Consider an open system through in which the working substance flows as a steady rate as shown in figure. The working substance entering the system at (1) and leaving the system at (2).

Let, **p1** be the pressure of the working substance entering the system **(N/m²)**

**v1** be the specific volume of the working substance entering the system in **m³/kg**.

**C1** be the velocity of the working substance entering the system

**u1** be the specific internal energy of the working substance entering the system in **J/kg.**

**z1** be the height above the datum level for inlet in **m**

**p2,v2,C2, u2** and **z2** are corresponding values for the working substance leaving the system.

**Q** be the heat supplied to the system in **J/kg**

**W** be the work delivered by the system in **J/kg**

∴ Total energy entering the system,

\begin{array}{l} =P \cdot E+K \cdot E+I \cdot E+F \cdot E+\text { Heat energy } \\ =g z_{1}+\frac{C_{1}^{2}}{2}+u_{1}+p_{1} v_{1}+Q \end{array}Total energy leaving the system,

=P . E+K . E+I E+F \cdot E+\text { Work } =g z_{2}+\frac{C_{2}^{2}}{2}+u_{2}+p_{2} v_{2}+WBy first law of thermodynamics,

Total energy entering the system = Total energy leaving the system

\begin{array}{c} g z_{1}+\frac{C_{1}^{2}}{2}+u_{1}+p_{1} v_{1}+Q=g z_{2}+\frac{C_{2}^{2}}{2}+u_{2}+p_{2} v_{2}+W \\ {[\because h=u+p v]} \\ \qquad g z_{1}+\frac{C_{1}^{2}}{2}+h_{1}+Q=g z_{2}+\frac{C_{2}^{2}}{2}+h_{2}+W \end{array}The above equation is known as steady flow energy equation **(SFEE)**. The above equation represents the energy flow per unit of mass of the working substance **(J/kg)**. When the equation is multiplied by mass of the working substance throughout, then all terms will represent the energy flow per unit time. (in **J/s**) Then the above equation becomes.

If the values of Q and W in kJ/kg, and h1 and h2 are substituted in kJ/kg, then the above equation becomes,

m\left(\frac{g z_{1}}{1000}+\frac{C_{1}^{2}}{2000}+h_{1}+Q\right)=m\left(\frac{g z_{2}}{1000}+\frac{C_{2}^{2}}{2000}+h_{2}+W\right)If Q and W are already kW, and h1 and h2 are substituted in kJ/kg, then the above equation becomes,

m\left(\frac{g z_{1}}{1000}+\frac{C_{1}^{2}}{2000}+h_{1}\right)+Q=m\left(\frac{g z_{2}}{1000}+\frac{C_{2}^{2}}{2000}+h_{2}\right)+W* Note :* In a steady flow system, the mass rate of the working substance is given by

*where,*

The mass is represented in **kg/s**.

**A1** and **A2** are areas of cross section at entry and exit in **m²**.

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