Can this problem be solved using conservation of mass and momentum?

[Physics_wiz]

Can this problem be done?

I just took a test with this problem on it (50% of the test grade) but I don't know if it can even be done or not.

We have a spacecraft landing on Mars. The spacecraft is landing "steadily at 1 m/s". It's basically a conic section with a "shell" around it (picture a thick vertical cylinder with inside diameter increasing except that the hollow part is the outside, not inside). It has rotors on the bottom which pull the air through the hollow part and accelerate it and push it out the bottom to balance out the force of gravity on the craft. The speed of the air going in from top and the area of the top hollow part are given. We need to find the speed of the air coming out of the bottom and the area of the hollow part where the air comes out from the bottom.

I don't know if this problem is right or wrong because the area*velocity has to be a constant (conservation of mass), but the area itself doesn't have to be a constant, nor does the velocity.

Conservation of mass:
(pAV)1 = (pAV)2
where p is the desnsity.
The density cancels out and we're left with
(AV)1 = (AV)2
We need one (area or velocity) to solve for the other.

I'm not going to go through everything I did on the test, but just give me your thoughts about this problem.

PS. This is a fluid mechanics class.

 

[Astronuc]

Well, somewhere one would need the weight of the craft from which one could calculate the thrust (unless thrust is given), which would give you a second equation.

http://www.grc.nasa.gov/WWW/K-12/airplane/turbth.html
http://www.grc.nasa.gov/WWW/K-12/airplane/thrsteq.html

 

[Physics_wiz]

The weight was given but I never saw those equations you supplied before. I tried using the linear momentum equation but the right hand side (sigma F) was 0 since the craft was moving at a constant velocity, so no acceleration. I guess maybe the partial with respect to time term isn't 0, but that would mean the flow was unsteady.

 

[FredGarvin]

This seems like a classic one dimension momentum problem. I guess I am a bit confused as to what exactly was given to you as data on the test. From what I can see you were given: Weight of the craft, speed of fluid at one area and the downward speed of the aircraft. Is there anything else that was given?

To be absolutely correct, there would be two P*a terms at the two areas that it looks like you would have to neglect in this case, but should be included in the calculations.