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Wednesday, 18 September 2019

September 18, 2019

EFFECT OF ACCELERATION AND FRICTION ON INDICATOR DIAGRAM OF RECIPROCATING PUMP

We were discussing the basics of reciprocating pumpmain components of a reciprocating pump, working principle of reciprocating pump and ideal indicator diagram of reciprocating pump in our recent posts. 

Today we will start here with the effect of acceleration and friction on indicator diagram of reciprocating pump. 

Effect of acceleration and friction on indicator diagram of reciprocating pump

As we have discussed in our previous post that the 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. 

Now we must note it here that we have not considered the effect of acceleration during drawing the ideal indicator diagram of reciprocating pump. Once we will consider the effect of acceleration then the graph will be changed. 

We will see here how the ideal indicator diagram will be changed after considering the effect of acceleration and friction in suction and delivery pipes. 

Following figure, shown here, indicates the 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. 

Let us see here, in following figure, effect of acceleration and friction on indicator diagram of 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 
h= Delivery head or vertical height of delivery point from the cylinder axis 
has = Pressure head due to acceleration in the suction pipe 
had = Pressure head due to acceleration in the delivery pipe 

When piston will execute the reciprocating motion within the tight fit cylinder, it will have acceleration and deceleration or retardation. Reciprocating movement of piston within the cylinder will be executed by the connecting rod and crank mechanism. 

The connecting rod will be much larger than the crank and the reciprocating movement of piston within the cylinder could be assumed as simple harmonic motion. So, we can consider that piston will execute the simple harmonic motion within the cylinder and there will be acceleration and deceleration or retardation. 

Therefore, pressure inside the cylinder will not be constant, as in idle case where we were not considering the effect of acceleration, during the suction and delivery stroke. Pressure inside the cylinder will be changing during suction and delivery stroke. 


Effect of acceleration and friction during suction stroke 

Now we will first see here the suction stroke. At the time of starting of suction stroke i.e. when piston will start to move from inner dead center to towards outer dead center, liquid will have an acceleration and zero velocity at inner dead center

Velocity of liquid will be increasing and acceleration of liquid will be decreasing at the beginning of suction stroke. Because of this acceleration, the suction head will be needed more as compared to the static lift hs

Liquid velocity and acceleration in the cylinder and in the suction pipe line will be related to their cross-sectional areas. As the cross-sectional area of suction pipe line will be less than the cross-sectional area of cylinder, liquid velocity and acceleration in the suction pipe line will be more than the liquid velocity and acceleration in the cylinder. 

Liquid velocity and acceleration in the suction pipe line and in the cylinder will be dependent over the velocity of the piston. 

Therefore, at the beginning of suction stroke i.e. θ = 0, pressure head inside the cylinder will be more than the static lift hs and it will be equivalent to (hs + has) lower than the atmospheric pressure head as shown in above figure by EA'. 

As we have discussed that Velocity of liquid will be increasing and acceleration of liquid will be decreasing at the beginning of suction stroke. At the middle of suction stroke i.e. when crank will be rotated by angle θ = 900, velocity of liquid will be maximum and acceleration of liquid will be zero. 

Therefore, at the middle of suction stroke, pressure head inside the cylinder will be equivalent to static lift which will be hs lower than the atmospheric pressure head as shown in above figure by point G'. 

Further, velocity will be decreasing from its maximum value at the middle of suction stroke and it will come to zero at the end of suction stroke. 

As we have discussed above that at the middle of suction stroke, acceleration of liquid will be zero and therefore further, deceleration or retardation will be started and it will be maximum at the end of suction stroke. 

Therefore, at the end of suction stroke i.e. θ = 1800, pressure head inside the cylinder will be equivalent to (hs - has) lower than the atmospheric pressure head as shown in above figure by FB'. 

Therefore, after considering the effect of acceleration in suction pipe, the head requirement during the suction stroke will be modified in idle indicator diagram. The indicator diagram for suction stroke will be now shown by A'G'B'. 

