Page 59 - Mechanical Engineers' Handbook (Volume 4)

48 Fluid Mechanics

are due to uniform linear accelerations or to centrifugal effects in rigid-body rotations, points
equidistant below the free liquid surface are all at the same pressure. Dashed lines in Figs.
1 and 2 are lines of constant pressure.
Pressure differences are the same whether all pressures are expressed as gage pressure
or as absolute pressure.

3.1 Manometers
Pressure differences measured by barometers and manometers may be determined from the
relation
p h. In a barometer, Fig. 3, h (p p )/ m.
b a v b
An open manometer, Fig. 4, indicates the inlet pressure for a pump by p h
inlet m m
y Pa gauge. A differential manometer, Fig. 5, indicates the pressure drop across an orifice,
for example, by p p h ( )Pa.
1 2 m m 0
Manometers shown in Figs. 3 and 4 are a type used to measure medium or large pressure
differences with relatively small manometer deflections. Micromanometers can be designed
to produce relatively large manometer deflections for very small pressure differences. The
relation
p
h may be applied to the many commercial instruments available to obtain
pressure differences from the manometer deflections.

3.2 Liquid Forces on Submerged Surfaces
The liquid force on any flat surface submerged in the liquid equals the product of the gage
pressure at the centroid of the surface and the surface area, or F pA. The force F is not
applied at the centroid for an inclined surface, but is always below it by an amount that
diminishes with depth. Measured parallel to the inclined surface, y is the distance from 0 in
Fig. 6 to the centroid and y y I CG /Ay, where I CG is the moment of inertia of the flat
F
surface with respect to its centroid. Values for some surfaces are listed in Table 1.
For curved surfaces, the horizontal component of the force is equal in magnitude and
point of application to the force on a projection of the curved surface on a vertical plane,
determined as above. The vertical component of force equals the weight of liquid above the
curved surface and is applied at the centroid of this liquid, as in Fig. 7. The liquid forces
on opposite sides of a submerged surface are equal in magnitude but opposite in direction.
These statements for curved surfaces are also valid for flat surfaces.
Buoyancy is the resultant of the surface forces on a submerged body and equals the
weight of fluid (liquid or gas) displaced.

Figure 1 Constant linear acceleration. Figure 2 Constant centrifugal acceleration.