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

Now it’s time to discuss few other types of
fluid machines such as centrifugal compressors, axial flow
compressors, fans and blowers where working fluid will be steam, air or
gases.

We have already seen the working
principle of centrifugal compressor, velocity
diagram of centrifugal compressor and slip phenomenon and slip factor for
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 secured there the work done on air in centrifugal
compressor.

Today we will be interested here to discuss a very
important criteria i.e. Mach number for centrifugal compressor with the help of
this post.

### Mach number for centrifugal compressor

Mach number is basically a dimensionless number
which is used to specify the flow in all types of machines that handles the
compressible fluid.

Mach number is basically defined as the ratio of
flow velocity to the velocity of sound related to the fluid flow at the state
of the fluid. It is indicated by Ma.

Mach number is very much dependent over the state of
fluid. State of fluid indicates the density and temperature of the fluid.

Mach number = Flow velocity /velocity of sound

Ma = V/a

Where,

Ma = Mach number

V = Flow velocity

a= Velocity of sound

### Now we will classify the types of flow on the basis of Mach number

When flow velocity is equal to the velocity of
sound, Mach number will be one and such flow will be termed as sonic flow.

When flow velocity is less than the velocity of
sound, Mach number will be less than one and such flow will be subsonic
flow.

When flow velocity is more than the velocity of
sound, Mach number will be greater than one and such flow will be supersonic
flow.

### Things to remember –

Sonic flow, V = a or Ma = 1

Subsonic flow, V < a or Ma < 1

Supersonic flow, V > a or Ma > 1

Incompressible flow, Ma < 0.3

Subsonic flow, V < a or Ma < 1

Supersonic flow, V > a or Ma > 1

Incompressible flow, Ma < 0.3

We have mentioned above incompressible flow.
Incompressible fluid flow indicates that density will not be changing with
respect to pressure. In case, if density is changing with respect to pressure
then it will be negligible and could be neglected and considered that density
of fluid is constant with respect to pressure.

If flow is supersonic i.e. Mach number is greater
than one, there will be some losses in the static pressure of the centrifugal
compressor and these losses will not be desirable and therefore a compressor
designer has to be very careful to avoid the unnecessary increment in Mach
number.

### Important Notes:

In above equation of mach number i.e. Ma = V/a,
V is the velocity of flow. Velocity of flow here is the velocity related to the
solid surface. In a turbo machine, solid surface is also moving and therefore
relative velocity of the fluid will be considered to determine the Mach number
in turbo machine i.e. centrifugal compressor.

Mach number = Relative velocity of fluid flow
/velocity of sound

Ma = V

_{r}/a
Mach number must be less than 1 to secure the
subsonic flow in order to avoid the losses in the static pressure of the
centrifugal compressor. A centrifugal compressor designer will determine the
Mach number for each and every section of the compressor.

Fluid flowing through centrifugal compressor will
gain the kinetic energy from the impeller and therefore velocity of fluid flow
will be high at the outlet of the impeller. Hence, Mach number will be maximum
at the outlet of the impeller tip.

In order to restrict the Mach number at the outlet
of impeller tip where it will be maximum, we need to check the mach number at
the inlet of the impeller tip. Therefore inlet design of centrifugal compressor
will be carried out in such a way that mach number at the inlet of the impeller
tip will be relatively low.

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### Reference:

Fluid mechanics, By Prof S.K. Som

Image courtesy: Google

Image courtesy: Google

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