As we know that there will be viscus losses in the suction pipe and in the cylinder. So, we will also consider the effect of losses of head due to fluid friction. 

As we know that viscus losses or loss of head due to fluid friction will be dependent over the liquid velocity. 


Loss of head due to fluid friction, hf α V

As we have seen above that velocity of liquid will be zero at inner dead center and outer dead center. Therefore, loss of head due to fluid friction, hf will be zero at these two dead centers i.e. at inner dead center and outer dead center. 

We have also seen that velocity of liquid will be maximum at the middle of suction stroke. Therefore, loss of head due to fluid friction, hf will be maximum at the middle of suction stroke. 

Therefore, after considering the effect of acceleration and friction, the head requirement during the suction stroke will be modified in idle indicator diagram. The indicator diagram for suction stroke will be now shown by A'IB'


Effect of acceleration and friction during delivery stroke 

Similarly, at the beginning of delivery stroke, pressure head inside the cylinder will be more than the hd and it will be equivalent to (hd + had) above the atmospheric pressure head as shown in above figure by FC'. 

Velocity of liquid will be increasing and acceleration of liquid will be decreasing at the beginning of delivery stroke. At the middle of delivery stroke, velocity of liquid will be maximum and acceleration of liquid will be zero. 

Therefore, at the middle of delivery stroke, pressure head inside the cylinder will be equivalent to hd above the atmospheric pressure head as shown in above figure by point H'. 

Further, velocity will be decreasing from its maximum value at the middle of delivery stroke and it will come to zero at the end of delivery stroke. 

As we have discussed above that at the middle of delivery stroke, acceleration of liquid will be zero and therefore further, deceleration or retardation will be started and it will be maximum at the end of delivery stroke. 

Therefore, at the end of delivery stroke, pressure head inside the cylinder will be equivalent to (hd - had) above the atmospheric pressure head as shown in above figure by ED'. 

Therefore, after considering the effect of acceleration in delivery pipe, the head requirement during the delivery stroke will be modified in idle indicator diagram. The indicator diagram for delivery stroke will be now shown by D'H'C'. 

As we know that there will be viscus losses in the delivery pipe and in the cylinder. So, we will also consider the effect of losses of head due to fluid friction. 

As we have seen above that velocity of liquid will be zero at inner dead center and outer dead center. Therefore, loss of head due to fluid friction, hf will be zero at these two dead centers i.e. at inner dead center and outer dead center. 

We have also seen that velocity of liquid will be maximum at the middle of delivery stroke. Therefore, loss of head due to fluid friction, hf will be maximum at the middle of delivery stroke. 

Therefore, after considering the effect of acceleration and friction, the head requirement during the delivery stroke will be modified in idle indicator diagram. The indicator diagram for delivery stroke will be now shown by C'JD'

Therefore, we have seen here the modification in the ideal indicator diagram of reciprocating pump after considering the effect of acceleration and friction. 

Ideal indicator diagram of reciprocating pump which was ABCDA is now modified to A'IB'C'JD'A after considering the effect of acceleration and friction. 

Do you have any suggestions? Please write in comment box and also drop your email id in the given mail box which is given at right hand side of page for further and continuous update from www.hkdivedi.com

Further we will find out, in our next post, . 


Reference: 

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

Monday, 16 September 2019

September 16, 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. 

Do you have any suggestions? Please write in comment box and also drop your email id in the given mail box which is given at right hand side of page for further and continuous update from www.hkdivedi.com

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  

Also read  

Sunday, 15 September 2019

September 15, 2019

WORKING PRINCIPLE OF RECIPROCATING PUMP

We were discussing a new topic i.e. reciprocating pump in our recent post and we have seen there the basics of a pump and main components of a reciprocating pump.  

Today we will start here with the working principle of reciprocating pump and we will also find out here the discharge through a reciprocating pump and work done by reciprocating pump with the help of this post. 

