The term involving normal stress must now be presented in a more usable form. A
complete expression for sii is stated in Chapter 9. For the present, we may say simply that
the normal stress term is the sum of pressure effects and viscous effects. Just as with shear
work, the work done to overcome the viscous portion of the normal stress is unavailable
to do mechanical work.We shall thus combine the work associated with the viscous portion
of the normal stress with the shear work to give a single term, dWm/dt, the work rate
accomplished in overcoming viscous effects at the control surface. The subscript, m, is used
to make this distinction.
The remaining part of the normal stress term, that associated with pressure, may be
written in slightly different form if we recall that the bulk stress, sii, is the negative of the
thermodynamic pressure, P. The shear and flow work terms may now be written as
follows: