Calculating Water's Landing Point From a Hole in a Pool

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The discussion focuses on calculating the distance water will land from a hole in a swimming pool, which is 2.50 m tall and has a 1.00 cm diameter hole located 0.50 m below the top. The user initially applies Torricelli's theorem to find the horizontal velocity of the water, calculating it to be 5.42 m/s. They then determine the time the water is in the air to be approximately 0.20 seconds, leading to a distance of 1.11 meters. There is a suggestion to use Bernoulli's equation for a more accurate solution, emphasizing the need to find the pressure at the hole's level. The conversation also includes a humorous note about visualizing the scenario of water leaking from the pool.
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Homework Statement


A swimming pool is filled with water. It is 2.50 m tall and 3.00 m in diameter. There is a small 1.00 cm (in diameter) hole in the side of the pool and its 0.50 m below the top. How far from the pool will the water coming out of the hole land?


Homework Equations





The Attempt at a Solution



Here's my attempt using Torricelli's theorem, however I need to use Bernoulli's equation any help is appreciated.

Vx = Sqrt 2g(2.50 - 1.00)
Vx = 5.42 m/s This is the horizontal velocity.

t= sqrt 2h/g = .20 seconds = time water is in air

x = t x Vx

x = 1.11 meters ?
 
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Well, do you know what Bernoulli's equation is?

If you know that, then so you basically just need to find the pressure at the level where the hole is, then set that equal to dynamic pressure and solve for the velocity value, which should all be in the x direction.
 
I'm really having trouble imagining a swimming pool (2.5 m tall) with a hole and water leaking out of the side of this swimming pool and landing somewhere. It's like watching a movie - you need to suspend your disbelief :mad:

Sorry, don't mind me - please go ahead and solve the problem.
 
Hello
just check the attached doc for the answer method.

tc
mo
 

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naresh said:
I'm really having trouble imagining a swimming pool (2.5 m tall) with a hole and water leaking out of the side of this swimming pool and landing somewhere. It's like watching a movie - you need to suspend your disbelief :mad:

Sorry, don't mind me - please go ahead and solve the problem.


The pool is standing above ground. Maybe imagine it as just a giant water tank/cylinder?
 

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