Working principle of reciprocating pump 

If the mechanical energy is converted in to stored mechanical energy or pressure energy by sucking the liquid in to a cylinder in which a piston is reciprocating backward and forward, which exerts the thrust on the liquid and increases its hydraulic energy or pressure energy, the hydraulic machine will be termed as reciprocating pump. 

There are following main components of a reciprocating pump mentioned here. Following figure displayed here indicates the reciprocating pump. 
  1. A cylinder with a piston, piston rod, connecting rod, crank and crank shaft 
  2. Suction pipe 
  3. Delivery pipe 
  4. Suction valve 
  5. Delivery Valve 

Above figure indicates the single acting reciprocating pump. Piston will move within a cylinder in forward and backward direction towards inner dead center and outer dead center i.e. piston will execute the reciprocating motion within the tight fit cylinder. 

Reciprocating movement of piston within tight fit cylinder will be executed by connecting the piston with crank with the help of connecting rod as displayed in figure. Crank will be fixed with crank shaft which will be rotated by an electric motor. 

Suction pipe and delivery pipe will be fixed with the cylinder by means of suction valve and delivery valve respectively as displayed in above figure. 

Suction valve and delivery valve will be check valve i.e. non return valve and hence water may flow in one direction only through these valves. 

Let us see how a reciprocating pump works 

When piston will move towards right i.e. towards outer dead center, there will be fall in pressure of liquid and hence due to reduction in pressure suction valve will be opened and liquid will enter in to the cylinder. This movement of piston inside the cylinder will be termed as suction stroke. 

When piston will move towards left i.e. towards inner dead center, there will be increase in pressure of liquid and hence due to increase in pressure of liquid suction valve will be closed and delivery valve will be opened and liquid under high pressure will flow through the delivery valve to delivery pipe of reciprocating pump. 

Discharge through a reciprocating pump 

Let us consider the following terms as mentioned here for a reciprocating pump displayed above in figure. 

D = Diameter of the cylinder 
A = Cross sectional area of the piston or cylinder 
r = Radius of crank 
N = R.P.M of crank 
L = Length of the stroke = 2 x r 
hs = Suction head or Height of the cylinder axis from the water surface in the sump 
hd = Discharge head or height of delivery point from the cylinder axis 

Volume of water delivered in one revolution = Area x Length of stroke 
Volume of water delivered in one revolution = A x L 
Number of revolution per second = N/60 
Volume of water delivered per second = Volume of water delivered in one revolution x Number of revolution per second 
Volume of water delivered per second = A x L x N/60 
Volume of water delivered per second = A L N/60 

Discharge of the pump per second = A L N/60 


Work done by reciprocating pump

Work done by reciprocating pump will be given by following equation as mentioned here

Work done by reciprocating pump = Weight of water lifted per second x Total water through which water is lifted 

Work done by reciprocating pump = ρ x g x Discharge of the pump per second x Total water through which water is lifted 

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


So, we have seen here the working principle of reciprocating pump. We have also secured here the expressions for discharge through a reciprocating pump and work done by reciprocating pump with the help of this post.  

Do you have any suggestions? Please write in comment box and also drop your email id in the given mail box which is given at right hand side of page for further and continuous update from www.hkdivedi.com

Further we will find out, in our next post, ideal indicator diagram of reciprocating pump.  

Reference: 

Fluid mechanics, By R. K. Bansal 

Image courtesy: Google  

Also read 

September 15, 2019

MAIN COMPONENTS OF A RECIPROCATING PUMP

In our last sessions, we were discussing the various important topics based on the centrifugal pumps and those topics could be accessed by finding the post centrifugal pump working principle

Today we will start here a new topic i.e. reciprocating pump. We will first find out here the basics of a pump, then we will introduce reciprocating pump and further we will see here main components of a reciprocating pump with the help of this post. We will also see the working principle of a reciprocating pump, but that will be discussed in our next post. 

