Final answer:
The mass flow rate of air through a 4.4-inch diameter pipe at 13.0 mph can be calculated by finding the cross-sectional area, the volume flow rate, and then multiplying by the air density.
Step-by-step explanation:
To calculate the mass flow rate of the air through a circular pipe with a 4.4-inch diameter, we must first determine the cross-sectional area of the pipe. Using the formula A = π(d/2)^2, where d is the diameter, and convert inches to feet, we find that the area equals A = π(4.4 in / 2)^2 *(1 ft/12 in)^2 = 0.08526 ft². With the velocity of air given as 13.0 mph, we convert it to feet per second (13.0 mph * 5280 ft/mi / 3600 s/hr = 19.07 ft/s). The volume flow rate (Q) is then A * velocity.
The density of air on a standard day at sea level is 1.225 kg/m³, which is 0.0023769 slugs/ft³. Therefore, to find the mass flow rate, multiply the volume flow rate by the air's density:mass flow rate = density * volume flow rate = 0.0023769 slugs/ft³ * 0.08526 ft² * 19.07 ft/s, giving us the mass flow rate in slugs per second. To convert to ten thousandths, we need to multiply by 10,000.