We were discussing the pumps and basic pumping system, total
head developed by the centrifugal pump, parts of centrifugal pump and their function in our previous post.

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Now we will find out the work done by
the centrifugal pump on water or we can say work done by the centrifugal pump
impeller on water with the help of this post.

In our previous post, we have studied
the basics concept behind the centrifugal pump. Now let us come to the point
and let us see here how to determine the work done by the centrifugal pump on
water.

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**Work
done by the centrifugal pump on water**

In case of centrifugal pump, work will
be done by the impeller on the water. Expression for the work done by the
impeller on the water will be determined by drawing the velocity triangles at
inlet and outlet of the impeller.

Let us see here a typical section of a centrifugal
pump that indicates the impeller blade as displayed here in following figure. We are interested here to find out the work
done by the centrifugal pump on the water. Energy interaction will take place
only in the rotor i.e. impeller of the centrifugal pump.

Velocity triangles will be drawn at the
inlet and outlet tips of the vanes fixed to an impeller.

For best efficiency of the pump, water
need to enter the impeller radially at inlet. Therefore, absolute velocity of
water at inlet will make an angle of 90 degree with the direction of motion of
the impeller at inlet.

As we have discussed above that absolute
velocity of water at inlet will make an angle of 90 degree with the direction
of motion of the impeller at inlet, therefore angle α = 0 and velocity of whirl at inlet V

_{w1 }= 0.
Let us assume the following data as
mentioned here.

N = Speed of the impeller in R.P.M

D

_{1}= Diameter of the impeller at inlet
u

_{1}=Tangential Velocity of impeller at inlet
V

_{1}= Absolute velocity of water at inlet
V

_{r1}= Relative velocity of water at inlet
α = Angle made by absolute velocity of
water at inlet with the direction of motion of vane

θ = Angle made by relative velocity of
water at inlet with the direction of motion of vane

D

_{2}= Diameter of the impeller at outlet
u

_{2}=Tangential Velocity of impeller at outlet
V

_{2}= Absolute velocity of water at outlet
V

_{r2}= Relative velocity of water at outlet
β = Angle made by absolute velocity of
water at outlet with the direction of motion of vane

φ = Angle made by relative velocity of
water at outlet with the direction of motion of vane

Tangential velocity of water at inlet, u

_{1}= π D_{1}N/60
Tangential velocity of water at outlet,
u

_{2}= π D_{2}N/60
As we know that in case of radially
inward flow reaction turbine, the work done by the water on the runner per
second per unit weight of the water striking per second will be given by
following equation as mentioned here.

Work done by the water on the runner per
second per unit weight of the water striking per second = (1/g) x [V

_{w1}u_{1}- V_{w2}u_{2}]
As we know that a centrifugal pump is
the reverse of a radially inward flow reaction turbine, therefore work done by
the impeller on the water in case of a centrifugal pump will be given by
following equation as mentioned here.

Work done by the impeller on the water per
second per unit weight of the water striking per second = - (work done in case
of turbine)

Work done by the impeller on the water
per second per unit weight of the water striking per second = (1/g) x [V

_{w2}u_{2}- V_{w1}u_{1}]
Work done by the impeller on the water
per second per unit weight of the water striking per second = (1/g) x V

_{w2}u_{2 }
Because, absolute velocity of water at
inlet will make an angle of 90 degree with the direction of motion of the
impeller at inlet, therefore angle α = 0 and V

_{w1 }= 0.
Above equation also provides the head
imparted to the water by the impeller or energy given by impeller to the water
per unit weight per second.

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**Work
done by the impeller on water per second = (W/g) x V**_{w2} u_{2}

_{w2}u

_{2}

Where, W = Weight of water

W = ρ x g x Q

Where, Q = Flow rate of water

Q = Area x Velocity of flow

Q =π x D

_{1}x B_{1}x V_{f1}= π x D_{2}x B_{2}x V_{f2 }
Where,

B

_{1}and B_{2}are the width of impeller and V_{f1}and V_{f2}are the velocities of flow at the inlet and outlet.
Therefore, we have seen here two very
important terms i.e. work done by the centrifugal pump on water and head
imparted to the water by the impeller or energy given by impeller to the water
per unit weight per second.

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**Work
done by the impeller on water per second = (W/g) x V**_{w2} u_{2}

_{w2}u

_{2}

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**Head
imparted to the water by the impeller or energy given by impeller to the water
per unit weight per second = (1/g) x V**_{w2} u_{2}

_{w2}u

_{2}

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

Further we will find out, in our next post, Head and efficiency of centrifugal pump.

Further we will find out, in our next post, Head and efficiency of centrifugal pump.

### Reference:

Fluid mechanics, By R. K. Bansal

Image courtesy: Google

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