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Monday, 26 August 2019

TOTAL HEAD DEVELOPED BY CENTRIFUGAL PUMP

We were discussing the pumps and basics of pumping system in our previous post. Today we will find out the total head developed by the centrifugal pump or net head developed by the centrifugal pump with the help of this post. 

Total head developed by the centrifugal pump or net head developed by the centrifugal pump could be easily determined if we have basic information about the pumping system and loss of head during flow of fluid through pumping system.  

So, Let us come to the point and see here how to determine the total head developed by the centrifugal pump or net head developed by the centrifugal pump. 

Following figure, displayed here, indicates a general pumping system which has been discussed in our last post. 

Understanding the loss of head during flowing of liquid through pumping system 

We will draw here a curve between head and flow for the given pumping system and then we will find out the various steps to secure the net head developed by the centrifugal pump. 
We will start here from free surface of liquid in lower reservoir. Head corresponding to the point A will be HA as displayed in figure. When liquid say water enters to the inlet pipe through mechanical strainer provided at the bottom of inlet pipe, there will be some losses of head due to the strainer and nose type of shape of pipe at its inlet. 

Let us say that head corresponding to the point B will be HB as displayed in figure. Head at point B will be slightly less as compared to the head at point A due to the frictional loss of head when water enters to the inlet pipe and it is shown in the curve displayed above. 

Therefore, we can also say that hin = HA – HB

Where, hin is the frictional head loss in the intake of water to the inlet pipe of pumping system. 

When water flow through the inlet pipe from point B to C, there will be again head loss due to friction and it is also displayed above in figure. Point C indicates the inlet of centrifugal pump. Head at point C will be HC and it will be lower than the head at point A. 

Therefore, we can also say that hf1 = HA – HC

Where, hf1 is the frictional head loss in the inlet pipe of pumping system. 

When water will enter in to the centrifugal pump, energy will be added to the water and pump will discharge the high pressurize water through its discharge end i.e. at point D. There will be sharp increase in head of the liquid, i.e. water here in this case, when it flows from C to point D. 

When water will flow through the outlet pipe or discharge pipe from point D to point E i.e. just at the outlet of the discharge pipe of pumping system, there will be again some loss of head due to friction and hence head at the point d i.e. HD will be higher than the head at the point E i.e. HE and it is displayed also in above figure. 

Therefore, we can also say that hf2 = HD – HE

Where, hf2 is the frictional head loss in the discharge pipe of pumping system. 

Now when water will flow from point E to F, there will be some head loss and this loss of head here will be termed as exit head loss i.e. he

When water will be at point E, it will have velocity of discharge or it will have kinetic head and when it comes to the point F i.e. when water comes to the higher reservoir, kinetic head will be lost as water will come to the rest inside the higher reservoir. 

Therefore we have seen here frictional loss of head during water flowing from lower reservoir to higher reservoir. 

Total head developed by the centrifugal pump 

Total head at free surface of lower reservoir or at A = HA

Total head at free surface of higher reservoir or at F = HS + HA

Height between F and free surface of higher reservoir could be neglected and we can assume that F is the point at free surface of higher reservoir. 

Static head will be the difference between the head at the free surface of higher reservoir and head at the free surface of lower reservoir i.e. HS

Head at the inlet to the pump, H1 = P1/ρg + V12/2g + Z1

Head at the outlet to the pump, H2 = P2/ρg + V22/2g + Z2

Where,
P1 and P2 are the pressure of liquid flowing through the pumping system at point 1 and 2 respectively.

V1 and V2 are the tangential velocity of liquid flowing through the pumping system at point 1 and 2 respectively.

Z1 and Z2 are the potential head of liquid flowing through the pumping system at point 1 and 2 respectively. 

Total head or net head developed by the pump = H2-H1

Now we will write down here the Bernoulli’s equation between point A and point C as mentioned here.
HA = P1/ρg + V12/2g + Z1 + hin + hf1
P1/ρg + V12/2g + Z1 = HA - hin - hf1
H1 = HA - hin - hf1

Similarly, Bernoulli’s equation between point D and point F

P2/ρg + V22/2g + Z2 = HS + HA
H2 = HS + HA + hf2 + he

Total head or net head developed by the pump = H2-H1

H2-H1 = HS + HA + hf2 + he – HA + hin + hf1
H2-H1 = HS + hf2 + he + hin + hf1
H2-H1 = HS + hf

Where,
Sum of all head losses, hf = hf2 + he + hin + hf1

Therefore we can say here

Net head developed by the pump = Static head + Sum of all losses of head

So, we have seen here the determination of net head developed by the centrifugal pump in a pumping system. We have also discussed here the losses of head during flow of liquid through the pumping system from lower reservoir to higher reservoir.  

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

Further we will find out, in our next post, parts of centrifugal pump and their function

Reference: 

Fluid mechanics, By R. K. Bansal 
Fluid Machines, By Prof. S. K. SOM
Image courtesy: Google  

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