Is the Bernoulli's equation for airplane wings using metric units correct?

[50936]

Hi everyone,

I read on a website that the Bernoulli's expression can be applied to airplane wings by using the equation:

Difference in pressure above and below wing
= 1/2 x air density x [(airflow velocity below wing)^2 - (airflow velocity above wing)^2]


I tried using it but the units don't seem to add up correctly when I use the metric system (kg/m^3 for density, m/s for velocity).
The website uses (slugs/ft^3) for density, and (ft/s) for velocity.

Can anybody tell me if this equation is correct?

 

[FredGarvin]

What they express is simply the difference in dynamic pressure. Dynamic pressure is the first term in the Bernoulli equation. This makes the assumptions that there is no friction, no potential energy change and no compressibility effects.

Since it is dynamic pressure, the units do work out.

[tex]\frac{1}{2}\rho V^2[/tex]

[tex]\frac{kg}{m^3}\frac{m^2}{s^2}[/tex]

[tex]\frac{kg*m^2}{m^3*s^2}[/tex]

[tex]\frac{kg*m}{s^2}\frac{m}{m^3}[/tex]

[tex]\frac{N}{m^2}[/tex]

 

[NatSusan]

Hi there,

I'm not an expert in aerodynamics, but from what I understand, the Bernoulli's principle can indeed be applied to airplane wings. However, the equation you mentioned may need to be modified based on the units you are using.

The original equation for Bernoulli's principle is:
Difference in pressure = 1/2 x density x (velocity^2)
So, if you are using the metric system, the equation would be:
Difference in pressure = 1/2 x (kg/m^3) x (m/s)^2

To convert the units from slugs/ft^3 to kg/m^3, you can use the conversion factor of 1 slug = 14.59 kg and 1 ft = 0.3048 m. So, the equation would become:
Difference in pressure = 1/2 x (14.59 kg/m^3) x (0.3048 m/s)^2

I hope this helps clarify the issue with the units. Keep in mind that the equation may also need to be adjusted based on other factors such as air temperature and altitude. It's always a good idea to double check your calculations and consult with experts in the field. Good luck!