This model represents a tank of fluid, open to atmospheric pressure at the top. Initially at the surface is an imaginary circular disk that we will use to illustrate the depth dependence of the fluid pressure. The disk is so thin that we may neglect any pressure variation over its thickness. To move the disk, click on the drawing area to pass the keyboard focus to that window and use the down arrow key to increase depth and the up arrow key to decrease depth.

As this disk is moved down, it generates an imaginary cylinder above it. The weight of the fluid in this cylinder divided by the disk area adds to the atmospheric pressure to give the total downward pressure on the hypothetical disk. Remember that the disk and the cylinder above it have no physical reality. These imaginary constructs cannot have any effect on the fluid. The fluid is at equilibrium, meaning that the downward pressure must be balanced by and equal upward pressure. Otherwise the particles making up the fluid would be pushed down by the weight of the fluid above. In fact it is the nature of fluids to transmit equal pressure in all directions from any point.

The magnitude of the fluid pressure may be found from our little imaginary cylinder. The weight of the fluid in the cylinder is the density, r, of the fluid multiplied by the volume, V, in the cylinder multiplied by the acceleration of gravity, g.

W = r*g*V

But the volume is just the cross section area, A, of the disk or cylinder multiplied by the depth, d, of the disk so:

W = r*g*A*d.

The pressure, Pf, from the weight of fluid then is the weight divided by the area of the disk.

Pf = r*g*A*d/A = r*g*d.

As you can see the pressure depends on the density of the fluid. The model opens with water as the fluid, with a density of 1000 kg/m^3. You may enter other densities from zero to that of mercury, about 13,600 kg/m^3. The total pressure, P, is Pf + the atmospheric pressure, P0, which is transmitted uniformly throughout the fluid.

For details on the operation of applet controls, see the Model Controls help page.