Final answer:
The maximum flow rate of air in a 4-inch diameter pipe at laminar flow can be calculated using Poiseuille's law, which depends on the pressure difference, pipe radius, length, and viscosity of the air. However, the viscosity value is not given in the question.
Step-by-step explanation:
The maximum flow rate of air that may occur at laminar condition in a 4 in diameter pipe can be calculated using Poiseuille's law. Poiseuille's law states that the flow rate is directly proportional to the pressure difference and the fourth power of the pipe radius, and inversely proportional to the length of the pipe and the viscosity of the air.
Given the diameter of the pipe is 4 inches, we can calculate the radius as 2 inches or 0.1016 meters. The absolute pressure is given as 30 psig, which can be converted to absolute pressure by adding the atmospheric pressure of 14.7 psi. The temperature is given as 100⁰F, which can be converted to Kelvin using the formula K = (°F - 32) * 5/9 + 273.15.
Using these values, we can calculate the maximum flow rate using Poiseuille's law:
- Convert the diameter to meters: 4 in = 0.1016 m
- Convert the absolute pressure to Pascals: (30 psig + 14.7 psi) * 6894.76 Pa/psi = 205552.61 Pa
- Convert the temperature to Kelvin: (100 - 32) * 5/9 + 273.15 = 310.93 K
- Calculate the maximum flow rate using Poiseuille's law: Q = π * (r^4) * ΔP / (8 * η * L)
Substituting the values into the formula, we get:
Q = π * (0.1016)^4 * 205552.61 / (8 * η * L)
Since the value of η (viscosity) is not provided in the question, we cannot calculate the maximum flow rate without this information.