Air quantity to blow up a tyre

[Andrea Vironda]

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

 

[haruspex]

apply the ideal gas law

And the equation is...?

supposed temperature and volume constant

The temperature will not be constant during pressurisation, but you can suppose it returns to the original temperature eventually.

 

[Chestermiller]

Do you know the approximate internal volume of an inflated tire, or how it might be determined?

 

[Andrea Vironda]

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?

 

[haruspex]

if i double it, i'll double also the pressure. is it correct?

Yes, so long as the tyre has not expanded much.

 

[Andrea Vironda]

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]?

 

[haruspex]

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.

 

[Andrea Vironda]

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

 

[Chestermiller]

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.