Steady flow energy equation and Bernoulli Equation
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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
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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 .
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