Methane at a temperature of 5◦C and a pressure of 500 kPa (absolute) flows in a straight 50-mm-diameter duct at the rate of 5 L/s. The duct is inclined upward at 10◦ to the horizontal, and the...

Methane at a temperature of 5◦C and a pressure of 500 kPa (absolute) flows in a straight 50-mm-diameter duct at the rate of 5 L/s. The duct is inclined upward at 10◦ to the horizontal, and the pressure drop over a 20-m segment of the duct is measured as 300 Pa. A literature search for the properties of methane at the given temperature and pressure indicates that the dynamic viscosity of the gas is 0.01054 mPa·s under these conditions. Estimate the friction factor and equivalent sand roughness of the duct.