Page 410 - Introduction to Continuum Mechanics

394 Irrotational Flows as Solutions of Navier-Stokes Equation

Solution. For a point on the free surface such as the point A, p -p 0, v « 0 and z = h.
Therefore, from Eq. (6.21.9)

At a point on the exit jet, such as the point 5, z = 0 and/? = p 0. Thus,

from which

This is the well known Torricelli's formula.

Fig. 6.13

6.22 Irrotational Flows as Solutions of Navier-Stokes Equation

For an incompressible Newtonian fluid, the equations of motion are the Navier-Stokes
equations:

For irrotational flows