Calculating Surface Area Under Pressure!

By: Ryan PedrigiResident

Scientist/Mathematician

What is Pressure? Pressure:

The application of a force over a surface Remember: Force is a push or a pull

The ratio (or relationship) between the amount of force applied (distributed) and the surface area that the force is applied over, for a given object.

Pressure Examples: Balloon

Pressure Applications: Bike Pump

Pressure Applications: Heart

Pump: Moves fluid by creating a pressure difference between the inlet (pump) and outlet

Pressure Examples: Water Press.

Mathematical Expression

Pressure Mathematically: For P – pressure, F – force, A – surface

area…

Units: Most common are… English: pounds/inches2 (psi) SI: Newtons/meter2 (pascal - Pa)

AFPorAFP :

The deepest part of the ocean is about 32,000 feet deep, at which the pressure is about 16,000 psi. What is the total force acting on a submarine with a surface area of 8,000,000 in2 (Remember P=F/A)?

Example Problem 1: Submarine

AFP 2000,000,8

000,16in

Fpsi

22

2 000,000,8000,000,8

000,000,8000,16 inin

Finpsi

poundspoundsF 000,000,000,128000,000,8000,16

The rupture pressure in a balloon is 0.25 psi. If the radius of the spherical balloon right before rupture is 6 inches, what is the force acting on the inner wall of the balloon (Surface area of a sphere, As = 4*pi*radius2)?

Example Problem 2: Balloon

AFP

2.64

25.0in

Fpsi

245225.0

inFpsi

poundsF 113

Nail Problem Question: Why is it much easier to

hammer the tip of a nail into wood versus the head? Assume that the hammer exerts a force of

200 pounds on the nail, and calculate the pressure exerted on the wood by the nail for the case…

When hammering the tip of the nail into the wood

When hammering the head of the nail into wood

Submarine Problem Pretend that the 3D object given to

your group is a submarine. Calculate the force acting over the entire surface area of your submarine if the dive depth is 1000 feet, which corresponds to a water pressure of 445 psi.