Answer to Question #146784 in Mechanical Engineering for jime

Question

A fluid of constant density flows at the rate of 15 liters/sec along a pipe AB of 100 mm diameter. This pipe branches at B into two pipes BC and BD each of 25 mm diameter and a third pipe BE of 50 mm diameter. The flow rates are such that the flow through BC is three times the flow rate through BE and the velocity through BD is 4 m/s. Find the flow rates in the three branches BC, BD, and BE and the velocities in pipes AB, BC, and BE.

Answer 1

Density, $\rho$=c

Flow-rate, Q = 15 litres/second.

$Q_{AB}=3Q_{AB}$

$V_{BD}=4m/s$

$Q_{BD}=\frac{\pi}{4}*(0.025)^4*4$

$Q_{AB}=Q_{CB}+Q_{BD}+Q_{BE}$

$15 l/s=1.963+Q_{BD}+3Q_{BE}$

$13.037=4Q_{BE} \implies Q_{BE}=3.259 lit/sec$

$Q_{BE}=A*V_{BE}=3.259 \implies V_{BE}=\frac{3.259}{\frac{\pi}{4}*0.05^2}=6.6391$

$Q_{BC}=3Q_{BE}=3*3.259=\implies Q_{BC}=9.777 lit/sec$

$V_{BD}= 3.9989 m/sec$

$V_{BC}= 19.9175 m/sec$