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Chapter Five: FLOW PROCESSES

5-1 FIRST LAW OF THERMODYNAMICS APPLIED TO OPEN SYSTEMS
Let us consider an open system as shown in Fig.(5.1) having inlet at section 1–1 and outlet at section 2–2. The cross-section area, pressure, specific volume, mass flow rate, energy at section 1–1 and 2–2 are
Section 1–1 = A1, p1, v1, m1, e1
Section 2–2 = A2, p2, v2, m2, e2
Open system is also having heat and work interactions Q, W as shown in figure above. Applying the energy balance at the two sections, it can be given as,
Energy added to the system + Stored energy of the fluid at inlet = Stored energy of the fluid at outlet
Quantifying the various energies;
Energy of fluid at inlet shall comprise of stored energy and flow energy as given here.
= m1(e1 + p1v1)
Similarly, energy of fluid at outlet shall comprise of stored energy and flow energy,
= Stored energy + Flow energy
= m2 (e2 + p2v2)
The energy added to the system shall be the net energy interaction due to heat and work interactions.
= Q – W
Writing energy balance, mathematically;
Q – W + m1 (e1 + p1v1) = m2 (e2 + p2v2)
or Q + m1(e1 + p1v1) = W + m2(e2 + p2v2)
If the mass flow rates at inlet and exit are same, then
Q + m(e1 + p1v1) = W + m(e2 + p2v2)
On unit mass basis
q + e1 + p1v1 = w + e2 + p2v2
Thus,
Heat + (Stored energy + Flow energy)1 = Work + (Stored energy + Flow energy)2
Stored energy at inlet and outlet can be mathematically given as,

and

where V1 and V2 are velocities at inlet and exit, u1 and u2 are internal energy at inlet and outlet, z1 and z2
are elevations of inlet and exit.

5-2 STEADY FLOW SYSTEMS AND THEIR ANALYSIS

Steady flow refers to the flow in which its properties at any point remain constant with respect to time. Steady system is the system whose properties are independent of time, i.e. any property at a point in system shall not change with time.
Let us take an open system having steady flow. Figure (5-2) shows steady
flow system having inlet at section 1–1, outlet at section 2–2, heat addition Q and work done by the system W.