Steady Flow Energy Equation

Steady Flow Energy Equation

From first law of Thermodynamics, we know that the total energy entering the system is equal to total energy leaving the system. This law is applicable to the steady flow systems.

Consider an open system-through which the working substance flows as a steady rate. The working substance entering the system at (1) and leaves the system at (2). Let,

P₁- Pressure of the working substance entering the system (N/m²)

V₁- Specific volume  of the working substance entering  the system (m3/kg)

C₁- Velocity of the, working substance entering  the system (m/s)

U₁ - Specific internal energy of the working substance entering the system (Jlkg)

Z₁ - Height above the datum level for inlet in (m).

P2, v2 , c2, U2 and Z2 - Corresponding  values for the working substance leaving the system. 

Q - Heat supplied  to the system (J/kg)

W - Work delivered by the system (J/kg).

Total energy entering the system = Potential energy (gZ₁) + Kinetic energy (c₁²/2)

+ Internal energy (U₁) + Flow energy (p₁ v₁) + Heat (Q)

Total energy leaving the system = Potential energy (gZ₂) + Kinetic energy (c₂²/2)

+ Internal energy (U₂) + Flow energy (p₂ v₂) + Work (W)

From first law of Thermodynamics,

Total energy entering the system = Total energy leaving the system

gZ₁ + (c₁²/2) + U₁ + p₁ v₁ + Q = gZ₂ + (c₂²/2) + U₂+ p₂ v₂ + W

gZ₁ + (c₁²/2) + h₁ +Q = gZ₂ + (c₂²/2) + W

[ i.e h = U + pv]

The above equation is known as steady flow energy equation.