Question

A triangular pipe network is shown in the figure



The head loss in each pipe is given by $h_f=r.Q^{1.8}$ with the variables expressed in a consistent set of units. The value of r for the pipe AB is 1 and for the pipe BC is 2. If the discharge supplied at the point A (i.e., 100) is equally divided between the pipes AB and AC, the value of r (up to 2 decimal places) for the pipe AC should be

• A. 0.62

Answer 1

The correct option is A 0.62

Given

$h_f=r.Q^{1.8}$

Because of the given condition of equal discharge distribution in pipe AB & AC, the discharge in AB and AC will be 50 and 50. Now satisfy continuity at point B and C
For close Loop ABCA

$\sum h_r=0$

$\Rightarrow 1(50{)}^{1.8}-2(20{)}^{1.8}-r(50{)}^{1.8}=0$
$\Rightarrow 1143.26-439.42=r(50{)}^{1.8}$
$r=0.62$