Hey guys I need some help with a fluid mechanics problem.
I have a capillary with the given dimensions $d=0,15 mm$ and $L=5 cm$ and the operating conditions $p_{1}=4\cdot10^{5} Pa$, $p_{2}=0.25\cdot10^{5} Pa$
I want to calculate the velocity of oxygen flowing from 1 to 2. So I start with the formula for pressure drop with laminar flow
$\Delta p=\zeta \frac{L}{d}\frac{\rho u^{2}}{2}$ with $\zeta =\frac{64}{Re}$
which gets me $u=261 \frac{m}{s}$
After calculating Reynoldsnumber to check wether laminar assumption was right, I see that flow is turbulent ($Re=10175$)
So instead I have to take $\zeta =\frac{0.3164}{\sqrt[4]{Re}}$ (Blasius)
But with a little help of wolfram alpha
solve p=(0.3164/((udrho)/eta)^(1/4))l/d(rho*u^2)/2 for u
I get a velocity of $u=142.9 \frac{m}{s}$.
Does this make any sense? I'm really not sure if I can calulate the velocity like this.