# Deriving relationship about water not falling down from a hole under a fast flowing stream [closed]

A gutter is tilted from an angle of $$\theta$$ with respect to earth. There is a hole on the gutter from a distance of $$l$$ (m) from the top of a gutter. What is the speed of the water that should flow above the hole so that water will not drop down from the hole. (Assume speed of the water stream in the gutter at the top is zero).

I can't identify the forces and principle behind this phenomenon to derive an relationship. I need to derive an equation. Variables that may affect are $$\theta$$, $$l$$, $$r$$ (radius of the hole), pressure difference (Bernoulli) etc. Can someone please help me to understand how water would not fall down and to derive an equation?

## closed as off-topic by Kyle Kanos, John Rennie, ZeroTheHero, Jon Custer, user191954 Nov 29 '18 at 14:41

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## 1 Answer

Yeah, this question is bogus.

I assume they're trying to model the water as if it were little billiard balls rolling down a plane. So one can imagine that there is a speed at which the ball will not fall enough during the transit time across the hole that it will "bump back up" onto the plane. Of course, for this one would need a large ball and a small hole.

Given that for this definition the size of the ball is effectively zero, and the size of the hole isn't even given, the answer is "90 degrees". The effect of gravity is independent of velocity; if there is any angle at all the water is going to go through the hole.

One can imagine adjustments for things like surface tension and the size of the hole, but the fact that neither is mentioned appears to be telling.

• It could be a stupid trick question with the expected answer of 90 degrees. OP does mention that "Variables that may affect are θ, l, r (radius of the hole), pressure difference (Bernoulli) etc." so perhaps they do want to go as far as surface tension. – JMac Nov 28 '18 at 15:14
• Maybe the "top of the gutter" is where the gutter is horizontal, and it bends down at an angle $\theta$. Then the water wouldn't go in the hole if it was going fast enough because it would shoot out into the air. – Ben51 Nov 29 '18 at 3:35