[bamster]

can be withdrawn through the stopcock?

[bromidewind]

Draw some water up in a straw and hold your finger over the top. No water comes up because the air pressure coming from underneath keeps it from flowing out. Now take your finger off, and the air pressure above pushes the water out. The same thing applies to sep funnels. Air pressure is pushing up into the nozzle, preventing the liquid from coming out. By removing the stopper, you're allowing air pressure to enter and "push" the liquid out. Also, opening the stopper or inverting and opening the stopcock from time to time is a good way to vent any gas buildup you may have as a result of your reaction.

[Smrt guy]

Draining from a closed system creates a vacuum inside the container.  This is why the air pressure will push the liquid back in, countering gravity.  Opening the container releases the vacuum, leaving gravity as the only force applied to the liquid inside.  Hence, it drains.

[Arctic-Nation]

During my time assisting first-year uni students in the lab, I would give them a full showdown of how to perform an extraction, explaining every step along the way, except removing the stopper. I would take it off, but not mention it. 60 to 80% of the students would later wonder why their separation funnel had the hiccups.

One of the few guilty pleasures I could afford.

[stewie griffin]

I do a full demo to start the lab too. I pour my solution into the funnel with the stopcock open on purpose, show them my sep funnel dance, etc. I always tell them to take the stopper off and then I say, " Every semester I tell my students that at least one of you will still forget to remove the stopper, and ever semester there's always someone who thinks their sep funnel is messed up." The students of course laugh at this and assume they would never be that... a.. ahem.. "silly" let's say. Then I walk around and point it out to the seven or eight that leave the stopper on. I love it. 

[Smrt guy]

I had a friend who last year was giving a demonstration on using a sep funnel and while mentioning the necessity of burping the funnel, a student who had chosen to work instead of listen had the thing blow its top spraying solvent everywhere.  Classic.

[nj_bartel]

better than exploding glass!

[bromidewind]

I haven't seen any sep funnels explode, but I've seen the stoppers shoot across the room, students break the stem off, pull their stopcock completely out, etc. The one explosion I have seen in the lab though was a distillation apparatus that had ether in it and had been boiled dry. Later, we found glass shards embedded quite far into the tile ceiling.

Also, I forgot to mention this before, but if you want to make sure you can get the stopcock out, use some good old silicon grease. Just a little though. It shows up at 0.07 ppm on H-NMR and is a big annoyance. I would recommend using a towel and gloves to prevent the chance of any liquid possibly leaking out the stopper. I burned my middle and index fingers with some nitric acid once because a slight amount of it got around the stopper.

[pacifyer]

Sometimes, pressure develops in a close separation funnel, and the stopper can (violently) pop-up. That can be dangerous.