Derive energy transfer equation for rotating machine
Answers
Answer:
Energy transfer in turbomachines
•
The impulse momentum equation is used to study the impact offluid jet striking a stationary or moving plate and also to studygeneral fluid flow characteristics.
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When the flowing fluid with initial velocity
V
1
is
obstructed by asurface such as vane, blade etc., the fluid undergoes a change inmomentum. The impulsive force acting on the fluid by the surfaceis:
•
According to Newton’s third law of motion –
for every action there isequal and opposite reaction. Therefore, the fluid reacts to this andexerts equal and opposite force on the obstructing surface, given by
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Similarly, the sum of all torques acting on the system is equal to therate of change of angular momentum.
Explanation:
Energy transfer components
•
Let
V
be the
absolute
velocity of the fluid entering the rotorat
1
at any angle. This velocity vector may be resolved into
three mutually perpendicular components:
•
Axial component
V
a
•
Radial component
V
r
•
Tangential component
V
w
•
Axial component :
This is parallel to the axis of rotation.Axial force is produced due to change in magnitude of thiscomponent. This axial force is taken by the thrust bearing
of the machine which is finally transferred to the housing.
•
Radial component :
This
is parallel to the radius of therotor. Radial force is produced due to change in themagnitude of this component. Radial forces are taken byjournal bearings.
•
It should be noted that no torque is exerted on the rotor bythese two forces, i.e., axial and radial.