Steady flow energy equation and Bernoulli Equation

Vishal Gautam
2 min readApr 15, 2021

Steady flow energy equation :

For steady flow energy equation , Consider a control volume, in which mass ∆m1/∆t enters through inlet with parameters

U = internal energy

v = Velocity

V = specific volume ( V1 = V2 )

P = pressure

Z= potential head

Control Volume

Similarly mass ∆m2/∆t exits through outlet.

Therefore mass concentrationin control volume is

(∆m/∆t) control volume = ∆m1/∆t — ∆m2/∆t

•(∆E/∆t) in = internal energy+ flow work + kinetic energy+ potential energy + heat

Therefore , (∆E/∆t) in = ∆m1/∆t { U1 + P1V1 + v12/2 + gZ1 } + ∆Q/∆t

At exit , (∆E/∆t)out = ∆m2/∆t { U2 + P2V2 + v2 2/2 + gZ2 } + ∆W/∆t

(E/∆t) control volume= (∆E/∆t)in — (∆E/∆t)out

(E/∆t) control volume= ∆m1/∆t { h1 + v12/2 + gZ1 } + ∆Q/∆t — ∆m2/∆t { h2 + v2 2/2 + gZ2} — ∆W/∆t

Assumptions :

• (∆m/∆t) control volume = 0

• (E/∆t) control volume= 0

Here , (∆m/∆t) control volume = ∆m1/∆t — ∆m2/∆t = 0

So , ∆m1/∆t = ∆m2/∆t = m

Similarly,

(∆E/∆t)in = (∆E/∆t)out

Therefore ,

m{ h1 + v12/2 + gZ1 } + ∆Q/∆t = m{ h2 + v2 2/2 + gZ2 } + ∆W/∆t

this is Steady flow energy equation or SFEE .

For More Visit : https://mechomotive.com/steady-flow-energy-equation-and-bernoulli-equation/

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Vishal Gautam
Vishal Gautam

Written by Vishal Gautam

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