Pressure

At any point in a fluid, whether liquid or gas, there is a pressure. If a body is placed in a fluid, its surface is bombarded by a large number of molecules moving at random. Under normal conditions the collisions on a small area of surface are so frequent that they cannot be distinguished as individual impacts. They appear as a steady force on the area. The intensity of this ‘molecular bombardment’ force is the static pressure.

Very frequently the static pressure is referred to simply as pressure. The term static is rather misleading. Note that its use does not imply the fluid is at rest.

For large bodies moving or at rest in the fluid, e. g. air, the pressure is not uni­form over the surface and this gives rise to aerodynamic force or aerostatic force respectively.

Since a pressure is force per unit area, it has the dimensions

[Force] + [area] = [MLT-2] [L2] = [ML-1T-2]

and is expressed in the units of Newtons per square metre or Pascals (Nm’2 or Pa).

Pressure in fluid at rest

Consider a small cubic element containing fluid at rest in a larger bulk of fluid also at rest. The faces of the cube, assumed conceptually to be made of some thin flexible material, are subject to continual bombardment by the molecules of the fluid, and thus experience a force. The force on any face may be resolved into two components, one acting perpendicular to the face and the other along it, i. e. tangential to it. Consider for the moment the tangential components only; there are three signifi­cantly different arrangements possible (Fig. 1.1). The system (a) would cause the element to rotate and thus the fluid would not be at rest. System (b) would cause the element to move (upwards and to the right for the case shown) and once more, the fluid would not be at rest. Since a fluid cannot resist shear stress, but only rate of change of shear strain (Sections 1.2.6 and 2.7.2) the system (c) would cause the element to distort, the degree of distortion increasing with time, and the fluid would not remain at rest.

The conclusion is that a fluid at rest cannot sustain tangential stresses, or con­versely, that in a fluid at rest the pressure on a surface must act in the direction perpendicular to that surface.

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