Consider a fluid which is moving from a pipe which is having area of cross section A1 and one point in space and in other its A2 area A1<A2 , we say that can visualize the flow by making streamlines from that one space to other space , consider the cross section to be both of circular sections , now my question is we know therr a infinie points on a circle so that means from A1 area we can make infinite streamlines called this as N1 (total streamlines) , now from A2 area though there are infinite points we can consider so there too infinite stream lines call this N2 , now we can observe that points we can select on bigger area would be more than small area , so doesnt this means streamlines from A2 will be different in numbers as compared to A1 cross section area ? Where is the fault ?
$\begingroup$
$\endgroup$
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
4
The streamlines will become "denser" in a smaller pipe, where the "density" of the streamlines corresponds to mass flow rate, $\rho\mathbf{v}$. Evidently, by your reasoning, the flow rate $\rho\mathbf{v}$ must scale inversely to cross-sectional area of the pipe (assuming uniform flow).
-
$\begingroup$ So consider we draw all the streamlines from the dense region , that means in the bigger area the distance between streamlines will have some gaps left out (some portion of area being empty with streamlines) , what does that means? If there exists gap then that means there fluid is not flowing ehich doesnt makes sense . $\endgroup$ Commented Mar 9, 2022 at 3:45
-
$\begingroup$ We treat the fluid as a continuous medium, so we can't really think about drawing all the streamlines. Rather, we draw streamlines to help us visualize the flow, with the density of streamlines corresponding loosely to the flow rate of the fluid. $\endgroup$– DanDan面Commented Mar 9, 2022 at 5:38
-
$\begingroup$ The streamlines aren't meant to be taken literally as the only trajectories that particles in the fluid can follow. $\endgroup$– DanDan面Commented Mar 9, 2022 at 5:38
-
$\begingroup$ Understood thanks Daniel $\endgroup$ Commented Mar 9, 2022 at 12:07