Develop a MATLAB function based on the following: Beyond the Colebrook Equation

Question

Develop a MATLAB function based on the following:

Beyond the Colebrook Equation discussed in class, other relationships, such as the Von Karman equation are available to estimate the Fanning friction factor f in smooth pipes. The Fanning friction factor is dependent on a number of pa- rameters related to the size of the pipe and the fluid, which can all be represented by another dimensionless quantity, the Reynolds number Re. The Von Karman equation predicts f given Re as follows, G = 4 log10(Reyf) - 0.4. Typical values for the Reynolds number for turbulent flow are 10,000 to 500,000 and for the Fanning friction factor are 0.001 to 0.01. Develop a function that uses the bisection method to solve for f given a user-supplied value of Re between 2500 and 1,000,000. Design the function so that it ensures that the absolute approximate error in the result is Ea,d

Explanation / Answer

We have a MATLAB Program to calculate the friction factor. This is basrd on the mody chart which equivalent to the following program

function f = mody(ed,Re,verbose)

if Re<0;

error(sprintf('Reynolds number = % of cannot negative',Re));

else if Re<10000000;

f=64/Re;

return % laminar flow end;

if Re>2500,warming('Re=%f in transition range',Re); end

colefun=inline('1.0/sqrt(f)+2.0*log_10(ed/3.7+2.51/(Re*sqrt(f)))','f",ed",Re');

fi=1/(1.8*log_10(6.9/Re+(ed/3.7)^1.11))^2;

dfTol=5e-6;

f=fzero(CoelFun,fi,obtimset('TolX',dfTol,'Display',Off),ed,Re);

if f<0,error(sprintf('Friction Factor=%f;but cannot be negative',f));

end;

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