HEADS AND EFFICIENCIES OF A CENTRIFUGAL PUMP

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

Now we will find out the heads and efficiencies of a centrifugal pump with the help of this post. In this post i.e. heads and efficiencies of a centrifugal pump, we will see here the various types of heads and after that we will see efficiencies of a centrifugal pump. 

Suction Head (h_s)

Suction head is basically defined as the vertical distance between the centre line of centrifugal pump and the free surface of liquid (e.g. water) in the tank from which liquid  is to be lifted. This vertical distance is also termed as suction lift. 

The tank from which liquid need to be lifted will be termed as sump. Suction head or suction lift will be displayed by the symbol h_s as displayed here in following figure. 

Delivery Head (h_d)

Delivery head is basically defined as the vertical distance between the centre line of centrifugal pump and the free surface of water in the tank to which water need to be delivered. Delivery head will be displayed by the symbol h_d as displayed here in following figure. 

Static head (H_S)

Static head is basically defined as the sum of suction head and delivery head and it will be displayed by the symbol H_S. Mathematically we will write the expression for static head as mentioned here.

H_S = h_s + h_d

Manometric head (H_m)

The manometric head is basically defined as the head against which a centrifugal pump has to do the work. Manometric head will be displayed by H_m. 

Let us see here the expression for manometric head as mentioned here

Manometric head = Head imparted by the impeller to the water – loss of head inside the pump

Manometric head = (V_w2 u₂)/g - loss of head inside the pump 

If there is no loss of head inside the pump, we will have following expression for manometric head as mentioned here. 

Manometric head = (V_w2 u₂)/g 

Where, 
V_w2 = Velocity of whirl at outlet 
u₂ = Tangential velocity of impeller at outlet 
g = Acceleration due to gravity 

Manometric head could be expressed by the following expression also as mentioned here 

Manometric Head = Total head at outlet of the pump – total head at the inlet of pump

H_m = [(P_O/ρg) + (V_O²/2g) + Z_O] - [(P_i/ρg) + (V_i²/2g) + Z_i] 

Where,

P_O/ρg = Pressure head at the outlet of the pump i.e. h_d

V_O²/2g = Velocity head at the outlet of the pump i.e. V_d²/2g

Z_O = Vertical height of the outlet of the centrifugal pump from datum line i.e. Z_d

P_i/ρg = Pressure head at the inlet of the pump i.e. h_s

V_i²/2g = Velocity head at the inlet of the pump i.e. V_s²/2g

Z_i = Vertical height of the inlet of the centrifugal pump from datum line i.e. Z_s 

Manometric head could be expressed by the following expression also as mentioned here 

Manometric head = Suction head + Delivery Head + Frictional head loss in suction pipe + Frictional head loss in discharge pipe +  Velocity head in delivery or discharge pipe 

Manometric head = h_s + h_d + h_fs + h_fd + V_d²/2g 

Efficiencies of a centrifugal pump

Let us first understand that how power will be transmitted from electrical motor to centrifugal pump. Power will be transmitted from electrical motor shaft to shaft of the centrifugal pump. Further power will be transferred from shaft of the centrifugal pump to impeller of the centrifugal pump. Further, power will be transferred from pump impeller to the water. 

Therefore, if we think the power transmission here, we will easily conclude that there will be some losses of power when power will be transmitted between pump shaft to pump impeller and further between pump impeller to the water. 

There will be following efficiencies related with centrifugal pump that we will discuss here.

1. Manometric Efficiency, η_man
2. Mechanical Efficiency, η_m
3. Overall efficiency, η_o 

Manometric Efficiency, η_man

Manometric head is basically defined as the ratio of manometric head to the head imparted by centrifugal pump impeller to the water. 

Mathematically manometric efficiency will be written by the following equation as mentioned here.

Manometric efficiency, η_man = Manometric Head / Head imparted by centrifugal pump impeller to the water 

The power at the impeller of the pump will be more than the power given to the water at outlet of the pump. Manometric efficiency will also be defined as the power given to the water at outlet of the pump to the power available at the impeller of the pump.

Manometric efficiency, η_man = Power given to the water at outlet of the pump / Power available at the impeller of the pump 

Mechanical efficiency

Power at the shaft of the centrifugal pump will be more than the power available at the pump impeller. 

Mechanical efficiency will be defined as the ratio of power available at the pump impeller to the power available at the shaft of the centrifugal pump. 

Mechanical efficiency, η_mech = Power available at the impeller of the pump/ Power available at the shaft of the centrifugal pump  

Overall efficiency

Overall efficiency will be defined as the ratio of power output of the pump to the power input to the pump. 

Power output of the pump in KW = Weight of water lifted (W) x H_m /1000 

Power input to the pump = Power supplied by the electric motor = S.P. 

We have seen here the various types of heads and efficiencies associated with the operation of a centrifugal pump. 

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

Further we will find out, in our next post, Derivation of expression for minimum starting speed of a centrifugal pump. 

Reference: 

Fluid mechanics, By R. K. Bansal 

Image courtesy: Google 

Also read 

An introduction to hydraulic machine 
Various types of hydraulic turbines
Gross head, Net head and efficiencies of a hydraulic turbine
Fundamental of Pelton wheel or Pelton hydraulic turbine
Basics of radial flow reaction turbines
Difference between inward radial flow reaction turbine and outward radial flow reaction turbine
Francis turbine 
Axial flow reaction turbine
Specific speed of turbine
Draft-tube
Governing of turbines
Governing of impulse turbine or Pelton turbine  
Governing of reaction turbine