We were
discussing the pumps and
basic pumping system, total
head developed by the centrifugal pump, parts
of centrifugal pump and their function, heads
and efficiencies of a centrifugal pump, work
done by the centrifugal pump on water, expression
for minimum starting speed of a centrifugal pump and multistage centrifugal pumps in our previous post.

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Now we
will find out the specific speed of a centrifugal pump (N

_{S}) with the help of this post. First of all we will see here the meaning of specific speed of a centrifugal pump and further we will derive here the expression of specific speed of a centrifugal pump.

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**Specific speed of a centrifugal pump**

The specific
speed of a centrifugal pump is basically defined as the speed of a geometrical
similar pump which would deliver one cubic meter of liquid per second against a
head of one meter.

Specific
speed of a centrifugal pump will be denoted by N

_{S}.

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**Expression for specific speed of a
centrifugal pump**

As we know
that the discharge for a centrifugal pump will be given by following equation
as mentioned here.

Discharge
for a centrifugal pump = Area x velocity of flow

Q = π D B
x V

_{f}
Where,

D =
Diameter of the impeller of centrifugal pump

B = Width
of the impeller of centrifugal pump

V

_{f}= Flow velocity
From above
equation of discharge for a centrifugal pump, we can say that discharge will be
directionally proportional to the diameter of the impeller, width of the
impeller and velocity of flow.

Q ∝ D x B x V

_{f }
We can also
write above equation as mentioned here

Q ∝ D

^{2}x V_{f }
Because, D
∝ B

Now we
will recall here the equation of tangential velocity and we will write here the
following equation as mentioned here.

u = π D N
/60

u ∝ D N

Tangential
velocity (u) and velocity of flow (V

_{f}) will be related with the manometric head as written here.
u ∝ V

_{f}∝ (H_{m})^{1/2 }
Therefore,
we have two equations here i.e.

u ∝ D N

&

u ∝ V

_{f}∝ (H_{m})^{1/2}
Considering
above two equations we can write here the following equation as mentioned below

(H

_{m})^{ 1/2 }∝ D N
D ∝ (H

_{m})^{ 1/2}/N
Now we
will put the value of D in above equation of discharge and we will have
following equation as mentioned below.

Where, K
will be considered as constant of proportionality.

Now let us
recall the definition of specific speed of a centrifugal pump. If we consider
that discharge Q is 1 m

^{3}/s and head H_{m}is also 1 m, then we will have specific speed i.e. N will become N_{S}.
Therefore,
by putting the value of discharge Q = 1 m

^{3}/s, manometric head H_{m}= 1 m and speed N = specific speed N_{S }in above equation of discharge and we will find out the value of constant of proportionality i.e. K.
K = N

_{S}^{2 }
Therefore,
we have secured here the value of constant of proportionality (K) and we will
place this value of K in equation of discharge to secure the expression for specific speed for a centrifugal pump.

So, we
have seen here the basic concept of specific speed of a centrifugal pump and
also the expression of specific speed of centrifugal pump.

Do you
have any suggestions? Please write in comment box.

Further we
will find out, in our next post, Performance characteristic of centrifugal pump.

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**Reference: **

Fluid
mechanics, By R. K. Bansal

Image
courtesy: Google

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