0
$\begingroup$

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 $A_1 v_1 = A_2 v_2$.

Improve this question
$\endgroup$
9
  • 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 Miller Feb 26 '20 at 13:17
  • $\begingroup$ 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 Mangla Feb 27 '20 at 9:25
  • $\begingroup$ I don't understand the second sentence in your comment. $\endgroup$ – Chet Miller Feb 27 '20 at 12:29
  • $\begingroup$ Is continuity equation derived by probability theory? $\endgroup$ – Vishesh Mangla Feb 28 '20 at 2:26
  • 2
    $\begingroup$ No. It is a mathematical expression based on conservation of mass. $\endgroup$ – Chet Miller Feb 28 '20 at 3:17
1
$\begingroup$

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.

Improve this answer
$\endgroup$
1
  • $\begingroup$ That is true and can be considered. $\endgroup$ – Vishesh Mangla Mar 11 '20 at 15:37
0
$\begingroup$

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.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.