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Elementary Theory of Centrifugal Pump

The document discusses the elementary theory of centrifugal pumps. It explains that within the pump, fluid velocity has three components: radial, tangential, and axial. The velocity can be written as a function of these components. The document further discusses velocity triangles at the pump inlet and outlet, which illustrate the tangential and absolute fluid velocities. It also covers how pump performance is affected by the blade angles at the inlet and outlet. The document concludes by defining concepts like shaft torque, angular momentum, and Euler turbomachine equation which relate to the energy transfer within the pump from the shaft to the rotor and fluid.

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101 views17 pages

Elementary Theory of Centrifugal Pump

The document discusses the elementary theory of centrifugal pumps. It explains that within the pump, fluid velocity has three components: radial, tangential, and axial. The velocity can be written as a function of these components. The document further discusses velocity triangles at the pump inlet and outlet, which illustrate the tangential and absolute fluid velocities. It also covers how pump performance is affected by the blade angles at the inlet and outlet. The document concludes by defining concepts like shaft torque, angular momentum, and Euler turbomachine equation which relate to the energy transfer within the pump from the shaft to the rotor and fluid.

Uploaded by

PIEAS
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Elementary Theory of Centrifugal Pump

2nd Lecture

Elementary Theory of Centrifugal Pump


At any point with in the blade passages, the
fluid velocity will in general have three
components:
Radial
Tangential
Axial
The velocity may then be written as a function
of the three components:
V = (r, , z)

Elementary Theory of Centrifugal Pump


contd

Elementary Theory of Centrifugal Pump


contd

Elementary Theory of Centrifugal Pump


contd
From assumptions 1 & 2, the velocity
becomes a function of radius only i.e.
V = (r)
Energy transferred will be determined by
velocity triangle drawn at the inlet and
outlet.

Elementary Theory of Centrifugal Pump


contd
Refer to velocity triangle figure, the blades
are curved between the inlet radius r1 and
outlet radius r2. A particle of fluid moving
along the broken curve is shown. Let:
1 and 2 be the angle subtended by the
blade at inlet and outlet, measured from
the tangent to the inlet and outlet radius.

Elementary Theory of Centrifugal Pump


contd
C1 and C2 is the absolute velocity of fluid
entering at the eye of the impeller and at
exit respectively.
U1 and U2 are tangential velocity of the
blade tip, can be denoted by r1 and r2,
where is the angular velocity of the
impeller

Elementary Theory of Centrifugal Pump


contd
1 and 2 are the angles between the

absolute velocity C1 and C2, and tangential


velocity U1 and U2.
It is seen that the blade angles at inlet and
outlet (1 and 2) are not equal to their
respective relative flow angles (1 and 2).
This affects the pump performance and will
be discussed in a subsequent section. For
this case we assume that 1 and 2 are equal
to 1 and 2.

Elementary Theory of Centrifugal Pump


contd
All of the turbomachines involve the rotation of an

impeller or a rotor about a central axis, it is appropriate


to discuss their performance in terms of torque and
angular momentum.
If the shaft torque (the torque that the shaft applies to
the rotor) and the rotation of the rotor are in the same
direction, energy is transferred from the shaft to the
rotor and from the rotor to the fluidthe machine is a
pump.

Elementary Theory of Centrifugal Pump


contd
Conversely, if the torque exerted by the shaft on the

rotor is opposite to the direction of rotation, the energy


transfer is from the fluid to the rotora turbine.
The amount of shaft torque (and, hence, shaft work)
can be obtained from the moment-of-momentum
equation i.e.

Elementary Theory of Centrifugal Pump


contd
For steady flow, the term

Therefore, the moment of momentum equation

becomes

Elementary Theory of Centrifugal Pump


contd
From velocity triangle figure, the sum of all torque

acting on the system is equal to the rate of change of


angular momentum, therefore,
= (r2Cx2 r1Cx1 )
This equation is often called the Euler turbomachine
equation.
Shaft torque is directly proportional to the mass flow

rate and it also depends on the tangential component


of the absolute velocity, Cx.

Elementary Theory of Centrifugal Pump


contd
For a rotating shaft, the power transferred

is given by

For a machine revolving at an angular velocity of

=U/r
after simplifying, the power transferred becomes
=

Elementary Theory of Centrifugal Pump


contd
= QE
hence,
QE =
E=

/ Q

Where
= g &

= Q , then

This is known as Euler head, or theoretical head some times

ideal head developed by the impeller only.

Questions?

Questions?

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