LESSON 21. Design of Reciprocating type of Pump

21.1 Introduction

Hydraulic systems are generally provided with positive displacement pumps. The piston sucks and pushes the same quantity (volume) of fluid every rotation of shaft .In these pumps there is hardly any slippage and the quantity of fluid pumped is nearly same for each rotation of shaft. Specially piston pumps exhibit this quality..

21.2 Design of Reciprocating type of Pump

In the reciprocating pump as the crank rotates the reciprocating motion  transmit a liquid from a pump inlet to its outlet.  When a piston moves to the, a partial vacuum  is created which draws  a liquid  through an inlet valve into a cylinder. When a piston moves other way an inlet valve is closed and the fluid is forced out of a cylinder through an outlet valve.    

Let us consider single acting reciprocating pump

 

            Let       D         =          diameter of cylinder

                        A         =          crosectional area

L          =          length of stroke

R         =          radius of crank

N         =          speed of crank

Qth      =          theoretical discharge

                        Qth      =          Ax LxN         discharge per min

=          Ax LxN/ 60   discharge per second

The ratio of actual discharge (Qac) to the theoretical discharge (Qth )is called discharge coefficient (cd). But when discharge coefficient is expressed in percentage it is called as volumetric efficiency.

cd            =      \[\frac{{{\text{Qac}}}}{{{\text{Qth}}}}\]

Slip

It can be defined as the difference between the theoretical discharge and the actual discharge. If S' is the slip,

then

                        S'         =          (Qth     -           Qac)   

Percentage slip can be given as-

                        S          =          [  1  - \[\frac{{{\text{Qac}}}}{{{\text{Qth}}}}\]   ] x 100

Work done and Power Requirement of Reciprocating Pump

It can be defined as the product of of weight fluid lifted and the total height through which it has been lifted .

Let                              W          =         work done / s

                                  w            =         weight of fluid lifted 

                                  H            =         Total height of fluid lifted

                                   Q           =         discharge of pump

 

W              =         w x Q x H

H             =         (hs + hd)

hs             =         suction head

hd              =         delivery head

Example

A reciprocating pump is having diameter of piston 260 mm with stroke length of 510 mm  operating at a speed of 32 rpm delivers 0.0125 m3/ s of fluid.Calculate the followings-

a) Theoretical discharge of pump

b) Coefficient of discharge

c) Slip

d) Percentage slip

Soln

Given

diameter of piston      D         =          260 mm           = 0.26 m

stroke length of          L          =          510 mm           =0.51 m

actual discharge         Qac      =          0.0125 m3/ s

Speed of pump           N         =          32 rpm

Qth      =  Ax LxN/ 60  

A         =  \[\frac{{\pi {D^2}}}{4}\]

= \[\frac{{\pi {{\left( {0.26} \right)}^2}}}{4}\]

= 0.053 m2

Now  Qth    = 0.053x 0.51x32 / 60  

=  0.0144 m3/ s

Coefficient of discharge         cd        =   \[\frac{{{\text{Qac}}}}{{{\text{Qth}}}}\]

                                                           = \[\frac{{0.0125}}{{0.0144}}\]

=  0.868

                                                            =  86.8%

Slip S'   = (Qth  - Qac)   

= (().0144 – 0.0125)

= 0.0019 m3/ s

Slip %   S = [  1  -  \[\frac{{{\text{Qac}}}}{{{\text{Qth}}}}\]  ] x 100

 =  [  1  - \[\frac{{0.0125}}{{0.0144}}\]   ] x 100

= 13.1 %

Last modified: Tuesday, 18 March 2014, 4:37 AM