Fluid flows in pipe networks can be analyzed in a manner similar to that used for electric resistance networks. Figure (a) shows a network with three pipes, which is analogous to the electrical network shown in part (b) of the figure. The volume flow rates in the pipes are q1, q2, and q3. The pressures at the pipe ends are pa, pb, and pc. The pressure at the junction is p1.
a. Assuming that the linear resistance relation applies, we have
q1 = 1/R1 (pa - p1)
Obtain the equations for q2 and q3.
b. The conservation of mass gives q1 = q2 + q3. Set up the equations in a matrix form Aq = b suitable for solving for the three flow rates q1, q2, and q3, and the pressure p1, given the values of the pressures pa, pb and pc, and the values of the resistances R1, R2, and R3. Find the expressions for matrix A and the column vector b.
c. Use MATLAB to solve the matrix equations obtained in part (b) for the case: pa = 30 psi. pb = 25 psi, and pc = 20 psi. Use the resistance values R1 = 10,000, R2 = R3 = 14,000 l/(ft-sec). These values correspond to fuel oil flowing through pipes 2 ft long, with 2 in. and 1.4 in. diameters, respectively. The units of the answers should be ft3/sec for the flow rates, and lb/ft2 for pressure.
a.

b.

Ph et 93 Pe Ph Ri R2 Pc