Page 378 - Introduction to Continuum Mechanics

362 Navier-Stokes Equation For Incompressible Fluids

wherep is density and g is gravitational acceleration. The quantity h is known as the piezometric
head. Show that for a uni-direction flow in any direction, the piezometric head is a constant
along any direction which is perpendicular to the flow.

Fig. 6.4

Solution. Letjq-axis be the direction of flow, then,

Thus, from Eqs. (6.7.2 b and c)

With z-axis pointing upward, the body force per unit mass B is given by:

where e z is the unit vector in the z-direction. Thus,