Question

A horizontal portion of a well-insulated ducting for a ventilation system operating at steady state has one inlet at 35 degrees C with a mass flowrate of 45 kg/min and a second inlet at 21 degrees C with a volumetric flowrate of 30.25 m^3/min. A single stream exits at 29 degrees C through a 1.1 m diameter pipe. The pressure for the entire system is 1 atm throughout. Assume air as an ideal.

a.) Draw a detailed schematic of the system, including all pertinent data given in the problem statement.

b.) Determine the mass flowrate of the exiting stream, in kg/min.

c.) Determine the velocity of the exiting stream, in m/s.

*** USE ONLY SI UNITS WHILE WORKING THIS PROBLEM, THANK YOU!

* ALSO, PLEASE AVOID USING DENSITY IF AT ALL POSSIBLE.

Answer 1

b)

Cross-section area at exit A_exit = 3.14 / 4 * 1.1² = 0.94985 m²

Air density = P / (RT)...where R is Gas constant. For air, R = 287 J/kg/K

At 1 atm = 101325 Pa, 21 deg C = 294 K, we get density = 101325 / 287 / 294 = 1.2 kg/m³

At 1 atm = 101325 Pa, 29 deg C = 302 K, we get density = 101325 / 287 / 302 = 1.17 kg/m³

Mass flow rate m = AV

Volume flow rate Q = A*V

By mass conservation

(AV)₁ + (AV)₂ = (AV)_exit........Here A is cross-section area, and V is velocity

45 + 1.2 * 30.25 = m_exit

m_exit = 81.3 kg/min

c)

81.3 = 1.17 * 0.94985 * V_exit

V_exit = 73.156 m/s

answered by: anonymous