Page 29 - Mechanical Engineers Reference Book

1/18 Mechanical engineering principles

in general, take the shape of its container. At rest a fluid is not
able to sustain shear forces.
Some ‘solids’ may flow over a long period (glass window
panes thicken at the base after a long time in a vertical
0 position). The substances considered in fluid mechanics are
those which are continously fluid.
Fluid mechanics is a study of the relationships between the
effects of forces, energy and momentum occurring in and
around a fluid system. The important properties of a fluid in
fluid mechanics terms are density, pressure, viscosity. surface
tension and, to some extent, temperature, all of which are
intensive properties.
Density is the mass per unit volume of the substance.
Pressure is the force per unit area exerted by the fluid on its
boundaries. Viscosity is a measure of the fluid’s resistance to
flow and may be considered as internal friction. The higher the
coefficient of viscosity, the greater the resistance. Surface
0 w tension is a property related to intermolecular attraction in the
free surface of a liquid resulting in the apparent presence of a
Figure 1.32 Wide-band process very thin film on the surface. The meniscus at the intersection
of a liquid and its container wall and capillarity are further
examples of intermolecular attraction.
Temperature is more relevant to thermodynamics than to
fluid mechanics. It indicates the state of thermal equilibrium
between two systems or, more loosely, the level of thermal
energy in a system.

1.5.2 Fluid statics
1.5.2.1 Pressure at a depth
s(w’ t The variation of pressurep and depth h in a fluid of density p is
given by
ir dp = I” pgdh (1.5)

Most liquids are assumed to be of constant density p. In such a
liquid the pressure at a depth h below a free surface is given by
-00 0 +00 w
P = Po + Pgh (1.6)
Figure 1.33 Narrow-band process where po is the pressure above the free surface.
For gases equation (1.5) may be solved only if the relation-
Further reading ship between p and h is known. A typical case is the atmos-
phere, where the relationship may be taken as polytropic or
Crandall, S. H., Random Vibration, Technology Press and John isothermal, depending on the altitude. Tables relating the
Wiley, Chichester (1958) properties of the atmosphere to altitude are readily available
Crandall, S. H. and Mark, W. D., Random Vibration in as the International Atmosphere (Rogers and Mayhew, 1980).
Mechanical Systems, Academic Press, London (1963)
Robson, J. D., An Introduction to Random Vibration, Edinburgh
University Press (1963)
Davenport,.W. B., ‘Probability and Random Processes, McGraw- 1.5.2.2 Pressure measurement
Hill, New York (1970)
Nigam, N. C., Introduction to Random Vibrations, MIT Press Pressure may be expressed as a pressure p in Pa, or as a
(1983) pressure head h in m of the fluid concerned. For a fluid of
Niwland, D. E., An Introduction to Random Vibrations and density p, p = pgh. There are various instruments used to
Spectral Analysis, second edition, Longman, Harlow (1984)
Helstrom, C. W., Probability and Stochastic Processes for measure pressure.
Engineers, Macmillan, London (1984)
Piszek, K. and Niziol, J., Random Vibration of Mechanical (a) Manometers Manometers are differential pressure-
Systems, Ellis Horwood, Chichester (1986). measuring devices, based on pressure due to columns of fluid.
A typical U-tube manometer is shown in Figure 1.34(a). The
difference in pressure between vessel A containing a fluid of
density PA and vessel B containing fluid of density p~ is given by
1.5 Mechanics of fluids
PA - PB = hgzB + (Pm - PBkh - P&zA (1.7)
1.5.1 Introduction
where h is the difference in the levels of the manometer fluid
Fluid is one of the two states in which matter can exist, the of density pm and pm > PA and pm > p~. PA = p~ = p, then
If
other being solid. In the fluid state the matter can flow; it will, the difference in pressure head is