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+// Example 9_8

+clc;funcprot(0);

+// Given data

+L=50;// Lengths of garden hose in ft

+D_A=3/4;// Diameter of hose A in inch

+D_B=1/2;// Diameter of hose B in inch

+p=40;// Pressure in the tank in psig

+nu=1.0*10^-6;// The kinematic viscosity in m/s^2

+rho=1*10^3;// The density of water in kg/m^3

+g=9.807;// The acceleration due to gravity in m/s^2

+epsilon=0;

+

+// Calculation

+D_A=D_A*2.54*10^-2;// m

+D_B=D_B*2.54*10^-2;// m

+L=L*0.3048;// m

+deltah_l1=(p*6.895*10^3)/(rho*g);// m

+deltah_A1=10;// m

+deltah_B1=18.12;// m

+sqrtoffintoRe_D_A=((2*g*deltah_A1*D_A^3)/(((nu)^2)*L))^(1/2);

+Re_D_A=-2*sqrtoffintoRe_D_A*log10(2.51/(sqrtoffintoRe_D_A));// Reynolds number

+Q_A1=(%pi*D_A*nu*Re_D_A)/4;// The volume flow rate in m^3/s

+sqrtoffintoRe_D_B=((2*g*deltah_B1*D_B^3)/(((nu)^2)*L))^(1/2);

+Re_D_B=-2*sqrtoffintoRe_D_B*log10((2.51/(sqrtoffintoRe_D_B)));// Reynolds number

+Q_B1=(%pi*D_B*nu*Re_D_B)/4;// The volume flow rate in m^3/s

+V_A=(4*Q_A1)/(%pi*D_A^2);// m/s

+V_B=(4*Q_B1)/(%pi*D_B^2);// m/s

+// Assume deltah=SigmaK*((V^2)/(2*g))

+deltah=((0.4*V_A^2)+(0.4*V_B^2))/(2*g);// m

+deltah_f=deltah_l1-deltah;// m

+// We decide to allocate this total to

+deltah_A2=2;// m

+deltah_B2=25.43;// m

+sqrtoffintoRe_D_A=((2*g*deltah_A2*D_A^3)/(((nu)^2)*L))^(1/2);

+Re_D_A=-2*sqrtoffintoRe_D_A*log10((2.51/(sqrtoffintoRe_D_A)));// Reynolds number

+Q_A2=(%pi*D_A*nu*Re_D_A)/4;// The volume flow rate in m^3/s

+sqrtoffintoRe_D_B=((2*g*deltah_B2*D_B^3)/(((nu)^2)*L))^(1/2);

+Re_D_B=-2*sqrtoffintoRe_D_B*log10((2.51/(sqrtoffintoRe_D_B)));// Reynolds number

+Q_B2=(%pi*D_B*nu*Re_D_B)/4;// The volume flow rate in m^3/s

+V_A=(4*Q_A2)/(%pi*D_A^2);// m/s

+V_B=(4*Q_B2)/(%pi*D_B^2);// m/s

+deltah_l2=((0.4*V_A^2)+(0.4*V_B^2))/(2*g);// m

+//Indicating the first and second guesses by '1' and '2' we find a third guess to be:

+deltah=deltah_A2-((Q_A2-Q_B2)*((deltah_A1-deltah_A2)/((Q_A1-Q_B1)-(Q_A2-Q_B2))));// m

+printf('\nThe flow rate through the hoses Q_A=%1.3e m^3/s;Q_B=%1.3e m^3/s;SigmaK(V^2/2g)=%0.4f m',Q_A2,Q_B2,deltah_l2);

+// The answer is vary due to roundoff error