3 40 points In fluid mechanics viscous flow i n a pipe is go

3. (40 points) In fluid mechanics viscous flow i n a pipe is governed by the Colebrook-White equation as, -210g10(7 + 2.517) =--2 log10 (3.7 + ReVf where f is the dimensionless Darcy Friction Factor, e is the dimensionless Relative Pipe Roughness and Re is the which exists in a pipe with a Darcy Friction Factor of f = 0.03 and a Relative Pipe Roughness of = 10-4. Use the lower initial guess of Re = 103, upper initial guess of Reu-105, and iterate until the approximate error is less than 10% dimensionless Reynolds Number. Use the Bisection method to find the Reynolds Number

Solution

f=0.03;
e=10^-4;
ReL=10^3;
ReU=10^5;

fun=100;
while abs(fun)>0.01
    Re=(ReL+ReU)/2;
    fun=1/sqrt(f)+2*log10(e/3.7+2.51/(Re*sqrt(f)));
    funL=1/sqrt(f)+2*log10(e/3.7+2.51/(ReL*sqrt(f)));
    funU=1/sqrt(f)+2*log10(e/3.7+2.51/(ReU*sqrt(f)));
    if fun/funL>0
        ReL=Re;
    else
        ReU=Re;
    end
end
Re

%output

Re =

1.1441e+004