Unformatted text preview: n the υ dP in these relations and P dυ is striking.
They should not be confused with each other, however, since P dυ is associated with reversible boundary work in closed systems (Fig. 7–41).
Obviously, one needs to know υ as a function of P for the given process to
perform the integration. When the working fluid is an incompressible fluid,
the specific volume υ remains constant during the process and can be taken
out of the integration. Then Eq. 7–51 simplifies to
wrev υ (P2 P1) ke pe (kJ/kg) P1) 2
1 2 g(z2 z1) 0 ∫ wrev = – υ dP
1 (a) Steady-flow system wrev (7–54) For the steady flow of a liquid through a device that involves no work interactions (such as a nozzle or a pipe section), the work term is zero, and the
equation above can be expressed as
υ (P2 wrev (7–55) which is known as the Bernoulli equation in fluid mechanics. It is developed
for an internally reversible process and thus is applicable to incompressible
fluids that involve no irreversibilities such as friction or shock waves. This
equation can be modified, however, to incorporate these effects.
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