Question

A pipe network is shown with all needful input data to compute the first iteration improved magnitudes of the initially assumed flows in the branches. What will be the such improved flow magnitudes in branches AB and CD? Consider to first decimal accuracy.

• A. A to B : 5.5; C to D : 3.8
• B. A to B : 5.1; C to D : 3.1
• C. A to B : 4.9; C to D : 3.4
• D. A to B : 5.7; C to D : 2.8

Answer 1

The correct option is B A to B : 5.1; C to D : 3.1

	$r{Q}^n$	$|rn{Q}^{n-1}|$
AB	$4Q^2=4\times 3^2=36$	$|4\times 2\times Q|=24$
BC	$3Q^2=-3\times 4^2=-48$	$|3\times 2\times Q|=24$
CD	$2Q^2=2\times 1^2=2$	$|2\times 2\times Q|=4$
DA	$5Q^2=-5\times 7^2=-245$	$|5\times 2\times Q|=70$
	$\sum r{Q}^2=-255$	$\sum |rn{Q}^{n-1}|=122$

$\Delta Q=\frac{-\sum r{Q}^n}{\sum |rn{Q}^{n-1}|}=\frac{-(-255)}{122}=2.09$

$Q_{AB}=3+2.09=5.09=5.1$

$Q_{CD}=1+2.09=3.09=3.1$