Define pressure.Explain the relationship in between pressure and force.Calculate pressure given pressure and area.

You are watching: Relation between force pressure and area

You have actually no doubt heard the word pressure being provided in relationship to blood (high or short blood pressure) and in relation to the weather (high- and low-pressure weather systems). This are just two of plenty of examples of pressure in fluids. Push P is characterized as

Pressure is defined as the force separated by the area perpendicular come the force over which the pressure is applied, or

P=\fracFA\\

A given force can have a considerably different effect depending upon the area over which the force is exerted, as presented in number 1. The SI unit for push is the pascal, where

1\text Pa=1\textN/m^2\\.

In enhancement to the pascal, over there are countless other devices for push that room in typical use. In meteorology, atmospheric press is often described in devices of millibar (mb), where

\text100 mb=1\times \text10^5\text Pa\\.

Pounds per square inch (lb/in2 or psi) is still occasionally used together a measure up of tires pressure, and also millimeters that mercury (mm Hg) is still often used in the measure of blood pressure. Push is identified for all says of matter yet is particularly important when pointing out fluids.

Figure 1. (a) when the human being poked v the finger can be irritated, the pressure has tiny lasting effect. (b) In contrast, the same force used to one area the dimension of the sharp finish of a needle is an excellent enough to rest the skin.

### Example 1. What pressure Does a push Exert?

An astronaut is working exterior the International an are Station wherein the atmospheric pressure is essentially zero. The push gauge on she air tank reads 6.90 × 106 Pa. What pressure does the air within the tank exert top top the flat finish of the cylindrical tank, a decaying 0.150 m in diameter?

Strategy

We can find the force exerted from the meaning of pressure offered in P=\fracFA\\, noted we can find the area A acted upon.

Solution

By rearranging the an interpretation of pressure to resolve for force, we check out that

F = PA

Here, the push P is given, as is the area the the finish of the cylinder A, given by π r2. Thus,

\beginarraylllF& =& \left(6.90\times \text10^6\textN/m^2\right)\left(3.14\right)\left(0.0750 \text m\right)^2\\ & =& 1.22\times \text10^5\text N\endarray\\.

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Discussion

Wow! No wonder the tank must be strong. Because we found F = PA, we check out that the pressure exerted through a pressure is straight proportional come the area acted upon and the pressure itself.

The force exerted on the finish of the tank is perpendicular come its within surface. This direction is due to the fact that the force is exerted through a revolution or stationary fluid. We have already seen that fluids cannot withstand shearing (sideways) forces; they cannot exert shearing forces, either. Fluid pressure has no direction, gift a scalar quantity. The forces because of pressure have well-defined directions: lock are constantly exerted perpendicular to any surface. (See the tire in number 2, for example.) Finally, note that pressure is exerted on every surfaces. Swimmers, and also the tire, feel pressure on all sides. (See number 3.)