Speed of escaping gas from a cylinder

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Homework Help Overview

The discussion revolves around understanding the speed of gas escaping from a cylinder through a small opening. The problem involves applying principles from fluid dynamics, particularly Bernoulli's equation, and assessing the conditions under which it is valid.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the applicability of Bernoulli's principle in the context of gas flow from a cylinder, questioning whether the flow can be considered steady given the conditions described. There is discussion about the implications of the "small opening" and "large cylinder" assumptions on the flow characteristics.

Discussion Status

The conversation is ongoing, with participants expressing differing views on the validity of applying Bernoulli's equation. Some provide reasoning for considering the flow as steady, while others remain uncertain about the assumptions involved.

Contextual Notes

Participants note the potential conflict between the assumptions of steady flow and the nature of the gas escaping through a small opening, raising questions about the relevant principles to apply in this scenario.

Jahnavi
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Homework Statement


escaping gas.jpg


Homework Equations

The Attempt at a Solution



I don't understand which concept to apply in this question . The hint says to apply Bernoulli's equation and uses ∆P (excess pressure ) = (1/2) ρ v2 . This does give right answer .

But I think this is wrong . We cannot apply Bernoulli's equation as it will not be a steady flow .

What is the relevant principle to be applied in this problem ?
 

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Bernoulli’s principle. The flow is approximately steady.
 
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Orodruin said:
The flow is approximately steady.

I think the gas would come out quite rapidly . No ?

Why does the question say " small opening " and " large cylinder " ? How do these assumptions help in applying Bernoulli's principle ?
 
Jahnavi said:
I think the gas would come out quite rapidly . No ?

Why does the question say " small opening " and " large cylinder " ? How do these assumptions help in applying Bernoulli's principle ?
If the opening is small, then the gas would not come out quite rapidly. Suppose point 1 is only a few oriface diameters upstream of the oriface, and point 2 is only a few oriface diameters downstream from the oriface. That would mean that, for fluid parcels to get from point 1 to point 2 would require only a fraction of a second. This would be small compared to the time scale required for the pressure in the large tank to change significantly. Therefore, for all intents and purposes, the flow would be considered steady.
 
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Thank you very much .
 

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