Page 367 - Introduction to Continuum Mechanics

Newtonian Viscous Fluid 351

Equations (6.3.4a, b) state that/? is a function of x^ alone and Eq. (6.3.4c) gives the pressure
difference between point 2 and point 1 in the liquid as

where h is the depth of point 2 relative to point 1. Thus, the static pressure in the liquid depends
only on the depth. It is the same for all particles that are on the same horizontal plane within
the same fluid.
If the fluid is in a state of rigid body motion (rate of deformation = 0), then Ty is still given
by Eq. (6.1.1), but the right hand side of Eq. (6.3.1) is equal to the acceleration a/, so that the
governing equation is given by

Example 6.3.1
A cylindrical body of radius r, length / and weight W is tied by a rope to the bottom of a
container which is filled with a liquid of density p (Fig. 6.1). If the density of the body p is less
than that of the liquid, find the tension in the rope.