## Tuesday, May 24, 2011

### MrsDrPoe: Pressure Variation in Fluids

Good morning and welcome to "Thesis Tuesday" on the blog! Today we're going to be investigating pressure variation in a static (or motionless) body of fluid with as little math as possible. If you do happen to be interested though, this relation can be derived by examining Newton's Second Law, which states that the sum of all the forces acting on an object is equal to the object's mass times its acceleration.

In a static fluid, pressure is a function of depth ONLY. This means that if we look at two points in a body of fluid (such as the ocean) that are right beside each other like this:

* *

the pressure at each point is the same as that at the other point because they are at the same depth. But, if we look at two points like this:

_______________*_________________________________*
_______________________________or this:
_______________*___________________________________________*

the pressure at each point is NOT the same as the one above or below it, respectively.

We also know that pressure is not just a function of depth, but that it actually INCREASES with increasing depth. If we think about our experiences, this physical reality should make sense to us. Why was it so much trouble to fix the Deepwater Horizon oil spill? "Every day" tools and equipment could not be used in this instance because the water pressure at the leak depth was SO great!

The pressure at a given depth in a given (incompressible) fluid can be calculated by multiplying the specific weight of a fluid by the depth. For instance, the specific weight of salt water is 64 pounds/cubic foot, and the depth of the oil leak was 5,000 feet, so the pressure at the leak was 320,000 pounds/square foot. The average surface area of a human is 18.6 square feet, which means that a person located at the oil spill would experience a force of 5,952,000 pounds on his/her body. The 2010 Mississippi State Football team weighed 25,357 pounds collectively...this means that the pressure force that a person located at the leak would feel is equivalent to taking this entire team:

cloning them approximately 233 times and setting ALL of these guys on top of him/her. Pretty crazy huh?