I am confused about air density/drag

[sdfsfasdfasf]

Homework Statement

x

Relevant Equations

x

Part a) Is fairly trivial, just multiply both the given numbers to find the total change in momentum per second, which by Newtons II/III law is the thrust produced.

Part d) is confusing me a great deal. I agree that pressure/density of air will decrease with altitude, this means that there will be less mass per second pushed by the fan which means there will be less thrust produced at higher altitudes. The question also wants me to explain why this results in a greater max speed, I know that drag is roughly proportional to v^2, so does a smaller thrust(at max speed drag and thrust are equal), not imply a smaller drag, and thus a smaller drag imply a smaller speed?

What am I missing? Thank you so much for helping me!

 

[pbuk]

What causes drag? At a given speed is the drag the same at different altitudes?

 

[Orodruin]

Drag counteracts the motion. Smaller drag will invariably lead to a higher velocity at a given thrust. But your thrust is not constant with altitude and so your task is to explain why the velocity still goes up at higher altitude even though thrust decreases.

How does drag vary with air density? How does the thrust vary with air density?

 

[sdfsfasdfasf]

Drag counteracts the motion. Smaller drag will invariably lead to a higher velocity at a given thrust. But your thrust is not constant with altitude and so your task is to explain why the velocity still goes up at higher altitude even though thrust decreases.

How does drag vary with air density? How does the thrust vary with air density?

Drag decreases for a fixed velocity as air density decreases, thrust decreases as air density decreases. How do I link less drag and less thrust to a higher velocity?

 

[Orodruin]

Drag decreases for a fixed velocity as air density decreases, thrust decreases as air density decreases. How do I link less drag and less thrust to a higher velocity?

You’ll have to consider how they both vary with density.

 

[sdfsfasdfasf]

I don't know what you mean by that, my specification does not reference the specifics. I have an exam tomorrow and I'd like to get this sorted, do you have any reading information or could you kindly tell me the answer?
Thank you

 

[Steve4Physics]

What am I missing? Thank you so much for helping me!

I think you have understood the physics but are overthinking what the answer requires.

From your other posts, I guess this is from a UK A-level exam’ paper and that part (d) carries 2 or 3 marks.

I don’t think that the question can be answered quantitively using the information provided or using what you are meant to know. Essentially a qualitative answer is required..

However, you’ve already given some of the key points for the answer:
- the density of the air decreases with altitude, and as a result...
- the drag (proportional to density for a given speed) decreases with altitude.

The question tells you that at high altitude there is ‘less thrust from the engine’. (But it doesn’t say how much less, or what the dependency on density is; the dependency will be a function of of the engine’s operating speed and design. You have no information on this – which limits how you can use the information.)

To some extent you have to know what the examiner is looking for. So, since you understand the physics, I don't think I’m giving away too much by saying that the answer should also include the following points:

a) the reduction in drag is bigger than the reduction in thrust (which is inferred from being told that the speed increases);

b) the speed will increase until the new drag force (which is approximately proportional to $v^2$ for a given density) equals the new thrust.

 

[haruspex]

To put a slightly different spin on @Steve4Physics' reply, you are not being asked to show that the speed will increase, only that, depending on what exactly the relationships between drag, thrust and density are, the speed could increase.

 

[sdfsfasdfasf]

I think you have understood the physics but are overthinking what the answer requires.

From your other posts, I guess this is from a UK A-level exam’ paper and that part (d) carries 2 or 3 marks.

I don’t think that the question can be answered quantitively using the information provided or using what you are meant to know. Essentially a qualitative answer is required..

However, you’ve already given some of the key points for the answer:
- the density of the air decreases with altitude, and as a result...
- the drag (proportional to density for a given speed) decreases with altitude.

The question tells you that at high altitude there is ‘less thrust from the engine’. (But it doesn’t say how much less, or what the dependency on density is; the dependency will be a function of of the engine’s operating speed and design. You have no information on this – which limits how you can use the information.)

To some extent you have to know what the examiner is looking for. So, since you understand the physics, I don't think I’m giving away too much by saying that the answer should also include the following points:

a) the reduction in drag is bigger than the reduction in thrust (which is inferred from being told that the speed increases);

b) the speed will increase until the new drag force (which is approximately proportional to $v^2$ for a given density) equals the new thrust.

Yeah I looked it up and found a higher level equation that uses some fancy Reynolds number (proportional to density) and the density term itself, thereby showing that the drag decreases by a greater factor than the thrust (for a given velocity) if you decrease the density, thereby showing the velocity must increase until the new drag = the new thrust (both of which are lower than the old forces), it all makes sense now.

I have my first A-Level paper in about 2 hours time so best of luck to me!

 

[haruspex]

the drag decreases by a greater factor than the thrust (for a given velocity) if you decrease the density

What did you take the reduction in thrust to be? I would guess that a lower density means the fan can turn faster for the same input power, so the thrust reduction might not be in proportion to the density's.

And indeed, good luck!

 

[Steve4Physics]

I have my first A-Level paper in about 2 hours time so best of luck to me!

It's too late (nearly 11:30am) to wish you good luck for your first paper. But I hope it went well. And good luck for the rest of the papers!

 

[Lnewqban]

I agree with @Steve4Physics.
Terrible confusing question for the level being studied by the OP, IMHO.

The answer seems more complicated if the ducted fan is powered by a naturally aspired internal combustion engine, which power output is also diminished with less mass of air flowing for combustion at higher altitudes.

It is not clear the type of airship either.
If simply buoyant (Zeppelin), only parasitic drag should be considered, but if flying on wings, induced-by-lift drag would greatly decrease if the airship is able to move at higher speeds (lower angle of attack of wings).

There is a unique flight velocity that requires minimum thrust force (most economic one).
We can’t know in what area of the total drag versus velocity our airship has been flying, both low and high.

 

[sdfsfasdfasf]

It's too late (nearly 11:30am) to wish you good luck for your first paper. But I hope it went well. And good luck for the rest of the papers!

OCR A was a difficult paper but I think I did good, if I just focus on paper 2 and 3 I should be able to get my A*. Further Maths was surprisingly easy however, so unsure what the 2nd paper will look like for that.