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

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In summary, a swimming pool with a height of 2.50 m and a diameter of 3.00 m has a small hole with a diameter of 1.00 cm located 0.50 m below the top. Using Torricelli's theorem, we can calculate the horizontal velocity of the water coming out of the hole to be 5.42 m/s. By setting the pressure at the hole equal to the dynamic pressure, we can solve for the velocity and find that the water will land 1.11 meters away from the pool. Bernoulli's equation can also be used to solve this problem.
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physhelp90
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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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  • #2
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.
 
  • #3
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.
 
  • #4
Hello
just check the attached doc for the answer method.

tc
mo
 

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  • pool_problem.doc
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  • #5
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?
 

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

1. How do you calculate the landing point of water from a hole in a pool?

The landing point of water from a hole in a pool can be calculated by using the basic principles of physics and mathematics. The formula for calculating the landing point is: x = (2gh)^(1/2), where x is the distance from the hole to the landing point, g is the acceleration due to gravity, and h is the depth of the hole.

2. What factors affect the landing point of water from a hole in a pool?

The landing point of water from a hole in a pool can be affected by several factors, including the depth of the water, the size and shape of the hole, the velocity of the water, and the surface tension of the water. These factors can all impact the trajectory and distance of the water as it exits the hole.

3. Can the landing point of water from a hole in a pool be predicted accurately?

Yes, the landing point of water from a hole in a pool can be predicted accurately by using the correct formula and taking into account all of the relevant factors. However, it is important to note that small variations in the initial conditions, such as the amount of water in the pool or the shape of the hole, can affect the accuracy of the prediction.

4. How does surface tension affect the landing point of water from a hole in a pool?

Surface tension is the force that causes the surface of a liquid to behave like a thin elastic sheet. It can play a role in the landing point of water from a hole in a pool by affecting the trajectory of the water as it exits the hole. If the surface tension is high, the water may form a more compact and streamlined shape, resulting in a longer distance traveled from the hole.

5. Are there any real-life applications for calculating the landing point of water from a hole in a pool?

Yes, there are several real-life applications for this calculation. One example is in the design and construction of water slides, where engineers need to consider the trajectory and landing point of water as it exits the slide. This calculation can also be useful in predicting the spread of contaminated water in case of a spill or leak in a pool or water system.

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