function Prob_5_2a2
clear, clc, format short g, format compact
xguess = 10.5 ; 
disp('Variable values at the initial estimate');
disp([' Unknown value ' num2str(xguess) '   Function Value ' num2str(NLEfun(xguess))]); 
xsolv=fzero(@NLEfun,xguess); 
disp(' Variable values at the solution');
disp([' Unknown value ' num2str(xsolv) '   Function Value ' num2str(NLEfun(xsolv))]); 
%- - - - - - - - - - - - - - - - - - - - - -
function fv = NLEfun(v); 
T = 60;  %Temperature (deg F)
epsilon = 0.00015;%Surface rougness of the pipe (ft) 
rho = 62.122 + T * (0.0122 + T * (-0.000154 + T * (0.000000265 - (T * 0.000000000224)))); %Fluid density (lb/cu. ft.) 
deltaz = 300; %Elevation difference (ft) 
deltaP = -150; %Pressure difference (psi)
vis = exp(-11.0318 + 1057.51 / (T + 214.624)); %Fluid viscosity (lbm/ft-s) 
L = 1000; %Effective length of pipe (ft) 
D = 7.981 / 12; %Inside diameter of pipe (ft) 
pi = 3.1416; %The constant pi 
eoD = epsilon / D; %Pipe roughness to diameter ratio (dimensionless) 
Re = D * v * rho / vis; %Reynolds number (dimesionless) 
if (Re < 2100) %Fanning friction factor (dimensionless) 
    fF = 16 / Re;
else
    fF = 1 / (16 * log10(eoD / 3.7 - (5.02 * log10(eoD / 3.7 + 14.5 / Re) / Re)) ^ 2);
end 
q = v * pi * D ^ 2 / 4 * 7.481 * 60; %Flow rate (gal/min) 
fv = v - sqrt((32.174 * deltaz + deltaP * 144 * 32.174 / rho) / (0.5 - (2 * fF * L / D))); %Flow velocity (ft/s)