Adiabatic: q = 0
Steady:_{}_{}
No body forces: P.E. = 0
No work done except that of
expansion: _{}
= 0
If
all of the above are true,
_{}
^{ }
^{so}
^{ }
_{}^{is a constant.}^{ }
Stagnation
enthalpy is constant along a streamline in steady adiabatic flow, where body
forces are negligible and the only work is that of expansion.
Energy
Equation for Steady OneDimensional Flow
Consider
an engine represented by a control volume as shown below. Fluid enters from the
left at the rate of _{}per unit time, and
leaves from the right boundary. Work_{}
is extracted from the
fluid per unit mass flow rate, and heat
_{}is added to the fluid
per unit mass flow rate.

Neglect
changes in potential energy of the fluid. Assume that steadystate conditions
exist, so that time derivatives are zero in the frame of reference moving with
the control volume. Ignore variations across the streamlines, so that integrals
such as _{}can be replaced by _{}.Thus, the energy
equation reduces to
_{}
or
_{}
Note:
Stagnation
enthalpy increases when heat is added, and decreases when work is taken out.