If a pipe (of unknown/arbitrary length) with cross section area $A$ and with a continuous supply of a simple fluid with a known pressure $p$ at the opening to the atmosphere, which has a pressure of $p_a$, what would be the rate of flow out of the pipe?
I have looked but not found an answer anywhere, but apologies if this seems trivial or seems to be a duplicate of another question.
Poiseuille's Law,
$$ Flow=\dfrac{π\cdot r^4 \cdot (P-Po) }{ 8\cdot η\cdot L} cm^3/s $$ And in your case assuming you have a Pipe with the area $Acm^2$,
$$ Flow= A\dfrac{r^2 \cdot (P-Po) }{ 8\cdot η\cdot L} cm^3/s $$
-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.
