# Pressure in a fLuid

A fluid exerts a force perpendicular to any surface in contact with it, such as a container wall or a body immersed in the fluid. This is the force that you feel pressing on your legs when you dangle them in a swimming pool. Even when a fluid as a whole is at rest, the molecules that make up the fluid are in motion; the force exerted by the fluid is due to molecules colliding with their surroundings. Imagine a surface within a fluid at rest. For this surface and the fluid to remain at rest, the fluid must exert forces of equal magnitude but opposite direction on the surface’s two sides. Consider a small surface of area dA centered on a point in the fluid; the normal force exerted by the fluid on each side is dF# (Fig. 12.2). We define the pressure p at that point as the normal force per unit area—that is, the ratio of dF to dA (Fig. 12.3):

If the pressure is the same at all points of a finite plane surface with area A, then

where F_{1} is the net normal force on one side of the surface. The SI unit of pressure is the pascal, where

1 pascal = 1 Pa = 1 N/m^{2}

We introduced the pascal in Chapter 11. Two related units, used principally in meteorology, are the bar, equal to 105 Pa, and the millibar, equal to 100 Pa. Atmospheric pressure pa is the pressure of the earth’s atmosphere, the pressure at the bottom of this sea of air in which we live. This pressure varies with weather changes and with elevation. Normal atmospheric pressure at sea level (an average value) is 1 atmosphere (atm), defined to be exactly 101,325 Pa. To four significant figures,

**Caution** Don’t confuse pressure and force In everyday language “pressure” and “force” mean pretty much the same thing. In fluid mechanics, however, these words describe very different quantities. Pressure acts perpendicular to any surface in a fluid, no matter how that surface is oriented (Fig. 12.3). Hence pressure has no direction of its own; it’s a scalar. By contrast, force is a vector with a definite direction. Remember, too, that pressure is force per unit area. As Fig. 12.3 shows, a surface with twice the area has twice as much force exerted on it by the fluid, so the pressure is the same.

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