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Monday, 16 September 2019

IDEAL INDICATOR DIAGRAM OF RECIPROCATING PUMP

We were discussing the basics of reciprocating pump, main components of a reciprocating pump and working principle of reciprocating pump in our recent posts. 

Today we will start here with the ideal indicator diagram of reciprocating pump and we will also find out here the importance of ideal indicator diagram of reciprocating pump to determine the work done by reciprocating pump with the help of this post. 

Ideal indicator diagram of reciprocating pump 

Ideal indicator diagram of reciprocating pump is basically a graph between the absolute pressure head in the cylinder and the distance travelled by the piston from inner dead centre for one complete revolution of the crank. 

As the maximum distance travelled by the piston will be equal to the stroke length and hence we can also say that ideal indicator diagram of reciprocating pump will be basically a graph between the absolute pressure head in the cylinder and stroke length of the piston for one complete revolution. 

As we know that volume of water delivered in one revolution will be the product of area of cross section of the piston or cylinder and length of stroke i.e. V = A x L 

Where, cross sectional area of the piston or cylinder will be constant and therefore volume of water delivered in one revolution will be directionally proportional to the length of stroke i.e. V α L. 

Therefore, ideal indicator diagram of reciprocating pump could also be considered as graph between the absolute pressure head and volume for one complete revolution of the crank. 

Let us draw here first the ideal indicator diagram of reciprocating pump and then we will understand this diagram in detail. 

Following figure, shown here, indicates the reciprocating pump. 

Where, 
Hatm = Atmospheric pressure head 
L = Length of stroke 
hs = Suction head or vertical height of the cylinder axis from the water surface in the sump 
hd = Delivery head or vertical height of delivery point from the cylinder axis 

As we have recently discussed that the graph between the absolute pressure head in the cylinder and stroke length of the piston for one complete revolution will be the ideal indicator diagram of reciprocating pump. 

Therefore, absolute pressure head will be taken as ordinate and stroke length will be taken as abscissa as displayed here in following figure. 

Following figure indicates the ideal indicator diagram of reciprocating pump, where line EF shows the atmospheric pressure head. 

In ideal case, if we neglect the velocity and acceleration of fluid in cylinder piston and suction pipe, the suction pressure should be sufficient enough to lift the liquid i.e. water by a vertical height hs

Therefore, suction pressure head will be equal to the vertical depth hs. In ideal case, the pressure head inside the cylinder will be constant throughout the process of suction stroke where piston moves towards outer dead centre. 

Therefore, AB line will indicate here the suction stroke and it will be below than the atmospheric pressure head EF as displayed in above figure. 

At the end of suction stroke, piston will push the liquid i.e. water. If we assume the liquid as fully incompressible, there will be instant increase in pressure of liquid as soon as piston will push the liquid. 

Because, if we recall the property of a fully incompressible liquid, liquid will be pressurised instantly without change in volume. BC line shows the instant pressure rise of liquid up to delivery pressure head when piston will push the liquid at the end of suction stroke. 

CD shows the delivery stroke in above figure. During delivery stroke, the pressure head in the cylinder will be constant and will be equal to the delivery head hd and it will be above the atmospheric pressure head by a height of hd as displayed in above figure. 

Total static lift of the pump will be hs + hd.  

Similarly, at the end of delivery stroke when piston will come to inner dead centre, there will be instant pressure drop when piston start to move towards outer dead centre. This instant pressure drop, when piston start to move towards outer dead centre, is shown by DA in above diagram of reciprocating pump. 

Therefore, for one complete revolution of the crank, pressure head in the cylinder will be indicated by the diagram A-B-C-D-A. This diagram is known as ideal indicator diagram of reciprocating pump. 

As we have already seen, in ore previous post, that work done by the reciprocating pump per second will be given by following equation as mentioned below. 

Work done by the reciprocating pump = ρ g A L N x (hs + hd) / 60  
Work done by the reciprocating pump = K x L x (hs + hd

Because, ρ g A N / 60 = Constant = K 

Therefore, we can say that 

Work done by the reciprocating pump = K x AB x BC 

Work done by the reciprocating pump = K x Area of indicator diagram 

Because, 
Length of stroke L = AB 
Total static lift of the pump will be hs + hd = BC 

Therefore, we have seen here the ideal indicator diagram of reciprocating pump and also we have concluded that work done by the reciprocating pump will be directly proportional to the area of indicator diagram. 

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Further we will find out, in our next post, effect of acceleration and friction on indicator diagram of reciprocating pump
  

Reference: 

Fluid mechanics, By R. K. Bansal 
Fluid machines, By Prof. S. K. Som 
Image courtesy: Google  

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