Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

the pressure difference between points 1 and 2 can be determined by inte-
gration to be

(1–21)

For constant density and constant gravitational acceleration, this relation
reduces to Eq. 1–18, as expected.
Pressure in a fluid at rest is independent of the shape or cross section of
the container. It changes with the vertical distance, but remains constant in
other directions. Therefore, the pressure is the same at all points on a hori-
zontal plane in a given fluid. The Dutch mathematician Simon Stevin
(1548–1620) published in 1586 the principle illustrated in Fig. 1–43. Note
that the pressures at points A,B,C,D,E,F, and Gare the same since they
are at the same depth, and they are interconnected by the same static fluid.
However, the pressures at points Hand Iare not the same since these two
points cannot be interconnected by the same fluid (i.e., we cannot draw a
curve from point Ito point Hwhile remaining in the same fluid at all
times), although they are at the same depth. (Can you tell at which point the
pressure is higher?) Also, the pressure force exerted by the fluid is always
normal to the surface at the specified points.
A consequence of the pressure in a fluid remaining constant in the hori-
zontal direction is that the pressure applied to a confined fluid increases the
pressure throughout by the same amount. This is called Pascal’s law,after
Blaise Pascal (1623–1662). Pascal also knew that the force applied by a
fluid is proportional to the surface area. He realized that two hydraulic
cylinders of different areas could be connected, and the larger could be used

¢PP 2
P 1 

2

1

rg dz

Chapter 1 | 25

P 1 = Patm

P 2 = Patm + rgh

h

1

2

FIGURE 1–42

Pressure in a liquid at rest increases

linearly with distance from the free

surface.

h

A B C D E

Water

Mercury

F G

H I

Patm

PA = PB = PC = PD = PE = PF = PG = Patm + rgh

PH ≠ PI

FIGURE 1–43

The pressure is the same at all points on a horizontal plane in a given fluid regardless of geometry, provided that the

points are interconnected by the same fluid.