What is the Velocity of Water Exiting a Hole in a Bucket?

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Homework Help Overview

The problem involves a bucket with a hole at the bottom, where water is sprayed horizontally. The setup includes a height of 1 meter from the ground and a hole diameter of 3.5 mm, with the water landing 60 cm away from the bucket. Participants are tasked with determining the velocity of the water exiting the hole and the height of the water in the bucket.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss using Bernoulli's principle and the relationship between vertical and horizontal motion. Questions arise about calculating the time it takes for water to hit the ground and the initial horizontal velocity required to reach the specified distance.

Discussion Status

The discussion includes various interpretations of the problem, with some participants suggesting methods to analyze the projectile motion of the water. There is acknowledgment of the need to find the height of the water to achieve the desired velocity, and some guidance has been offered regarding the relationship between horizontal and vertical motion.

Contextual Notes

Participants note constraints related to the information provided, such as the need to derive time from distance in both the x and y directions, and the role of gravitational acceleration in the vertical motion of the water.

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Homework Statement


This was a problem on a test today, and it is driving me nuts that I cannot figure it out. We were told that we had a bucket 1 meter off of the ground with a 3.5 mm hole in the bottom. The water sprayed a horizontal stream 60 cm from the bucket. We are asked to find the


Homework Equations


I know we need to use bernoulli's just not sure how.


The Attempt at a Solution


I tried to solve for velocity and height.. but it seems like you need one to get the other.
 
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HelpMePleez said:

Homework Statement


This was a problem on a test today, and it is driving me nuts that I cannot figure it out. We were told that we had a bucket 1 meter off of the ground with a 3.5 mm hole in the bottom. The water sprayed a horizontal stream 60 cm from the bucket. We are asked to find the
Find the... ?
 
How long will the water take to hit the ground? If it lands 60cm away, how fast is it moving horizontally?
 
Oh sorry asked to find the height of the water in the bucket
 
HelpMePleez said:
Oh sorry asked to find the height of the water in the bucket

Start with haruspex's advice. If you consider the water stream to be composed of a series of discrete slugs of water, each behaving like a free-falling projectile, can you determine the initial horizontal velocity one such slug must have in order to land 60cm away?

After that you can worry about how deep the water in the bucket has to be to produce this velocity (as you surmised, Bernoulli is involved).
 
horizontal distance

I cannot seem to find a way to find the time it takes to hit the ground, when all I know is distance in the y and x direction. Is acceleration g? and if so does that mean it's zero in the x?
 
HelpMePleez said:
I cannot seem to find a way to find the time it takes to hit the ground, when all I know is distance in the y and x direction. Is acceleration g? and if so does that mean it's zero in the x?
Yes, the water is falling under the influence of gravity. So how long does it take something to fall 1m from rest?
 
I found the right equation. Solved for t in the y direction and then used that to find initial v in the x direction, then used bernoulli's to find height! Thanks you guys very much for the help!
 

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