Suppose that the pressure in a car tire is discovered to be 20 psig, which is well below the 30 psig recommended for that type of tire. A nearby service station provides compressed air at P₁ = 50 psig. The air is delivered through a smooth rubber hose of diameter D = 6 mm and length L = 5 m. It is desired to estimate the time needed to correct the tire inflation, if the flow is isothermal at 20 °C. The air properties at that temperature and the average tire pressure (P₂ = 25 psig) are ρ₂ = 3.3 kg/m³ and ν₂ = 5.5 × 10^–6 m²/s.

(a) Show how to calculate the mass flow rate w for specified values of P₁ and P₂.

(b) As an estimate of the average mass flow rate, calculate w for steady flow at P₂ = 25 psig. Confirm that Eq. (12.4-24) and the Blasius equation are both applicable.

(c) Car tires are rigid enough to have a nearly constant air volume. If V = 600 in³, what is the approximate inflation time?

Transcribed Image Text:

• (X) = (2 = (1/₁ - FX)" '. (12.4-24)