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Wednesday, 25 September 2019

MAXIMUM SPEED OF A RECIPROCATING PUMP

We were discussing the basics of reciprocating pumpmain components of a reciprocating pumpworking principle of reciprocating pumpideal indicator diagram of reciprocating pumpeffect of acceleration and friction on indicator diagram of reciprocating pumpexpression for acceleration head in the suction pipe of a reciprocating pump, double acting reciprocating pump: working principle, discharge, work done and power required  and slip and negative slip in reciprocating pump in our recent posts.  

Today we will see here another important topic i.e. maximum speed of a reciprocating pump with the help of this post. 

Maximum speed of a reciprocating pump 

Maximum speed of a reciprocating pump will be determined on the basis of fact that the pressure in the cylinder during suction and delivery stroke, should not fall below than the vapour pressure of liquid, flowing through suction and delivery pipe. 

If the pressure in the cylinder will be lower than the vapour pressure of liquid, there will be problem of cavitation inside the cylinder and also there will not be continuous flow of liquid or we can say that separation of liquid will take place. 

The pressure at which separation of liquid will take place will be considered as separation pressure and head corresponding to separation pressure will be termed as separation pressure head. 

Now we will determine here the maximum speed of reciprocating pump during its suction stroke and delivery stroke. 

Maximum speed of reciprocating pump during suction stroke

Let us recall the indicator diagram of reciprocating pump. We can say that the absolute pressure at the start of suction stroke will be lower and hence separation of liquid may take place at the start of suction stroke only. 

In that case, absolute pressure head in the cylinder at the start of suction stroke will be equal to the separation pressure head of liquid and we can write the following equation as mentioned below. 

Where, 

hsep = Separation pressure head
hs = Suction head  
Hatm = Atmospheric pressure head
has = Acceleration head in suction pipe 

Above equation is the equation for maximum speed of reciprocating pump during suction stroke without any problem of separation of liquid during suction stroke. 

Maximum speed of reciprocating pump during delivery stroke 

During delivery stroke, the probability of liquid separation will be only at the end of delivery stroke. The pressure head in the cylinder at the end of delivery stroke will be given by following equation as mentioned here. 

Pressure head in the cylinder at the end of delivery stroke = (Hatm + hd - had

In order to avoid the separation of liquid, above pressure head must be higher than the separation pressure head i.e. hsep

In limiting case, we can have the following equation as mentioned below. 


Where,
has = Acceleration head in delivery pipe 

Expression of acceleration head in suction pipe and delivery pipe could be found here. 

Above equation is the equation for maximum speed of reciprocating pump during delivery stroke without any problem of separation of liquid during delivery stroke. 

Now we have seen here the expression for maximum speed of reciprocating pump for two cases i.e. suction stroke and delivery stroke. 

We will find out the minimum value of reciprocating pump speed from above two cases and that value will be the maximum speed of reciprocating pump without separation of liquid during suction and delivery strokes. 

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Further we will find out, in our next post, air vessel in reciprocating pump.   

Reference: 

Fluid mechanics, By R. K. Bansal 
Image courtesy: Google   

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