Pressure

Pressure

Consider a small rigid surface suspended in a bulk of air at rest.
The molecular motion causes molecules continually to strike, or
tend to strike, the immersed surface, so that a rate of change of
molecular momentum occurs there. This cannot have a component
parallel to the surface, or the condition of rest would be disturbed.
Thus, when the gas is apparently at rest, the aggregate rate of
change of momentum is normal to the surface ; it can be
represented by a force which is everywhere directed at right
angles towards the surface. The intensity of the force per unit
area is the pressure pt sometimes called the hydrostatic or static
pressure.

It is important to note that the lack of a tangential component to
p depends upon the condition of stationary equilibrium. The
converse statement, that fluids at rest cannot withstand a tangential
or shearing force, however small, serves to distinguish liquids from
solids. For gases we must add that a given quantity can expand to
fill a volume, however great.

It will now be shown that the pressure at a point in a fluid at rest is
uniform in all directions. Draw the small tetrahedron ABCO, of

* In this system, the units of length and time are the foot and the second, whilst
forces are in pounds weight. It is usual in Engineering, however, to omit the word ' weight/ writing

*Ib.' for 'lb.-wt.,' and this convention is followed. The
appropriate unit of mass is the 'slug,' viz. the mass of a body weighing g Ib.
Velocities are consistently measured in ft. per sec., and so on. This system being
understood, specification of units will often be omitted from calculations for brevity.
For example, when a particular value of the kinematic viscosity is given as a number,
sq. ft. per sec. will be implied. It will be desirable occasionally to introduce special
units. Thus the size and speed of aircraft are more easily visualised when weights
are expressed in tons and velocities in miles per hour. The special units will be
duly indicated in such cases. Non-dimeasional coefficients are employed wherever
convenient.