How does the size of a hole affect the rate of water drainage from a barrel?

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Homework Help Overview

The discussion revolves around a problem involving fluid dynamics, specifically how the size of a hole affects the rate of water drainage from a barrel. The original poster presents a scenario with a 33-gallon barrel and a one-inch hole, seeking to understand the drainage rate and how it relates to water being pumped in.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the depth of water and the drainage rate, with some questioning the initial conditions necessary for calculations. Others explore the implications of different hole sizes on water flow and drainage time.

Discussion Status

The conversation is ongoing, with some participants providing insights into the necessary calculations for flow rate and velocity. There is a recognition of the need for additional parameters, such as the height of the water, to proceed with accurate calculations. Various interpretations of the problem are being explored.

Contextual Notes

Participants note the importance of the barrel's height and the depth of the water in relation to the hole, indicating that these factors are crucial for determining the drainage rate. There is also mention of external resources that could provide further information on the topic.

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I've got a math problem, that's way over my head, here it is.
Figurativly I have a 33 gallon barrel and it has a one inch hole in the bottom, if the barrel is full of water, how many gallons would escape a minute, the top is open, I need to know to figure out how much water being pumped in would be needed to keep the barrel full?
If it turns out to be a simple answer, what would the result be if it was a two inch hole?
 
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You have to put in the same amount as is leaving.
Unless you know the depth (under water) of the hole,
you can't even start (the speed is 0 if depth is 0).
 
Not sure what your saying , but the barrel is full of water when the spigot at the bottom is opened, and the extra water is being fed into it at the top, at this same rate, from another source.
 
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Although I can't figure it out, I've seen in these forums that it can be calculted how long it would take a cubic mile by a cubic mile container of water to finally drain out of a one inch hole, is this a different mindset?
 
It the barrel remain full you need height of the barrel to find the velocity of water draind given by v = sq.rt.(2gh)
then the volume flow rate will be A*v should be equal to the water to be pumped in where A is the cross-section area of the hole.
 
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Just found this http://www.ap.stmarys.ca/demos/content/fluids/pressure_head/pressure_head.html
Thanks
 
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