Be it in cooking or an experiment, when transferring liquid from one container to another using a funnel should you:
(a) pour it all straight into the funnel, filling it up and waiting for the liquid to drain through
(b) pour it such that the end of the funnel is still always filled but the volume of 'blocking' liquid in the funnel is small – so you pour it slowly
Does one of the above options achieve a faster rate flow of liquid through the funnel? I'm thinking bernoulli's principle is going to come into this? Intuitively the blocking liquid in (a) is going to increase the pressure at the bottom of the funnel and hence 'force' more liquid through…
Best Answer
The Bernoulli equation for a non-turbulent fluid with density $\rho$ is
$$ P_\text{fluid} + \frac12 \rho v^2 + \rho g h = \text{constant}. $$
At the top and the bottom of the funnel, where the fluid is exposed to the atmosphere, the fluid surface will move until the fluid pressure and the atmospheric pressure are the same. For an ordinary funnel, that effectively means that the inlet and outlet pressures are identical. If you are continuously filling the funnel, so that the fluid speed $v$ at the top is zero --- or alternatively, if the top of the funnel is so much larger than the outlet that the flow speed at the top is negligible --- then the outlet speed is
$$ v = \sqrt{2g\Delta h}. $$
So doubling the distance $\Delta h$ between the exit of your funnel and the surface of your fluid will make your exit velocity about 40% larger.
An engineer friend of mine once solved a problem with a water reservoir that was draining too slowly by adding a longer hose to dangle under the outlet. It's the same trick: increase the flow rate by increasing $\Delta h$.