Matlab required Weve run an experiment to determine the volu

Matlab required.

We?ve run an experiment to determine the volumetric flow rate of water in a pipe given the diameter and slope (steady state). You suspect that the flow rate is some multiple of the diameter and slope since increasing either increases the rate, however, you?re unsure as to what power each variable is raised to and how the whole product is scaled. The following formula looks generally correct, but there are three unknown constants (a0, a1, a2) Using the data below, determine the value of the parameters (ai) and plot the surface of best fit. See ?mesh? or ?surf for helpful commands in this regard

Solution

figure
X= 0.3:0.6:0.9:0.4:0.6:0.9
Y= .01:.01:.01:.05:.05:.05
Z= 0.13:0.82:2.38:0.31:1.95:5.66]
D=10:20:30:40:50:60
M=5;
[X,Y,Z,D]=ndgrid(X,Y,Z,D);

for i=1:size(X,1)
for j=1:size(X,2)
V(i,j)=X(i,j)*D(i,j)*Y(i,j)*M*Z(i,j);
end
end
surf(X,Y,Z,V)
colormap hsv
alpha(.4)