7.2: Force

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Pressure is the force applied over a specific area. It is the weight of water expressed as pounds divided by the area expressed as inches squared (in\(^2\)). Therefore, the resulting unit is pounds per square inch (psi). However, in the previous section we looked at pressure based on the height or elevation of a column of water and compared it against a conversion factor.

Recall the following conversion factors:

0.433 psi = 1 foot and 1 psi = 2.31 feet

Let’s take a look at what 1 psi is actually saying. One (1) pound of force per square inch of surface area. Therefore, if you have one (1) pound of water and place it on one (1) square inch of area, the resulting pressure would be 1 psi.

The definition of force can be explained as the push or pull which an object can change the velocity of the object on which it is applied. If the pressure is known and the area of which the pressure is being applied, the force can be calculated. See the example below:

A pressure of 100 psi exerts how much force against an area of 1 in\(^2\)?

In this example, there is

\[\dfrac{100 \text {lbs}}{\text{in}^{2}} \times \text{in}^{2} \nonumber \]

This would equate to 100 lbs of force because the in\(^2\) would cancel.

This says that 100 pounds of force is being exerted. Another example of calculating the force in pounds would be by calculating the entire volume of water and then converting to the water of the volume of water. Look at the example below.

If a tank with a 100 ft diameter and is 20 ft tall, what is the force at the bottom? In this example, the dimensions of the tank can be used to calculate the volume of water.

\[V=0.785 \times(100 \mathrm{ft}) 2 \times 20 \mathrm{ft} \times 7.48=1,174,360 \mathrm{gal} \nonumber \]

This volume can now be converted to pounds.

\[1,174,360 \text { gal } \times 8.34 \text { lbs/gal }=9,794,162 \text { lbs } \nonumber \]

This is the force exerted.

Exercise 7.2

Calculate the force exerted on a 6” diameter valve with a pressure of 90 psi.
What is the force at the base of a 100 ft tall tower filled with water and a diameter of 10 ft?
A water tank is 50 feet tall and half full. If the diameter is 75 feet, what is the force exerted at the bottom?
A fire hydrant with a 2 ½” opening has a pressure of 130 psi. What is the corresponding force?