Fluid Pressure & Fluid Force - Calculus 2

The final application of definite integrals that we encounter in Calculus 2 is the ability to find the fluid force on a vertically submerged surface. 

If you've ever been swimming in a pool, river, ocean, or any other body of water, you've probably noticed that when you try to submerge an object in the water (or "push" it down), you feel pressure on that object. Additionally, you may have also noticed that the deeper you submerge the object, the stronger that pressure is that you feel. That pressure is known as fluid pressure, which is directly related to another concept known as fluid force. 

When submerging a specific type of object known as a plane surface, we can easily calculate the fluid pressure and fluid force on that surface if it is submerged horizontally. The fluid pressure is equal to the weight-density of the fluid times the depth that the surface has been submerged to in the fluid (in most cases that fluid will be water). A surface submerged horizontally will be located at one specific value of depth, and so calculating the pressure on that entire surface is fairly easy. The fluid pressure on a surface can then be used to calculate the fluid force as well, which is equal to the fluid pressure times the area of the surface.

However, if a surface is not submerged horizontally, but rather vertically, then the surface is no longer located at one specific value of depth. Instead, it will be located over a range of depth values. As a result, the pressure on the surface will depend on what part of the surface you are interested in. The pressure will NOT be constant for the entire surface as it would be if it was submerged horizontally.

This is where calculus comes in. Since the pressure on a vertically submerged surface will be variable instead of constant, calculating the fluid force on that surface will require calculus, or more specifically, a definite integral. Determining how to set up an integral to calculate the fluid force on such surfaces is the main focus of this lesson in Calculus 2.

In this lesson, you will learn:

• The concepts of fluid pressure and fluid force
• How to find the fluid force on a surface submerged horizontally in a fluid
• How to find the fluid force on a surface submerged vertically in a fluid

I hope you find this video to be helpful!

-Josh