 kg/m3. Assume that acceleration of free fall is 10 m/s2. Answer. At the top face of the cube, depth h = 10 m. So pressure p = hρg = 10 x 1000 x 10 = 100000 Pa. At the bottom face, depth h = 11 m. So pressure p = hρg = 11 x 1000 x 10 = 110000 Pa. Area of each face is 1 m2. Force is pressure times area. So the force on the top face is 100000 x 1 = 100000 N downwards. The force on the bottom face is 110000 x 1 = 110000 N upwards. Resultant is 110000 - 100000 = 10000 N upwards. (This is also called the upthrust.)
Copyright 2010 by Kai Hock. All rights reserved.
Last updated: 10 October 2010.