Air quantity to blow up a tyre

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  • Thread starter Thread starter Andrea Vironda
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Discussion Overview

The discussion revolves around predicting the air quantity needed to inflate a tire to a specific pressure, utilizing the ideal gas law and exploring related fluid dynamics principles. Participants examine the assumptions of constant temperature and volume, as well as the implications of pressure changes during the inflation process.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant suggests using the ideal gas law to predict the air quantity needed, assuming constant temperature and volume.
  • Another participant notes that temperature will not remain constant during pressurization but may return to the original temperature eventually.
  • A question is raised about determining the approximate internal volume of an inflated tire.
  • One participant proposes modeling the tire's volume as a torus and applies the equation PV=mRT, suggesting that doubling the air mass would double the pressure, provided the tire does not expand significantly.
  • Concerns are expressed regarding the assumption of constant temperature during pressurization, with a suggestion that the air will heat up, affecting flow dynamics.
  • Another participant wishes to calculate the flow from a high-pressure source to the tire, proposing the use of Bernoulli's equation and flow rate equations.
  • A later reply challenges the appropriateness of Bernoulli's equation, stating that flow through the valve is dominated by viscous friction and that the relationship between pressure drop and flow rate should be quantified experimentally.

Areas of Agreement / Disagreement

Participants express differing views on the assumptions regarding temperature during inflation and the applicability of Bernoulli's equation, indicating that multiple competing views remain unresolved.

Contextual Notes

Participants acknowledge limitations in their assumptions, particularly regarding temperature changes during pressurization and the need for experimental quantification of flow rates.

Andrea Vironda
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Hi
i would to know how to predict the air quantity need to blow up a definite-shaped object, like a tyre, to a certain pressure.
i would to apply the ideal gas law, i should obtain something like P/m=cost.
is it correct? i supposed temperature and volume constant
 
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Andrea Vironda said:
apply the ideal gas law
And the equation is...?
Andrea Vironda said:
supposed temperature and volume constant
The temperature will not be constant during pressurisation, but you can suppose it returns to the original temperature eventually.
 
Do you know the approximate internal volume of an inflated tire, or how it might be determined?
 
the Volume of a inflated tyre can be seen as a torus. The equation i would use is PV=mRT, with R the specific air constant, 287 J/(Kg*K)
at P_0=1 bar i have a certain air mass. if i double it, i'll double also the pressure. is it correct?
 
Andrea Vironda said:
if i double it, i'll double also the pressure. is it correct?

Yes, so long as the tyre has not expanded much.
 
i wish to calculate the flow passing from an high pressure source to the tyre. I think it is only function of ΔP.
should i use Bernoulli for finding speed and Q=A*v, [m3/s]?
 
Andrea Vironda said:
i wish to calculate the flow passing from an high pressure source to the tyre. I think it is only function of ΔP.
should i use Bernoulli for finding speed and Q=A*v, [m3/s]?
As I mentioned, you cannot assume constant temperature during pressurisation. The air will heat up, producing some pushback and slowing the flow. Not completely adiabatic, but probably closer to that than to isothermal.
 
I think adiabatic is better. but how can i link a thermodynamic process to the flow speed? if i use, for example, the P-T relation for an adiabatic process, i have not any info about speed
 
Andrea Vironda said:
I think adiabatic is better. but how can i link a thermodynamic process to the flow speed? if i use, for example, the P-T relation for an adiabatic process, i have not any info about speed
The flow through the valve is dominated by viscous friction, so the Bernoulli equation is not appropriate. The rate of flow through the valve is going to depend on the pressure difference across the valve. The relationship between pressure drop and flow rate needs to be quantified experimentally.
 

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