Euler’s Work Equation-Turbomecines-Lecture Slides, Slides for Turbomecines. B R Ambedkar National Institute of Technology

Turbomecines

Description: Main topics for the course are how to create electricity, design of Kaplan turbine and runner, hydraulic turbines, flow momentum, Fracnis turbine, Euler work equation, ancient power resources, Pelton turbine plant, HEPP development, redial inflow turbine. This lecture includes: Euler, Work, Equation, Torque, Flow, Angular, Momentum, Shaft, Output, Whirl, Velocity, Conservation, Energy, Steady
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Euler’s Work Equation
Torque exerted by flow on blade row = shaft output torque
= Rate of change of Angular momentum of fluid =
kVjViVV rx ˆ
ˆˆ
Euler Theory:
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dt
dL
Define, L as Angular momentum
Angular momentum is moment of linear momentum of
angular velocity, V
rmVL
For a steady flow through a turbomachine:
Inlet rate of angular momentum : 11rVm
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Exit rate of angular momentum at exit: 22rVm
Change in Rate of angular momentum: 1122 rVmrVm
1122 rVrVm
Power :
1122 rVrVmP

A change Whirl Velocity of fluid is only responsible for Power
Exchange between fluid and rotor in a turbo-machine !
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This is known as Euler Turbo-machinery Equation.

1201021122 zzghhmrVrVmP

CV
CV Pgz
V
hmgz
V
hmQ
2
2
1
2
22
First Law for Steady Flow Steady State Turbo Machine:
Avoid heat transfer across surface of a turbo-machine.
CV
Pgz
V
hmgz
V
hm
2
2
1
2
22
Conservation of Energy
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