For a biological experiment I am trying to calculate at which angle I should set my rocking plate to create a specific flow in my microfluidic chip (gravity driven flow)
I used The Bernoulli equation with frictional head loss (Darcy Weisbach). From the Bernoulli equation I would like to calculate the height difference between my two reservoirs. From this height difference I can calculate the angle.
My Reynolds number is super low namely 3.62*10^-2. Therefore, I wonder whether I am using the right equations. Maybe Bernoulli is not the one?
My calculation bring me to an angle of 0.02 degrees which is practically impossible of course.
I use:
P1 + 0,5ρ v1^2 + ρgh1 = P2 + 0,5ρ v2^2 + ρgh2 + fh ρg
With two assumptions:
- P1=P2=Patm because the tank is open, cancells out
- v1=0 as the reservoir is big compared to the channel
This gives me: v2=squareroot(2g(h1-fh))
I want to know h1 so: h1=(0,5v2^2 + fh)/g
Is this the correct equation or should I use another?