Problem 38P

A tire is filled with air at 15°C to a gauge pressure of 220 kPa. If the tire reaches a temperature of 38°C, what fraction of the original air must be removed if the original pressure of 220 kPa is to be maintained?

Solution 38PIntroductionThis question can be solved using the Poiseuille’s equation.Step 1Given that,Length l = 4.0 cm 2l = 4.0 × 10 mRadius r = 1.0 mm 3r = 10 mTherefore, cross-section of the needle A = × r 2A = 3.14 × (10 3) m 2A = 3.14 × 10 6 m 2Given, velocity v = 10 m/sTherefore, volume flow rate of the water is Q = Av = 3.14 × 10 6 m × 10 m/s = 3.14 × 10 5 m /s