Open pipe and relation between pressure and flow rate

Poiseuille's Law,

$$ Flow=dfrac{πcdot r^4 cdot (P-Po) }{ 8cdot ηcdot L} cm^3/s $$ And in your case assuming you have a Pipe with the area $Acm^2$,

$$ Flow= Adfrac{r^2 cdot (P-Po) }{ 8cdot ηcdot L} cm^3/s $$

-P = pressure at the entrance, Bar

-P0 = atmosphere pressure, Bar

-eta = viscosity at dyne second/cm2 for water at 20c it is 0.01

-L = length cm.

If you don't know the length L, then you'll have to disregard head losses. Then you can simply apply the Bernoulli equation:

$$ p + rho *(c^2/2) + rho*g*z = constant $$

$p$ is the pressure, $rho$ the density, $c$ the speed, $g$ the gravity, $z$ the height.

Apply this equation in the entry and in the exit and clear $c^2$. After that, multiply $c_2$ by $A_2$ and you'll get the flow rate.

Sorry for the wrong formatting, I still don't know how to format equations properly.