I wanted to know how would I go about calculating the flow rate of a syringe with a metal tip that is dispensing water using a pressurized air.
I have had a look on internet about this and on this form and I though that laminar flow equation might be the solution for this.
$$\text{Flowrate}=\frac{\pi r^4(P-P_0)}{8\eta l}$$
From this equation the variable I can obtain are as follows:
- $r = \text{radius of the metal tip}$
- $\eta = \text{viscosity of water}$
- $L = \text{length of the metal tip}$
However, I don't quite understand how can I get $P$ and $P_0$
Since I'm supplying a certain pressure from the top of the syringe, this could be $P$ and the pressure that comes out of the syringe metal tip could be $P_0$. If what I said is right, how would I calculate the pressure at the tip?
Thank You
I have a follow up question for this:
If I have $P$(compressed air) – $P_0$(atmospheric pressure) and the $P_0$ is higher than $P$, then the value will be negative. So in this case would I do $P_0$ – $P$? I'm asking this as my pressure will range from 0Bar to 5bar and when it's 0.04Bar, atmospheric pressure is higher than the compressed air. what do I do in this case?
Best Answer
I that equation of flow rate the term (P-P0) is the change in the pressure of the column of liquid in the tube. In this case P0 is the atmospheric pressure that is experienced by the fluid on the other end, that is, at the other end of the metal tube.