# Fluid Mechanics: Pressure Question

1. May 22, 2014

### MechEngJordan

1. The problem statement, all variables and given/known data

A tyre pressure gauge indicates 20 N/cm2 for a tire at 34°C after a fast motorway run. Assuming that the volume of the air in the tyre is constant, atmospheric pressure is 760 mmHg and the air gas constant is 0.287 kJ/kg.K:

i) Estimate the indicated pressure when the tyre has cooled to 10°C.

ii) If the tyre is treated as a tube of cross-sectional area 0.015 m2 rolled into a ring of mean diameter 0.035 m, estimate the mass of air in the tyre.

2. Relevant equations

Combined Gas Law:

$$\frac{p_1V_1}{T_1}=\frac{p_2V_2}{T_2}$$

Equation of State for Ideal Gas:

$$pV = mRT$$

3. The attempt at a solution

For i)

Converting units into SI and recognising volume = constant gives:

$$\frac{p_1}{T_1}=\frac{p_2}{T_2}$$

$$\frac{p_1T_2}{T_1}=p_2$$

$$\frac{(200kPa)(283.15K)}{307.15K}=p_2$$

$$p_2 = 184kPa$$

I am unsure how exactly how to proceed with ii)

Any help would be appreciated.

Last edited: May 22, 2014
2. May 22, 2014

### SteamKing

Staff Emeritus
Do you know how to calculate the volume inside the tire given the data in part ii?

If you know the volume, the temperature, and the pressure, can you calculate the mass of air consistent with these properties?

3. May 22, 2014

### MechEngJordan

I am unsure of how I would calculate the volume -- which is particularly annoying, as I am aware that would solve my problem by application of the ideal gas law.

4. May 22, 2014

### tms

The shape of the tube is called a torus. Think of it as a cylinder with the ends connected. Calculate the volume in the obvious, straightforward fashion.

5. May 22, 2014

### MechEngJordan

Thanks for the help.