Steady Flow Energy Equation

Steady Flow

Steady flow the flow of fluid in which the properties of the fluid does not vary with time but can be varied w.r.t. space co-ordinates. All the open system are studied by using steady flow energy equation. Most of the engineering devices are assumed to have steady flow.

Let us consider an open system

Let point (1) denote inlet and point (2) denote outlet.

2

Let P = Pressure in N/m

3

𝑣 = Specific volume in m/Kg

u = Specific internal

V = velocity in m/s

Z = Datum height in m

Q = Heat supplied at inlet in J/Kg

W = Work obtained in J/Kg

Where subscripts 1 and 2 denotes the conditions at inlet and outlet respectively.

Fig. open system

The specific energy at inlet = K.E. + P.E. + I.E. + Heat input + Flow energy

We know that

Flow energy = Pressure × Volume

2

Specific energy at inlet = (½)V₁ +gZ₁+u₁+Q₁₋₂+P₁× 𝑣₁

2

= (½)V₁ +gZ₁+h₁+ Q₁₋₂ -----(1)

The specific energy at outlet = K.E. + P.E. + I.E. + Work transfer + Flow energy

2

Specific energy at outlet = (½)V₂ +gZ₂+u₂+W₁₋₂+P₂× 𝑣₂

2

= (½)V₂ +gZ₂+h₂+ W₁₋₂ -----(2)

From 1st Law of Thermodynamics

Energy at inlet = Energy at outlet

2 2

(½)V₁ +gZ₁+h₁+ Q₁₋₂ = (½)V₂ +gZ₂+h₂+ W₁₋₂ -----(3)

This equation is applicable for per unit mass and if the effect of mass is also to be considered then eq.(3) must be multiplied by mass.

2 2

(½)mV₁ +mgZ₁+mh₁+ mQ₁₋₂ = (½)mV₂ +mgZ₂+mh₂+ mW₁₋₂ -----(4)