We were discussing the
basic principle of operations, functions of various parts and performance
characteristics ofÂ different types of fluid machines such asÂ hydraulic
turbines,Â centrifugal
pumpsÂ andÂ reciprocating
pumpsÂ in our previous posts. We have seen there that working fluid for
above mentioned fluid machines was liquid such as water.Â Â

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Ïƒ
=Â VÏ‰

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Now itâ€™s time to discuss
few other types of fluidÂ machinesÂ such as centrifugal compressors,
axial flow compressors, fans and blowers where working fluid will be steam, air
or gases.Â Â

We have already seen
theÂ working
principle of centrifugal compressorÂ and velocity diagram of centrifugal compressor in our last posts, where we were also discussing the various
important parts of centrifugal compressor and their functions and we have also
find out there the work done on air in centrifugal compressor.Â

Today we will be interested
here to discuss a very important phenomenon of centrifugal compressor i.e. slip
phenomenon and slip factor for centrifugal compressor.Â

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**Slip phenomenon and slip factor for centrifugal
compressorÂ **

When a fluid flows through
a curved vane and the vane rotates, there will be the difference in pressure at
two sides of the vane due to the combined effect of tangential flow and the
radial flow and the curved vanes.Â

In the leading edge of the
curved vane, the pressure will be high and fluid will be decelerated and in the
trailing edge of the curved vane, the pressure will be less and fluid will be accelerated.Â

Therefore, there will be a
small re-circulatory flow and it will happen in all passages and it will lead
to the non-uniform distribution of velocity.Â

Because of the development
of this small re-circulatory flow due to the difference in pressure in leading
edge and trailing edge of curved vane, there will be change in the direction of
the velocity of the fluid relative to the vane.Â

Therefore, the velocity
triangle at the outlet of impeller blade will be changed as displayed here in following
figure. Relative velocity at the outlet of the impeller blade will not be
radially outward.

Therefore, fluid will be
said to have slipped with respect to the impeller during its flow across it.Â

So, this is the phenomenon
of slip in centrifugal compressor and we must note it here that due to this phenomenon
of slip in centrifugal compressor, velocity triangle at the outlet of the
impeller blade will be changed.Â

As we can see in above
figure, dotted line diagram indicates the ideal conditions and solid line
diagram indicates the actual conditions.Â

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**Slip Factor (**Ïƒ**)Â **

Slip factor is basically defined as the
ratio of velocity of whirl at outlet to the mean blade velocity at outlet.Â

Slip factor,Â Ïƒ = Velocity of whirl at
outlet i.e.Â VÏ‰

_{2Â }/Â Mean blade velocity at outletÂ i.e.Â u_{2}_{2Â }/Â u

_{2}

Slip factor is a very
important information which is needed by compressor designed to design a
compressor with estimation of correct value of energy transfer between impeller
and fluid.Â

Stanitz found that slip
velocity does not depend upon the blade exit angle and therefore he has given
one equation to determine the slip factor and this equation is provided here as
mentioned below.Â

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**Stanitzâ€™s EquationÂ **

Slip factor, Ïƒ = 1 â€“ 0.63 Ï€/nÂ

Where, n is the number of bladesÂ

From above equation, we can conclude that
slip factor will be increased with increase in the number of blades. Slip
factor will only tend to one when number of blades tend to infinity.Â

We can also say that slip factor will be decreased
with decrease in the number of blades. Therefore, less amount of energy will be
transferred to the fluid per unit mass with decrease in number of blades.Â Â

Therefore, we can say that
slip factor depends on the number of blades and it is usually 0.9.

So, we have seen here the phenomenon
of slip in centrifugal compressor and the basic concept of slip factor also.Â

Do you have any
suggestions? Please write in comment box and also drop your email id in the
given mail box which is given at right hand side of page for further and
continuous update fromÂ www.hkdivedi.com.Â Â

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**Reference:****Â Â **

Fluid mechanics, By R. K.
BansalÂ

Image courtesy:
GoogleÂ Â Â

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