Pressure

LEARNING OBJECTIVES

By the end of this section, you will be able to:

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

You have no doubt heard the word pressure being used in relation to blood (high or low blood pressure) and in relation to the weather (high- and low-pressure weather systems). These are only two of many examples of pressures in fluids. Pressure P𝑃 is defined as

P=FA𝑃=𝐹𝐴

11.6

where F𝐹 is a force applied to an area A𝐴 that is perpendicular to the force.

PRESSURE

Pressure is defined as the force divided by the area perpendicular to the force over which the force is applied, or

P=FA.𝑃=𝐹𝐴.

11.7

A given force can have a significantly different effect depending on the area over which the force is exerted, as shown in Figure 11.5. The SI unit for pressure is the pascal, where

1 Pa=1N/m2.1 Pa=1N/m2.

11.8

In addition to the pascal, there are many other units for pressure that are in common use. In meteorology, atmospheric pressure is often described in units of millibar (mb), where

100 mb=1×104Pa .100 mb=1×104Pa .

11.9

Pounds per square inch (lb/in2orpsi)lb/in2orpsi is still sometimes used as a measure of tire pressure, and millimeters of mercury (mm Hg) is still often used in the measurement of blood pressure. Pressure is defined for all states of matter but is particularly important when discussing fluids.

Figure 11.5 (a) While the person being poked with the finger might be irritated, the force has little lasting effect. (b) In contrast, the same force applied to an area the size of the sharp end of a needle is great enough to break the skin.

EXAMPLE 11.2

Calculating Force Exerted by the Air: What Force Does a Pressure Exert?

An astronaut is working outside the International Space Station where the atmospheric pressure is essentially zero. The pressure gauge on her air tank reads 6.90×106Pa6.90×106Pa. What force does the air inside the tank exert on the flat end of the cylindrical tank, a disk 0.150 m in diameter?

Strategy

We can find the force exerted from the definition of pressure given in P=FA𝑃=𝐹𝐴, provided we can find the area A𝐴 acted upon.

Solution

By rearranging the definition of pressure to solve for force, we see that

F=PA.𝐹=PA.

11.10

Here, the pressure P𝑃 is given, as is the area of the end of the cylinder A𝐴, given by A=πr2𝐴=πr2. Thus,

F==(6.90×106N/m2)(3.14)(0.0750 m)21.22×105N.𝐹=6.90×106N/m23.140.0750 m2=1.22×105N.

11.11

Discussion

Wow! No wonder the tank must be strong. Since we found F=PA𝐹=PA, we see that the force exerted by a pressure is directly proportional to the area acted upon as well as the pressure itself.

The force exerted on the end of the tank is perpendicular to its inside surface. This direction is because the force is exerted by a static 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, being a scalar quantity. The forces due to pressure have well-defined directions: they are always exerted perpendicular to any surface. (See the tire in Figure 11.6, for example.) Finally, note that pressure is exerted on all surfaces. Swimmers, as well as the tire, feel pressure on all sides. (See Figure 11.7.)

Figure 11.6 Pressure inside this tire exerts forces perpendicular to all surfaces it contacts. The arrows give representative directions and magnitudes of the forces exerted at various points. Note that static fluids do not exert shearing forces.

Figure 11.7 Pressure is exerted on all sides of this swimmer, since the water would flow into the space he occupies if he were not there. The arrows represent the directions and magnitudes of the forces exerted at various points on the swimmer. Note that the forces are larger underneath, due to greater depth, giving a net upward or buoyant force that is balanced by the weight of the swimmer.