Torque of a turbine using Euler's equation

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kn24
kn24 on 13 Oct 2022
Answered: VBBV on 14 Oct 2022
My code is trying to have a general code for solving turbine torque and optimizing it, along with having a way to plug in numbers and get the answers to a velocity triangle. My idea is to input a loop to find the optimal angle and graph it. I'm having trouble getting this graph to plot and not sure what I am doing wrong. I am fairly new to matlab and some general guidance with this code would be appreciated. I'm still working on the velocity triangles part and that is mostly just to have something down as guidance for myself. If anyone has any ideas on where to go from here to get a graph of the torque in order to optimize it for my project, as well as a good way to solve velocity triangles of a turbine.
clc;
clear all;
% T = pQ(r1V1cosa1 - r2V2cosa2) % Alpha is the angle between turbine linear
% velocity and absolute
p = 1.94; % fluid density of water, slugs/ft^3
Q = .0089; % 4 gallons per minute to ft^3/s, volumetric flow rate
r1 = 3; %radius one in.
r2 = 4; %radius two in.
V1 = 3; %abs velocity at inlet
V2 = 6; %abs velocity at outlet
g = 32.2; % gravity in ft/s
for i = 100:80
a(i) = i;
T(i) = p*Q*(r1*V1*cos(a(i)) - r2*V2*cos(a(i)));
end
%velocity triangle
% speeds at entrance
u1 = w*r1;
u2 = w*r2;
H_u = (u1*V1*cos(a)-u2*V2*cos(a))/g;
V = u + v;
%find angles a and B
V*sin(a) = v*sin(B);
V*cos(a) = v*sin(B);
plot (T(i),a(i))

Answers (1)

VBBV
VBBV on 14 Oct 2022
clc;
clear all;
% T = pQ(r1V1cosa1 - r2V2cosa2) % Alpha is the angle between turbine linear
% velocity and absolute
p = 1.94; % fluid density of water, slugs/ft^3
Q = .0089; % 4 gallons per minute to ft^3/s, volumetric flow rate
r1 = 3; %radius one in.
r2 = 4; %radius two in.
V1 = 3; %abs velocity at inlet
V2 = 6; %abs velocity at outlet
g = 32.2; % gravity in ft/s
T = zeros(size(100:80));
for i = 100:-1:80
a(i) = i;
T(i) = p*Q*(r1*V1*cos(a(i)*pi/180) - r2*V2*cos(a(i)*pi/180));
end
%velocity triangle
% speeds at entrance
w = 0.2
w = 0.2000
u1 = w*r1;
u2 = w*r2;
% H_u = (u1*V1*cos(a)-u2*V2*cos(a))/g;
% V = u + v;
%find angles a and B
% V*sin(a) = v*sin(B);
% V*cos(a) = v*sin(B);
plot(a,T)

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