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//Fluid Systems - By - Shiv Kumar
//Chapter 12- Reciprocating Pumps
//Example 12.9
//To Determine the Pressure on the Cylinder at the Begining of the Stroke (a)When no air vessel is fitted, (b)When air vessel is fitted at the cylinder level.
clc
clear
//Given Data:-
d_s=150; //Diameter of Suction Pipe, mm
l_s=12; //Length of Suction pipe, m
H_s=3; //Suction Head, m
D=225; //Cylinder Diameter, mm
L_s=375; //Stroke Length, mm
L=1.5; //Length of Connecting Rod, m
N=20; //Crank Speed, rpm
l_v=1.5; //m
f=0.04; //Co-efficient of friction
//Data Used:-
g=9.81; //Acceleration due to gravity, m/s^2
//Computations:-
d_s=d_s/1000; //m
D=D/1000; //m
L_s=L_s/1000; //m
a_s=(%pi/4)*d_s^2; //m^2
A=(%pi/4)*D^2; //m^2
omega=2*%pi*N/60; //rad/s
r=L_s/2; //m
printf("Without Air Vessel : \n\t")
//(i) Assuming Simple Harmonic Motion :
printf("(i) Assuming Simple Harmonic Motion\n\t\t")
H_as=(l_s/g)*(A/a_s)*omega^2*r; //m of water
H=H_s+H_as; //Pressure at the begining of stroke, m of water (vaccum)
//Result (a) (i)
printf(" Pressure at the begining of stroke=%.2f m of water (vaccum) \n\t",H) //The answer vary due to round off error
//(ii) If Simple Harmonic Motion is not assumed :
printf(" (ii) If Simple Harmonic Motion is not assumed : \n\t\t")
H_as=H_as*(1+r/L);
H=H_s+H_as; //Pressure at the begining of stroke, m of water (vaccum)
//Result (a) (ii)
printf(" Pressure at the begining of stroke=%.3f m of water (vaccum) \n\n",H) //The answer vary due to round off error
//(b) When Air Vessel is fitted
printf(" When Air Vessel is fitted : \n\t")
Us=(A/a_s)*L_s*N/60; //m/s
h_fs=(f*(l_s-l_v)/d_s)*(Us^2/(2*g)); //m of water
//(i) Assuming Simple Harmonic Motion :
printf("(i) Assuming Simple Harmonic Motion\n\t\t")
H_as=(l_v/g)*(A/a_s)*omega^2*r; //m of water (vaccum)
H=H_s+H_as+h_fs; //Total Pressure Head in the Cylinder, m of water below atmospheric
//Result (b) (i)
printf(" Total Pressure Head in the Cylinder =%.4f m of water below atmospheric or vaccum \n\t",H) //The answer vary due to round off error
//(ii) If Simple Harmonic Motion is not assumed :
printf(" (ii) If Simple Harmonic Motion is not assumed : \n\t\t")
H_as=H_as*(1+r/L);
H=H_s+H_as+h_fs; // Total Pressure Head in the Cylinder , m of water below atmospheric
//Result (b) (ii)
printf(" Total Pressure Head in the Cylinder =%.4f m of water below atmospheric \n",H) //The answer vary due to round off error
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