# Is this application of Bernoulli's Equation valid?

We were studying fluid dynamics and our professor was explaining Bernoulli's Theorem to us, which is:

For points in a tube of flow of liquid, the following rule is applicable: $$P + \rho g y + \frac{1}{2}\rho v^2 = \text{constant}$$

Here, $$P_1 + \rho g y_1 + \frac{1}{2} \rho (v_1)^2 = P_2 + \rho g y_2 + \frac{1}{2} \rho (v_2)^2$$

After explaining this, he further went on to explain the lift caused on a strip of paper by blowing across one side.

He told us to assume Point 1 on the side of the paper we're blowing across, and 2 at the other side.

We get:
(i) $v_2 \approx 0$ (since no wind beneath)
(ii) $y_1 \approx y_2$ (neglecting thickness of paper)

Applying Bernoulli's theorem, we get: $$P_1 = P_2 - \frac{1}{2} \rho (v_1)^2$$ $$\therefore P_2 > P_1$$

Difference in pressure will provide an upward lift - rising the paper.

Is this valid?

Bernoulli's Theorem is only applicable in a tube of flow. Clearly, Point 1 and 2 are not in the same tube of flow. How can we then apply it to these two points?

Or is my professor's reasoning wrong?

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You might want to check physics.stackexchange.com/questions/31019/… –  Johannes Aug 4 '13 at 13:43
@Johannes I understand the reason why airplanes fly. It's just that our professor gave this reason - which I didn't think is correct, because you cannot apply Bernoulli's equation if the points aren't in the same tube. Wanted to know if he is actually correct and I'm mistaken? –  mikhailcazi Aug 4 '13 at 13:46
the reasoning your professor provided is, to say the least, incomplete. You can apply Bernouilli's equation to both sides of the airfoil, but you still have to reason why the air flows faster on the top side of the wing (no, it's not the wing cross section, you can fly with barn doors as wings and also in an upside-down airplane). –  Johannes Aug 4 '13 at 13:55
@Johannes So you can apply Bernoulli's equation even if the points do not belong in the same tube of fluid flow? –  mikhailcazi Aug 6 '13 at 12:33
you can apply Bernouilli twice, but that in itself doesn't lead to an explanation for airfoil lift. –  Johannes Aug 6 '13 at 14:18
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