Steady flow means that the rates of flow of mass and energy across the control surface is constant.
Steady-state steady flow (SSSF) refers to all mass flow rates and all thermodynamic states remain steady and do not vary with time.
Thus (dm / dt )cv = 0, (de / dt)cv =0
So equation (5.2) becomes
Σ m out = Σ m in = m (say)
Q + m( h+v2 /2 + gz) in = m ( h + v2 /2 + gz) out + w
Let q = Q / m and w = W /m we have
Q + ( h +v2 /2 + gz ) in = ( h+ v2 / 2 + gz)out + w
Unit of q = Q /m = KJ /s / kg /s = kj / kg
Unit of w = W/ m = kj/s / kg/s = kj / kg
Thus q and w can be thought of as the heat transfer and flow work per unit mass
flowing into and out of the control volume for this particular SSSF process.
Equation (5.8) is known as steady-state steady flow energy equation.
Equation (5.9) can be written in differential form as
dq = dh + vdv + gdz + dw