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Fluid of density $\rho$ is flowing through a pipe with area $A$ with velocity of $V$. The pipe divides into two different pipes of area $\frac{1}{2}A$ and $\frac{3}{2}A$ with the right end opened. All the pipes are at the same height. How do I represent the velocity of fluid at each paths?

I tried using Bernoulli's equation and continuity equation and got the following results: $ p_0+\frac{1}{2}\rho V^2 = p_1+\frac{1}{2}\rho V_1^2 = p_2+\frac{1}{2}\rho V_2^2 $, $V_1 + 3V_2 = 2V$.

However, I can't find any more equations from here. Also, I'm stuck at the second question too, where the two pipes are separated by height $H$ and have the same area $A$.

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Thank you in advance.

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  • $\begingroup$ Add equations: in the first case $p_1=p_2$, in the second case $p_1=p_2+\rho gH$ $\endgroup$ – Alex Trounev Apr 15 '19 at 14:08
  • $\begingroup$ @AlexTrounev How do you know that $p_1 = p_2$? $\endgroup$ – Dimen Apr 16 '19 at 2:51
  • $\begingroup$ Are the outlets of the pipe discharging into atmosphere (or some other common reservoir)? $\endgroup$ – Deep Apr 16 '19 at 4:44