obviously, the driving force behind tea pouring is gravity. gravity pulls the liquid, and part of the pot isn't supporting the liquid when tilted downwards: the spout opening.
since the teapot is rigid, the only things that can change how the liquid flows out are:
- swinging the teapot around
- the air pressure at the exposed surfaces
the exposed liquid surfaces are inside the teapot and at the spout opening.
call the pressures at these surfaces P
in and P
out, respectively.
liquid flowrate increases with increasing P
in and decreasing P
out.
P
out is clearly fixed -- it's atmospheric pressure.
also, P
in is only going to be at most atmospheric pressure unless you're blowing into the lid hole while pouring:
however, if the lid hole is small enough (resisting airflow), gravity can pull the liquid out of the pot faster than air rushing into the pot can equalize the pressure between the pot interior and exterior. in this case, a vacuum is created (P
in < P
atm).
increasing lid hole size is only going to help up to the point where the pressure can fully equalize to atmospheric pressure inside the pot while you pour.
making the hole smaller than that will always make it pour slower, and making it bigger will never make it pour faster (or slower for that matter).