Question

Water is flowing inside a loop as shown in the figure below. The elevations of all three nodes “A”, “B” and “C” are the same. The table below gives the information about lengths, diameters and friction factors of the three pipes of this loop. At node “A”, the inflow is 25 kg/s. At node “B”, the outflow is 10 kg/s. At node “C”, the outflow is 15 kg/s. Take density (�) of water as 1000 kg/m3 and “g” as 10 m/s2 . a) Apply the Hardy-cross iterative method to calculate the mass flow rates in all three pipes (mAB=?, mBC=?, mAC=?) 

Answer 1

$h_2 = Rm^2\\ Pipe \space AB\\ R_1=\frac{8fL}{g \rho \pi^2 D^5}=\frac{8*0.02*1000}{10 *1000* \pi^2 * 0.25^5}=1.66\\ R_2= \frac{8*0.02*1200}{10 *1000* \pi^2 * 0.15^5}=25.62\\ R_3= \frac{8*0.02*1200}{10 *1750* \pi^2 * 0.2^5}=8.86\\$

$\sum h_L= -4143\\ 2 \sum (\frac{h_L}{m})=361.4\\ \Delta m = \frac{4143}{361.4}=11.46$

$\therefore m_{AB}=16.46 kg/s\\ m_{BC}=6.46 kg/s\\ m_{CA}=8.54kg/s\\$