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//Fluid Systems - By Shiv Kumar
//Chapter 17- Dimensional and Model Analysis
//Example 17.18
//To Find the Velocity and Rate of Flow in the Model.
clc
clear
//Given:-
//For Model ( Working Fluid is Water),
Dm=150; //Diameter of Pipe, mm
mu_m=0.01; //Viscosity of Water, Poise
//For Prototype ( Working Fluid is Oil),
Dp=1.5; //Diameter, m
Sp=0.9; //Specific Gravity of Oil
mu_p=3*10^-2; //Viscosity of Oil, Poise
Qp=3000; //Discharge of Oil, Litres/sec
//Data Required:-
rho_m=1000; //Density of Water, Kg/m^3
//Computations:-
Dm=Dm/1000; //m
Qp=Qp/1000; //m^3/s
Ap=(%pi/4)*Dp^2; //m^2
Am= (%pi/4)*Dm^2 ; //m^2
Vp=Qp/Ap; //m/s
rho_p=Sp*rho_m; //Kg/m^3
//From Reynold's Law of Similarity,
Vm=Vp*(Dp/Dm)*(mu_m/mu_p)*(rho_p/rho_m); //Velocity of Water in Model, m/s
Qm=Am*Vm*1000; //Rate of Flow in Model, Litres/sec
//Results:-
printf("The Velocity in the Model, Vm=%.3f m/s\n",Vm) //The Answer Vary due to Round off Error
printf("The Rate of Flow in the Model, Qm=%.2f Litres/sec\n",Qm) //The Answer Vary due to Round off Error
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