Calculating Air Speed Diff. of Plane Lifts

[Studphy]

Homework Statement

We have a plane which lift area is A=500 m² and weight of plane is m= 540 000 kg.
That the plane can stay in air the pressure difference between top and bottom of the lifts have to be:
B>G --> Δp= (m*g)/A = 10 594.8 Pa.

Homework Equations

Bernoulli equation

The Attempt at a Solution

Then we have to calculate what is air speed difference between top and bottom of the lifts.

Attempt:
From bernoulli equation, when we assume Δh=0, we get
Δp = 0.5*ρ(atmosphere)*(v(bottom)²-v(top)²)
→ v(bottom)²-v(top)²=2*Δp/ρ(atmosphere)
But how I get speed difference of air between top and bottom? Or is there another way to get speed difference?

 

[BvU]

Hi Stud,

If I understand you well, you have $\Delta(v^2)$ and you want $\Delta v$ . Right ?

If so, what is the relationship between what you have and what you want ?

 

[Studphy]

We can do this: $$ v(bottom)^2 - v(top)^2 = (v(bottom) - v(top))*(v(bottom) + v(top))$$
so $$\Delta(v) = \frac {\Delta(v^2)}{v(bottom) + v(top)} $$
Value of $$\Delta(v^2)$$ we have, so we can calculate how v(bottom) depends on v(top)
$$ v(bottom) = \sqrt{\Delta(v^2) + v(top)^2}$$ And use this to calculate$$\Delta(v)$$

Is this reasonable?

 

[BvU]

You still have to fix something. I'd estimate $\ \ v_\text { bottom} + v_\text { top} = 2\; v _\text { airplane}$

 

[cjl]

You could estimate that, but it's likely not very accurate. If you just want an estimation, it'll be alright, but in general that's not an equation that will hold.

Was there no other information given with the problem?

EDIT: As a side note, that's a very high wing loading. I'd expect a 500m^2 wing to lift more like 330 metric tons.

 

[Studphy]

No. That is form basic course. Proper course about fluid mechanics will be later. This is very simplified, but idea of this exercise is just learn how Bernoulli equation can be used in other situations than just pipes. And values of lifts and mass aren't real in my question.

 

[rcgldr]

There doesn't seem to be any restriction on what the average velocity is, so you could just v_bottom to zero.