Physics Help Forum Energy conservation in mixing streams
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 Jul 18th 2019, 07:47 AM #1 Junior Member   Join Date: Jul 2019 Posts: 1 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
 Jul 18th 2019, 08:20 AM #2 Senior Member   Join Date: Oct 2017 Location: Glasgow Posts: 474 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. topsquark likes this. Last edited by benit13; Jul 18th 2019 at 08:39 AM.

 Tags bernoulli, conservation, energy, fluid, mixing, streams

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