So let us start here with the basics of a pump and introduction to reciprocating pump 

Hydraulic machines which convert the mechanical energy in to stored energy of fluid will be termed as pumps. Compressors, fans and blowers are also come under this category of hydraulic machines as they also convert mechanical energy in to stored energy of fluid. 

But, we will be interested here only about the pumps. So we will not discuss here about the compressors, fans and blowers. These types of hydraulic machines will be discussed further in our next posts. 

Stored energy of fluid is also termed as hydraulic energy and hence pumps are basically defined as the hydraulic machines which convert the mechanical energy in to hydraulic energy. 

We can also say that output of pumps will be in the form of stored mechanical energy. In case of pumps, stored mechanical energy comes in the form of static pressure or static head. 

If the mechanical energy is converted in to stored mechanical energy or pressure energy by means of centrifugal force acting on the fluid, the hydraulic machine will be termed as centrifugal pump. 

If the mechanical energy is converted in to stored mechanical energy or pressure energy by sucking the liquid in to a cylinder in which a piston is reciprocating backward and forward, which exerts the thrust on the liquid and increases its hydraulic energy or pressure energy, the hydraulic machine will be termed as reciprocating pump. 

Main components of a reciprocating pump 

There are following main components of a reciprocating pump mentioned here. Following figure displayed here indicates the reciprocating pump. 



  1. A cylinder with a piston, piston rod, connecting rod, crank and crank shaft 
  2. Suction pipe 
  3. Delivery pipe 
  4. Suction valve 
  5. Delivery Valve 

Above figure indicates the single acting reciprocating pump. Piston will move within a cylinder in forward and backward direction towards inner dead center and outer dead center i.e. piston will execute the reciprocating motion within the tight fit cylinder. 

Reciprocating movement of piston within tight fit cylinder will be executed by connecting the piston with crank with the help of connecting rod as displayed in figure. Crank will be fixed with crank shaft which will be rotated by an electric motor. 

Suction pipe and delivery pipe will be fixed with the cylinder by means of suction valve and delivery valve respectively as displayed in above figure. 

Suction valve and delivery valve will be check valve i.e. non return valve and hence water may flow in one direction only through these valves. 

When piston will move towards right i.e. towards outer dead center, there will be fall in pressure of liquid and hence due to reduction in pressure suction valve will be opened and liquid will enter in to the cylinder. 

When piston will move towards left i.e. towards inner dead center, there will be increase in pressure of liquid and hence due to increase in pressure of liquid suction valve will be closed and delivery valve will be opened and liquid under high pressure will flow through the delivery valve to delivery pipe of reciprocating pump. 

So, we have seen here the basic of a pump and we have also find out the meaning of a reciprocating pump. Before completing this post, we have also seen the main components of a reciprocating pump and their function too in a reciprocating pump operation. 

Do you have any suggestions? Please write in comment box and also drop your email id in the given mail box which is given at right hand side of page for further and continuous update from www.hkdivedi.com.  

Further we will find out, in our next post, working principle of reciprocating pump

Reference: 

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

Also read 

September 15, 2019

CENTRIFUGAL PUMP WORKING PRINCIPLE

In our recent posts, we were focused on centrifugal pump working principle. We have seen various posts based on the centrifugal pump working principle and these posts are as mentioned below.

Here we have written each post based on centrifugal pump working principle for easy access and to secure complete information about the centrifugal pump working principle.

Posts based on centrifugal pump working principle
  1. Pumps and basic pumping system 
  2. Total head developed by the centrifugal pump 
  3. Parts of centrifugal pump and their function 
  4. Heads and efficiencies of a centrifugal pump
  5. Work done by the centrifugal pump on water 
  6. Expression for minimum starting speed of a centrifugal pump
  7. Multistage centrifugal pumpscavitation in hydraulic machine 
  8. Specific speed of a centrifugal pumpcavitation in hydraulic turbines
  9. Cavitation in centrifugal pumps 
  10. Maximum suction lift of centrifugal pump
  11. Net positive suction head of centrifugal pump
  12. Axial flow pump working principle


Do you have any suggestions? Please write in comment box and also drop your email id in the given mail box which is given at right hand side of page for further and continuous update from www.hkdivedi.com

Further we will find out, in our next post, main components of reciprocating pump. 

