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Old Jul 18th 2019, 07:47 AM   #1
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Energy conservation in mixing streams



Is it correct to apply two separate Bernoullis equation - for sections 1-3 and for 2-3? Why/why not?

I ve seen such solution to this problem on the internet but I have some doubts.
I think that energy between sections 1 and 3 is not conserved because of energy exchange with the other stream.

Energy conservation for the whole system
Q1(v1^2/2 +p1/rho)+Q2(v2^2/2 +p2/rho)=(Q1+Q2)(v3^2/2 +p3/rho)
is not enough to determine (p3-p2) needed for Y momentum conservation.

system of:
v1^2/2 +p1/rho +deltaE=v3^2/2 +p3/rho
v1^2/2 +p1/rho -deltaE=v3^2/2 +p3/rho
needs an additional equation as well

I would be thankful for every help
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Old Jul 18th 2019, 08:20 AM   #2
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You also need to consider the continuity equation:

$\displaystyle Q_3 = Q_1 + Q_2$

$\displaystyle Q_3 = A_1 v_1 + A_2 v_2$

Since each pipe has the same diameter, $\displaystyle A_1 = A_2 = A$ and since $\displaystyle Q_3$, $\displaystyle A$ and $\displaystyle v_1$ are known,

$\displaystyle v_2 = \frac{Q_3}{A} - v_1 $

That's one less unknown, so you should be able to solve for $\displaystyle p_2$ and $\displaystyle p_3$.

You will get some head loss at the junction, but for an estimation you can assume that the head loss is negligible.
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Last edited by benit13; Jul 18th 2019 at 08:39 AM.
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