Question

Three pipes deliver water to a large exit pipe. The velocity at section 2 is 5 ms^-1, and the exit flow rate, Q₄ is 120 m³hr^-1. Find the velocities at 1, 3 and 4 if it is known that Q₃/Q₄ = 0.5

Answer 1

Continuity equation for fixed CV with ID flow and discrete CS's

$0= \sum m_ {out}- \sum m_{in}$

where m $= \rho Q= \rho VA$ , thus

$0=(\rho Q_4)-( \rho V_1A_1+\rho V_2A_2+\rho V_3A_3)$

Since $Q_3=0.5Q_4$

$V_3= \frac{Q_4}{0.5A_3}= \frac{120}{\frac{\pi}{2}0.06^2}=5.89 m/hr$

substituting $V_3$

$0=120 -(V_1 \frac{\pi}{4}0.04^2+5 \frac{\pi}4 0.05^2+5.98 \frac{\pi}40.06^2)$

$V_1=5.43 m/hr$