Reference: 

Fluid mechanics, By R. K. Bansal 

Fluid Machines, By Prof. S. K. Som
Image courtesy: Google 

Also read 

Saturday, 14 September 2019

September 14, 2019

AXIAL FLOW PUMP WORKING PRINCIPLE

We were discussing the pumps and basic pumping systemtotal head developed by the centrifugal pumpparts of centrifugal pump and their functionheads and efficiencies of a centrifugal pumpwork done by the centrifugal pump on waterexpression for minimum starting speed of a centrifugal pumpmultistage centrifugal pumpscavitation in hydraulic machinespecific speed of a centrifugal pumpcavitation in hydraulic turbinescavitation in centrifugal pumps, maximum suction lift of centrifugal pump and net positive suction head of centrifugal pump  in our previous post.

Today, we will find out here a new topic i.e. axial flow pump working principle with the help of this post. We will find out here the basics behind the axial flow pump, components of axial flow pump and further we will see the working principle of axial flow pump. 

Axial flow pump working principle 

Axial flow pump could be defined as a pump where liquid i.e. water will flow in axial direction. Here we have used one term i.e. axial direction. Axial direction means liquid will flow in the direction of axis of rotation. 

In case of axial flow pump, inlet and outlet of fluid will not vary in radial location from its axis of rotation. 

Axial flow pump could be considered as the converse of an axial flow reaction turbine.
Axial flow pumps will be used when we need to deliver the higher flow rate and relatively lower head. 

Axial flow pump: Components and their function 

Following figure shows here the basic schematic view of an axial flow pump. 


There will be a central hub in an axial flow pump as shown in figure and a number of vanes or blades will be mounted over this central hub of axial flow pump. Therefore, the central hub with a number of vanes or blades will be called as the rotor or impeller of the axial flow pump. 

Impeller blades will be mounted over the central hub of axial flow pump in such a way that liquid i.e. water may flow axially through these impeller blades. 

Impeller will be rotated within a cylindrical housing as displayed in above figure. There will be a clearance between impeller and cylindrical housing and this clearance should be as less as possible in order to avoid the leakage. 

Now we will see here the stationary inlet guide vanes of an axial flow pump as shown in above figure. These stationary guide vanes are provided at inlet of an axial flow pump in order to direct the liquid i.e. water in correct way to the impeller blades without any shock. 

There will also be some stationary outlet guide vanes at the outlet of an axial flow pump as shown in above figure. Stationary outlet guide vanes are basically provided at the outlet of an axial flow pump in order to change the direction of motion of liquid coming from the outlet of impeller. 

When liquid will come from the impeller outlet, it will have whirling component of velocity along with the axial component of velocity. Stationary outlet guide vanes will reduce this whirling component of velocity. After passing through the stationary outlet guide vanes, liquid will flow almost in axial direction i.e. in a direction parallel to the axis of rotation. 

We must note it here that the number of impeller blades will vary from 2 to 8 in an axial flow pump.
Ratio of hub diameter to the rotor diameter for an axial flow pump will be in the range of 0.3 to 0.6. 

Therefore, we have seen here the basics of axial flow pump. We have also discussed here the various important components of axial flow pump and their function too with the help of this post. 

Do you have any suggestions? Please write in comment box and also drop your email id in the given mail box which is given at right hand side of page for further and continuous update from www.hkdivedi.com

Further we will find out, in our next post. 

Reference: 

Fluid mechanics, By R. K. Bansal 
Fluid Machines, By Prof. S. K. Som

Image courtesy: Google 

Also read