Conservation of Mass of Air Flowing in Duct

[Red_CCF]

Homework Statement

The problem asks, air at 20 degrees celsius enters a 2-m long closed channel with 5mm x 5mm square duct at 0.2 m/s. One part of the question asks, if someone clams that the average velocity of the exiting air is slightly more than 0.2m/s, does this violate the conservation of mass? Explain

Homework Equations

mdot = density * velocity * area

The Attempt at a Solution

My reasoning was that, since 0.2m/s << 343m/s which is the speed of sound in air, the Mach number is very small, so air is basically incompressible and inlet and exit density is equal. Given that cross sectional area does not change, and by conservation of mass mdot must be the same in and out, therefore Vin must be equal to Vout so the exiting air cannot have a higher velocity.

However, I got marked wrong on this question and on my test paper the prof wrote that density decreases. Since it costs money for remarking, I want to be sure if I am correct or not before going for recheck

Any help is appreciated

 

[RTW69]

It isn't clear to me why the density of the air decreases. Is the duct being heated?

 

[Red_CCF]

It isn't clear to me why the density of the air decreases. Is the duct being heated?

It seems I made a very stupid mistake. Upon a second look at the question I found that the duct was being heated and it seems that I forgot about it. The prof always assumed velocity didn't change when there's a temperature variation for the flow which is how I probably got tricked by this question.

Thanks very much for pointing that out, this was an important lesson learned for me