Q & A: Squirting Liquid

Please explain why the mass and amount of a liquid in a cup with a hole in the side near the bottom would affect the distance which the liquid would squirt out.
- Zaineb Abdulla (age 7)
Universal School, Bridgeview, IL, USA

Hi,

Imagine a paper cup full of water. If you dropped a small rock in it, some of the water would splash out a little bit. But if you dropped a huge weight on it, then the water would go flying all over. Or if you take one of those packets of ketchup, then the harder you stomp on it, the farther the ketchup will fly (but don't try it in the house).

Well, it's really the same thing with a cup that has a hole in the side. Water is pretty heavy, and all the water above the hole is forcing the water down at the bottom to spray out the side. The more water there is above the hole, the more weight there is pushing down. You can feel how real the weight of water is when you swim in a pool. It feels a lot different to swim below 10 feet of water than it does to swim below 2 feet of water (think about your ears).

So now imagine a cup as tall as a giant building. If there's only an inch of water in it, then not much would happen when you poked a hole in it. But if it was filled with hundreds of feet of water, then there would be thousands and thousands of pounds of weight above the bottom. And if you poked a hole in the cup way down there at the bottom, then all that weight from the water above you would be like a huge foot stomping on the water by the hole and it would send it flying a long way.

Write again if you have more questions.

Jesse

(published on 10/22/2007)

Why then in a water tower a hole that would be half way down rather than at the bottom would quirt out a further stream, one that is equal to the height of the water column?
- Anonymous
Canton, Ohio US of A

Great question- I hadn’t even realized this was true.

The original question asked something a little different. If you have the hole at a fixed place, the higher the water goes above the hole, the more pressure there will be and the farther the water will squirt.

Your question assumes that the water has a fixed height (the tower height) and asks where to put the hole to get the maximum stream distance. This involves a tradeoff. If you put the hole too high, there won’t be much pressure on it. If you put the hole too low, the stream will hit the ground before it travels far.

If you assume:
1. The stream goes out straight sideways initially.
2. You can ignore the viscosity and calculate the water speed from Bernoulli’s principle.
3. You can ignore air friction.

then it’s a straightforward calculation to show that putting the hole halfway up gives the farthest distance sideways, and that that distance is also just the height of the water column.

Mike W.

Amazing but true. 
Just like Mike, I’ve never done the calculation.
’You learn something every day’

LeeH

(published on 01/27/2008)