Work-Done by Centrifugal Pump

Work Done at The Centrifugal Pump moving Water 

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Fig. Velocity triangle at inlet also an outlet 

• Within the case of the centrifugal pump, work is done with the impeller on the water.
• Such expression to the work done by the impeller in the water is obtained through drawing velocity triangles above each inlet also an outlet of the impeller.
• Some water enters the impeller radially through the inlet for best efficiency of the pump which means this absolute velocity of water at inlet produces an angle of 90° with a specific direction of motion of the impeller at the inlet.
• Hence angle α = 90° and vwi  = 0. Fig. shows that velocity triangles at the inlet also outlet tips of the vanes fixed to an impeller. 

Let

• N  = Speed from the impeller in r.p.m.,
• D1 = Diameter of impeller at inlet, 
• u1 = Tangential velocity of impeller at inlet, = (πD1N/60)
• D2 = Diameter of impeller at outlet, 
• u2 = Tangential velocity of impeller at outlet = (πD2N/60)
• v1 = Absolute velocity from water at inlet, 
• vr1 = Relative velocity from water at inlet,
• α = Angle made at absolute velocity (v1) at inlet with the direction from motion of vane,
• θ = Angle made at relative velocity (vr1) at inlet with the direction from motion of vane, 
• and v2, vr2, β and ϕ are corresponding values at outlet. 

• While the water enters the impeller radially which means the absolute velocity from water at the inlet is in each radial direction and hence angle α = 90° also vw1 = 0. 
• Some centrifugal pump is that reverse of a radially inward flow reaction turbine.
• Just in case of a radially inward flow reaction turbine some work done by the water at the runner per second per unit weight of the water striking per second is given by, 

=(1/g)[Vw1u1-Vw2u2]

Work is done by some impeller on some water per second per unit weight of water striking per second  

= - [Work was done in a case from turbine] 

= - (1/g)[Vw1u1-Vw2u2]

=(1/g)[Vw2u2+Vw1u1]

=(1/g)[Vw2u2] [As Vw2=0]

Work is done by impeller on water per second

=(w/g)[Vw2u2]   

where,

W = Weight of water

= ρ x g x Q

Q = Volume of water

= Area x Velocity of flow

= πD1B1 x vf1

= πD2B2 x vf2

• B1 and B2 = width from the impeller at inlet also outlet
• vf1 and vf2 = velocities from flow at inlet also outlet.