How Can Air Velocity Be Calculated at a Nozzle's End Over Time?

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Discussion Overview

The discussion revolves around calculating the air velocity at the end of a nozzle over time, specifically in the context of a piston moving in a cylinder that pushes and pulls air through the nozzle. The scenario is likened to a bicycle pump, and the focus is on understanding the dynamics of compressible flow and unsteady flow conditions.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant describes a piston translating in a cylinder, pushing and sucking air through a nozzle, and notes the non-linear (exponential) velocity of the piston until it reaches the cylinder wall.
  • The same participant expresses uncertainty about using Bernoulli's principle due to the compressible nature of the flow and questions how pressure builds up given that airflow through the nozzle may negate this buildup.
  • There is a mention of unsteady flow, with the participant indicating difficulty in understanding the unsteady flow equations relevant to their scenario.
  • Another participant suggests modeling the problem as a tire pump and provides a link to a resource, indicating that the problem is not trivial.
  • A later reply clarifies that the original poster is not looking to pump air into a tire but rather into the environment, where atmospheric pressure is constant and no pressure builds up due to an infinitely large volume.
  • A request for further insights into fluid dynamics is made, indicating a desire for more technical discussion.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the best approach to calculate air velocity, and multiple competing views and uncertainties remain regarding the application of fluid dynamics principles to the scenario described.

Contextual Notes

The discussion highlights limitations in understanding the application of Bernoulli's principle to compressible flow, the complexities of unsteady flow equations, and the assumptions regarding pressure buildup in the environment.

Who May Find This Useful

Individuals interested in fluid dynamics, particularly those exploring compressible flow and unsteady flow conditions in practical applications such as piston-driven systems.

scientist0523
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Hi,

This is not homework, it's for myself. I'm trying to understand it for me only.

I have a piston that is translating in a cylinder and pushing/sucking air through a nozzle.
It's much comparable to a bicycle pump.
The piston is moving with non-linear (exponential) velocity until it slams against the cylinder wall.

I need a formula to find the air velocity at the end of the nozzle in function of time.

I have tried using Bernoulli's principle, but it does not apply because we are dealing with a compressible flow. And I'm not sure how pressure builds up, as the airflow through the nozzle 'negates' the pressure buildup
Also the volume and position (even velocity?) of the air particles in the cylinder change in time, so that means it's an unsteady flow?
I have looked at the unsteady flow equation but I can't seem to understand it either.

Help is appreciated.
 
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Thank you very much for this link!
I knew it wasn't easy, but this will help me a lot.

EDIT: as useful as it may be, I'm not looking to pump the air into a tire, but to pump it in the environment with P=atm and so no pressure builds up as it's volume is infinitely big.
 
Last edited:
Anyone with more insight of fluid dynamics?
 

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