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

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

### 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

### 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 u2
Ïƒ =Â VÏ‰2Â /Â u2

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

### 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

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Further we will find out, in our next post,Â mach number for centrifugal compressor.Â

### Reference:Â Â

Fluid mechanics, By R. K. BansalÂ