MATLAB Question, please help! If the velocity distribution of a fluid flowing th
ID: 3664101 • Letter: M
Question
MATLAB Question, please help!
If the velocity distribution of a fluid flowing through a pipe is known, the flow rate Q can be computed using the formula: Q = integral vda where v is the velocity and A is the pipe's cross sectional area. For a circular pipe, A = pir^2 and dA = 2pir dr, therefore: Q = integral ^'_0 v(2pir)dr where r is the radial distance measured outward from the center of the pipe. If the velocity distribution is given by the following profile: v = 2 (1 - r/r_0)^1/6where r_0 is the radius of the pipe (3 cm in this case), compute Q using the trapz function in MATLAB.Explanation / Answer
Solution: See the code below:
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%This program calculates the flow rate Q of a fluid flowing through a pipe of radius r and velocity distribution v.
PI=3.1416; %value of constant PI
r0=3.0; %radius of pipe in cm
r=[0.0,3.0]; %range over which integral is to be performed.
n=1.0/6.0; %value of exponent in velocity distribution function
v=2.0*(1-r./r0).^n; %velocity distribution function of pipe
%calculation of Q using trapz method
Q=2.0*PI*trapz(r,v);
printf("Q:%.2f ",Q);
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