surface tension and air pressure

My 5th grader has a science project. He chose a water bottle trick.

We know that when you poke a pinhole into a sealed bottle of water the water will not flow because of the lack of air pressure but when you unscrew the cap the water will flow out of the hole.

He is hypothesizing that if you leave the cap on the bottle and also poke a pinhole in the top cap of the bottle that the water will flow out of the pinhole at the bottom of the bottle at a slower rate than if he were to poke 2,3,4 holes in the cap or entirely unscrew the cap because he is letting in only a small amount of air through the top.

He tested this and there was almost no difference in the time it took for the bottle to drain. Why would only a small pinhole in the cap allow the bottle to drain at the same rate as removing the cap entirely?

• @TáMéCeart This looks like an answer rather than a comment. Jan 7 '17 at 19:01

2 Answers

When the air pressure pushing on the top surface of the water is equal to the air pressure pushing back on the water trying to come out of the pinhole at the bottom, those two pressures cancel out.   Then the rate of the water coming out of the pinhole at the bottom depends only on the pressure due to the weight of the water and the size of the bottom pinhole.   With either a pinhole in the cap or with the cap removed, the pressure at the top is able to stay equal, because it is so much easier for air to flow through a pinhole than for water to flow through a pinhole.   In other words, the change in volume of air at the top can keep up with the slow change in volume of the water just as easily with a pinhole as with the cap removed.

If you drilled a big hole at the bottom so the water came out fast, I'm quite sure that you would get a measurable difference in emptying time between one pinhole in the cap and several pinholes.

• +1 However your last statement is not obvious and needs experimental verification.
– Deep
Jan 9 '17 at 6:35
• @Deep You are right. I've edited that statement. Jan 9 '17 at 11:07

When you have a bottle or jar that is sealed on tight , no matter how hard you twist it or stick it in a door jamb, you can't open it. Yet if you jab a tiny little hole in the jar lid, the top opens easily. It's basically the same reason, once you equalise the pressure, that's all you need do