Question

Water flows into junction J from reservoirs A and B through connecting pipes, the head loss through these being, respectively $10.Q_A^{2}and4.Q_B^2$. The water level elevations at the reservoirs at A and B are 25.9 m and 18 m, respectively. The inflow at J is discharged out at C into the atmosphere. The head loss through pipe JC is $1.Q_C^2$. The gauge pressure at J is 9 m. What is the residual gauge pressure of the outflow at C?

• A. 2.56 m
• B. 1.86 m
• C. 1.16 m
• D. 0.46 m

Answer 1

The correct option is C 1.16 m

Using continuity equation,

$Q_C=Q_A+Q_B$

Head loss in pipe,

$AJ=10Q_A^2=25.9-9=16.9m$

$\therefore Q_A=1.3m^3/s$

Head loss in pipe,

$BJ=4Q_B^2=18-9=9m$

$Q_B=15m^3/s$

$\therefore Q_C=1.3+1.5=2.8m^3/s$

Head loss in pipe,

$JC={10}_C^2=7.84m$

Residual head at,

C = 9 -7.84 = 1.16 m