In the simplified depiction of an ice rink with an ice resurfacing machine opera
ID: 819921 • Letter: I
Question
In the simplified depiction of an ice rink with an ice resurfacing machine operating (shown in Figure), points 1 and 3 represent the ventilation air intake and exhaust for the entire ice rink, and point 2 is the resurfacing machine's exhaust. Conditions at each point are (C indicates the concentration of carbon monoxide, CO): point 1: Q1=3.0 m3/s, C1=10 mg/m3; point 2: emission rate = 8 mg/s of nonreactive CO; point 3: Q3, C3 unknown. The ice rink volume (V) is 5.0 x 104 m3. (a) Define a control volume as the interior of the ice rink. What is the mass flux of CO into the control volume, in units of mg/s? (b) Assume that the resurfacing machine has been operating for a very long time, and that the air within the ice rink is well mixed. What is the concentration of CO within the ice rink, in units of mg/m3?
Explanation / Answer
A) Mass flux is the equivalent of the volumetric flow rate times the mass of CO2 per volume:
Q1*C1 = 3.0 m^3/s * 10mg/m^3 = 30mg/s
B)Given the flow rate, determine how long it takes air to move from Point 1 to Point 3. If Q1 = 3.0m^3/s, and the ice rink is 5.0*10^4m^3, then it takes 16,666.7 seconds for air to move through the entire rink. During this time, 8mg/s of CO2 is released, meaning there is 133,333 mg/s of CO2 within the control volume. Divide this number by the overall volume of the rink, 5.0*10^4m^3 to get the concentration of CO2 within the rink due to the resurfacing machine, 2.67mg/m^3. Add this to the preexisting concentration of 10mg/m^2 to get the new concentration, 12.67mg/m^3.