General energy equation for transfer of energy between fluid and machine

Q.  What is the general energy equation for transfer of energy between the fluid and machine?

Where,
Vw1 = Tangential component of the velocity of fluid at the entry of the rotor
Vw2 = Tangential component of the velocity of fluid at the exit of the rotor
u1 = Peripheral velocity of fluid at the entry of the rotor
u2 = Peripheral velocity of fluid at the exit of the rotor
ṁ = Flow rate of fluid
- Published on 16 Sep 15

a. E = ṁ (Vw1 – Vw2) x (u1 – u2)
b. E = ṁ (Vw1 – Vw2) / (u1 – u2)
c. E = ṁ (Vw1 u1 – Vw2 u2)
d. E = ṁ (Vw1 u1 – Vw2 u2)2

ANSWER: E = ṁ (Vw1 u1 – Vw2 u2)

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    Discussion

  • Pankaj   -Posted on 06 Oct 15
    In case of a turbine, the torque produced by the fluid on rotor is used in producing useful work or developing power.

    Therefore, rate of energy transfer can be given by,

    Power = Torque x Angular velocity of rotor

    E = T x ω

    E = ṁ ((Vw1 x r1) – (Vw2 x r2)) x ω

    But peripheral velocity of the fluid at inlet and outlet can be given as,

    u = ω r

    Therefore,

    E = ṁ ((Vw1 x u1) – (Vw2 x u2))

    The equation represents the general energy equation for transfer of energy between the fluid and machine.

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