I am modelling the flow of fluid through a cylinder of length L.The cylinder is divided into three segments(each segment of length L/3), there are four nodes(i=0,1,2,3). I'm trying to compute the inlet velocity and outlet velocity in each segment.

The known value is the average velocity of the fluid flowing through the cylinder of radius r and length L.

Using the average velocity of the fluid, the pressure drop across the cylinder of length L is computed using the Hagen-Poiseuille equation. $$v=\frac{r^2}{8\mu L}\Delta P$$ $$v=\frac{r^2}{8\mu L}(P_o-P_i)$$

Pressure at the inlet $P_i$ and outlet $P_o$ of the cylinder of length L.

I'm computing the outlet velocity($v_1$) of the first segment assuming equal pressure drop in all three segments. $$v_1=\frac{r^2}{8\mu L/3}\frac{(P_o-P_i)}{3}$$

Is this a right way to proceed? EDIT: I'm confused about the following, If the pressure drop in each segment is not constant, would the variation in velocity along axial direction violate the equation of continuity?

  • $\begingroup$ Your approach is correct if you have assumed fully developed flow at the pipe inlet. Also equation of continuity expresses mass conservation, so it must always hold. $\endgroup$ – Deep Oct 18 '18 at 5:18
  • $\begingroup$ For cylindrical coordinates, the equation of continuity simplifies to $$\frac{\partial v_z}{\partial z }=0$$ Wouldn't this mean the velocity doesn't change along the axial direction? Please correct me if my understanding is wrong. $\endgroup$ – Natasha Oct 18 '18 at 7:16
  • $\begingroup$ Yes- that's the definition of "fully developed flow". $\endgroup$ – Deep Oct 18 '18 at 10:13

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