When a fluid molecule suffers decrease in area whether smoothly or sharply its velocity vector strikes the wall but both in case of elastic and inelastic collision it looses/changes its velocity direction and magnitude. Then how its velocity increases when it has passed through the orifice/smaller area which is inferred by using the continuity equation $A_1 v_1 = A_2 v_2$.
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2$\begingroup$ Do you think that the continuity equation refers to a single molecule? Irrespective of the conservation of momentum and energy, do you think that mass is conserved? $\endgroup$– Chet MillerFeb 26, 2020 at 13:17
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$\begingroup$ Continuity equation talks about the flux passing through an area. So to visualize I take an area $A_1$ and consider vector field(arrows) passing through it in a single direction. Then I take an area $A_2$ again with the same vector field but now densely filled than its prior one considering $A1 > A2$. $\endgroup$– Vishesh ManglaFeb 27, 2020 at 9:25
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$\begingroup$ I don't understand the second sentence in your comment. $\endgroup$– Chet MillerFeb 27, 2020 at 12:29
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$\begingroup$ Is continuity equation derived by probability theory? $\endgroup$– Vishesh ManglaFeb 28, 2020 at 2:26
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2$\begingroup$ No. It is a mathematical expression based on conservation of mass. $\endgroup$– Chet MillerFeb 28, 2020 at 3:17
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2 Answers
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In many cases the pressure is much lower beyond an orifice. The molecules are being pushed from behind. With a decrease in area, again where the velocity is higher, the pressure is lower.
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$\begingroup$ That is true and can be considered. $\endgroup$ Mar 11, 2020 at 15:37
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I think an answer lies in the assumption that velocity of a particle is always along the streamline and we usually we talk about steady state flow in which the streamline has already been bent in that direction of the flow. The $\nabla \psi$ where $\psi$ is the stream function is the $\vec{V}$ or velocity vector. If you consider transition state flow it would definately suffer momentum loss and there would be a mass reflux and continuity equation wouldn't be valid.