Use matlab program Please do not attempt if you cannot use Matlab program Numeri

Question

Use matlab program Please do not attempt if you cannot use Matlab program Numerical methods only for experts I will give you negative review if you ask for more info. DO NOT ATTEMPT if you dont know MATLAB! Fully developed flow moving through a 40am dameter pipe has the following velooity profile r (om) 00 26 50 75 100 125 15.0 175 20.0 (m/s) 0.914 0800 0.87 0.705 0719 0.613 427 0204 0 problem using three different approaches 1. Use tapz function 2. Fita quadratic polynomial ourve to the veiooty data and then evaluate the integral using the analytical solution. 3 Use quad function to integrate the polymomial A r 0.01100, 25. 76 100 125, 160 176 200:

Explanation / Answer

1) enter the following code in matlab to get the integral using traps function

% Integral using trapz function

r=0.01*[0,2.5,5,7.5,10,12.5,15,17.5,20];

v=[0.914,0.890,0.847,0.795,0.719,0.543,0.427,0.204,0];

Q=2*pi*r.*v;

I=trapz(Q)

the answer is

I =

2.2855

2) for the polynomial fit method enter the following code in matlab

% Integral using polynomial fit and the integration

r=0.01*[0,2.5,5,7.5,10,12.5,15,17.5,20];

v=[0.914,0.890,0.847,0.795,0.719,0.543,0.427,0.204,0];

p4 = polyfit(r,v,3);

r1 = 0:0.025:0.2;

y2 = polyval(p4,r1);

Q=2*pi*r1.*y2;

I=sum(Q)

the result is as follows

I =

2.2855

3) enter the following code to get the result using quad function

% Integral using quad function

v=20*0.914;

Q=@(r)2*pi*r.*v;

I = quad(Q,0,.2)

the result is as follows

I =

2.2971

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