# Pressure equations problem

1. May 17, 2006

### whoknows123

Question: a) Find the pressure difference on an airplane wing where air flows over the upper surface with a speed of 110 m/s and along the bottom surface with a speed of 105 m/s. _____Pa

b) if the area of the wing is 20m^2, what is the net upward force exerted on the wing? ______N

Can anyone tell me what equations to use for this problem?

2. May 17, 2006

### Andrew Mason

You are expected to use Bernouilli's equation:

$$P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2$$

The problem is that this is probably not the correct way to analyse the lift. It is more complicated than Bernouilli. There is still scientific debate over the physics of airplane lift.

AM

3. May 17, 2006

### nrqed

Bernouilli's equation ${v^2 \over 2} + g h + {p \over \rho} = constant$. Assuming that the difference of height plays a negligible role, you can use the two speeds and the density of air to find the difference of pressure (notice that the higher the speed, the smaller the pressure is which is good since the speed of the air flow is larger on the top of the wing!). For the second part, you need to use that force is pressure times area, so the difference of force is the difference of pressure times the area (again, you should see easily why the net force is upward).

Patrick

4. May 17, 2006

### whoknows123

so what exactly do i do, what is P suppose to be?

5. May 17, 2006

### whoknows123

ok, i'm confused.

6. May 17, 2006

### whoknows123

can someone explain step by step? I reallly dont understand this topic.

7. May 17, 2006

### whoknows123

nevermind, thanks nrqed, i got it =)

8. May 17, 2006

### nrqed

Just for the benefit of others: I had sent this private message to the OP:

The sum of the three terms is constant means that it has the same value above and below the wing. Neglecting the gh term, you get

${1 \over 2} v_{top}^2 + {P_{top} \over \rho} = {1 \over 2} v_{bottom}^2 + {P_{bottom} \over \rho}$

Just solve for (P_bottom - P_top) (this should be positive since there is a net force upward on the wing so the pressure on the bottom should be larger than on the top). That's the pressure difference you are looking for.

Hope this helps.

Patrick

9. Sep 14, 2007

### akoma714

Is that Bernoulli's equation? The one in my book is different.

10. Sep 14, 2007

### cristo

Staff Emeritus
This thread's over a year old, plus it's not clear which post you're talking about. If you have a specific question, feel free to start a new thread in the appropriate forum.