We were discussing the pumps and basic pumping systemtotal head developed by the centrifugal pumpparts of centrifugal pump and their functionheads and efficiencies of a centrifugal pumpwork done by the centrifugal pump on water, expression for minimum starting speed of a centrifugal pump and multistage centrifugal pumps in our previous post.

Now we will find out the specific speed of a centrifugal pump (NS) 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.

### 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 NS

### 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 Vf

Where,
D = Diameter of the impeller of centrifugal pump
B = Width of the impeller of centrifugal pump
Vf = 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

We can also write above equation as mentioned here

Q D2 x V

Because, D

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 (Vf) will be related with the manometric head as written here.

u Vf   (Hm)1/2

Therefore, we have two equations here i.e.

u D N
u Vf   (Hm)1/2

Considering above two equations we can write here the following equation as mentioned below

(Hm) 1/2 D N

D (Hm) 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 m3/s and head Hm is also 1 m, then we will have specific speed i.e. N will become NS

Therefore, by putting the value of discharge Q = 1 m3/s, manometric head Hm = 1 m and speed N = specific speed NS in above equation of discharge and we will find out the value of constant of proportionality i.e. K.

K = NS

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

### Reference:

Fluid mechanics, By R. K. Bansal