%************************************************
%* Name: Meghan McDuff Date: 02/26/16 *
%* Seat: 00 File: Fluid Mechanics Program *
%* Instructor: DMG 12:40 *
%************************************************
fprintf (‘\n’)
fprintf (‘\n************************************************’)
fprintf (‘\n* Name: Meghan McDuff Date: 02/26/16 *’)
fprintf (‘\n* Seat: 00 File: Fluid Mechanics Program *’)
fprintf (‘\n* Instructor: DMG 12:40 *’)
fprintf (‘\n************************************************’)
fprintf (‘\n\n’)
fprintf(‘ Fluid Mechanics Program \n’);
fprintf(‘This program is written for a rectangular channel that, when given\n’);
fprintf(‘any n-1 of the following parameters: \n’);
fprintf(‘(1) Volumetric Flow Rate\n’);
fprintf(‘(2) Width\n’);
fprintf(‘(3) Height\n’);
fprintf(‘(4) Length\n’);
fprintf(‘(5) Delta P\n’);
fprintf(‘(6) Viscosity\n’);
fprintf(‘will calculate the missing parameter along with the average velocity,\n’);
fprintf(‘shear stress at the wall, Reynolds number and the entrance length.\n’);
fprintf(‘The program will output the calculated values in a table along with\n’);
fprintf(‘a plot of the velocity and shear stress across the channel.\n’);
fprintf(‘The user will be prompted to enter the number corresponding to the\n’);
fprintf(‘missing parameter. The user will then be prompted to enter the values\n’);
fprintf(‘for the known values, entering the number then pressing the <enter> key.\n’);
fprintf(‘Once all the values have been obtained, the program will perform the\n’);
fprintf(‘neccesary calculations and output the values and the plot.\n’);
fprintf(‘If the user wants to run the program again, they can simply hit the\n’);
fprintf(‘<run> button again.\n\n’);
fprintf(‘Which of the following parameters is unknown?\n’);
fprintf(‘(1) Volumetric Flow Rate?\n’);
fprintf(‘(2) Width?\n’);
fprintf(‘(3) Height?\n’);
fprintf(‘(4) Length?\n’);
fprintf(‘(5) Delta P?\n’);
fprintf(‘(6) Viscosity?\n’);
parameter=input(‘Enter the number corresponding to the missing parameter\n’);
if parameter==1
W=input(‘Enter the value for the width of the channel\n’);
H=input(‘Enter the value for the height of the channel\n’);
L=input(‘Enter the length of the channel\n’);
deltaP=input(‘Enter the delta p value for the channel\n’);
u=input(‘Enter the viscosity for the channel\n’);
Q=(W*H^3*deltaP)/(12*u*L);
end
if parameter==2
Q=input(‘Enter the value for the volumetric flow rate\n’);
H=input(‘Enter the value for the height of the channel\n’);
L=input(‘Enter the length of the channel\n’);
deltaP=input(‘Enter the delta p value for the channel\n’);
u=input(‘Enter the viscosity for the channel\n’);
W=(12*Q*L*u)/(deltaP*H^3);
end
if parameter==3
Q=input(‘Enter the value for the volumetric flow rate\n’);
W=input(‘Enter the value for the width of the channel\n’);
L=input(‘Enter the length of the channel\n’);
deltaP=input(‘Enter the delta p value for the channel\n’);
u=input(‘Enter the viscosity for the channel\n’);
H=((Q*12*u*L)/(deltaP*W))^(1/3);
end
if parameter==4
Q=input(‘Enter the value for the volumetric flow rate\n’);
W=input(‘Enter the value for the width of the channel\n’);
H=input(‘Enter the value for the height of the channel\n’);
deltaP=input(‘Enter the delta p value for the channel\n’);
u=input(‘Enter the viscosity for the channel\n’);
L=(W*H^3*deltaP)/(12*u*Q);
end
if parameter==5
Q=input(‘Enter the value for the volumetric flow rate\n’);
W=input(‘Enter the value for the width of the channel\n’);
H=input(‘Enter the value for the height of the channel\n’);
L=input(‘Enter the length of the channel\n’);
u=input(‘Enter the viscosity for the channel\n’);
deltaP=(Q*12*u*L)/(W*H^3);
end
if parameter==6
Q=input(‘Enter the value for the volumetric flow rate\n’);
W=input(‘Enter the value for the width of the channel\n’);
H=input(‘Enter the value for the height of the channel\n’);
L=input(‘Enter the length of the channel\n’);
deltaP=input(‘Enter the delta p value for the channel\n’);
u=(W*H^3*deltaP)/(Q*L*12);
end
p=1;
v_avg=(H^2*deltaP)/(12*u*L);
twall=((H/2)*deltaP)/(L);
Dh=(4*W*H)/(2*W+2*H);
Re=(p*v_avg*Dh)/u;
Le=(0.06*Re*Dh);
%all parameters, v_avg, twall, Re, Le
fprintf(‘\n Fluid Mechanics Program Output \n’);
fprintf(‘Volumetric flow rate %.3f cm^3/s\n’,Q);
fprintf(‘Width of channel %.3f cm \n’,W);
fprintf(‘Height of channel %.3f cm \n’,H);
fprintf(‘Length of channel %.3f cm \n’,L);
fprintf(‘Delta P of channel %.3f cm \n’,deltaP);
fprintf(‘Viscosity %.3f g/cm*s\n’,u);
fprintf(‘Average velocity %.3f cm/s \n’,v_avg);
fprintf(‘Shear stress at the wall %.3f dynes/cm^2\n’,twall);
fprintf(‘Reynolds number %.3f unitless\n’,Re);
fprintf(‘Entrance length %.3f cm \n’,Le);
fprintf(‘\n’);
for x=1:1:100
y(x)=-H/2+(x-1)*H/100;
v(x)=(deltaP/(8*u*L))*((H^2)-4*(y(x)^2));
twall(x)=deltaP*abs(y(x))/L;
end
figure()
plot(y,v)
title(‘Velocity vs. Height of Channel’);
xlabel(‘Height of channel (cm)’);
ylabel(‘Velocity (cm/s)’);
figure()
plot(y,twall);
title(‘Shear Stress at the Wall vs. Height of Channel’);
xlabel(‘Height of channel (cm)’);
ylabel(‘Shear Stress dynes/cm^2’);