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How do you figure out the pressure exerted by a fluid?

Gold Barometer indicating atmospheric pressure change.

By now, you are probably very familiar with air pressure. The pressure that is exerted on our bodies all the time is called atmospheric pressure. It is about 14.7 pounds per square inch, which seems like a lot because we can’t feel anything. Without it, though, our bodies wouldn’t hold together. Atmospheric pressure is caused by the weight of the atmosphere, so as you go up in elevation, it decreases. The air is less dense and the molecules are farther apart. This is why airplanes need to have pressurized cabins, and it is also why there is less oxygen at high altitudes. In outer space, there is no pressure, and astronauts who do space walks have to have special pressurized suits.

Let's contrast that with the pressure as you descend in water. As you go deeper and deeper, the pressure that you will feel on your body will continue to increase until your body cannot withstand it any longer. In fact, the pressure at 10,000 ft below sea level is 4,400 pounds per square inch—much higher than the atmospheric pressure.

Both air and water obey the concept of fluid pressure. The amount of pressure exerted by a fluid is based on the density of the fluid, gravity, and the height or depth at which the point of observation is. For the air pressure on the surface of the Earth, the depth would be equal to the depth of the atmosphere at that point. You can find the pressure of a fluid using an equation.

Fluid Pressure

\(\large\mathsf{ P = \rho gh }\)

...where P is the pressure exerted by a stationary fluid, ρ is the density of the fluid, g is the acceleration of gravity, and h is the depth of the fluid.

It is interesting to note that the pressure of the fluid does not depend on the volume of the fluid. In other words, no matter if the fluid is a column, a cube, or some other odd shape, the only determining factors are the density, the acceleration of gravity, and the depth of the fluid.

Question

A penny is placed at the bottom of a cone full of water. Another penny is placed at the bottom of a column of water of the same height as the cone. Which penny has more pressure exerted on it by the water?

Both pennies would have the same pressure exerted on them, because the height of the water in each case is the same.