/sci/ - Science & Math

>>11518690
first I want 1-2 paragraphs detailing specifically why you can't compute this right now without help

>>11377314
>>11377314
Is this is the sweetheart with the HVAC lab again? Just use the average airspeed and the hydraulic diameter of the duct. In general, the hydraulic diameter of a cross-section is [math] D_H=4A/P [/math] where [math] A [/math] is the area and [math] P [/math] is the perimeter. So for a rectangular duct with side lengths [math] a [/math] and [math] b [/math], you get [eqn] \text{Re}=\frac{D_Hv}{\nu}=\frac{(4ab)v}{2(a+b)\nu} [/eqn]

>>11181909
Let's say I'm building an airplane and I need to design a wing. The problem is that I don't fully understand the physics of a wing because it turns out fluid mech is very complicated, but still I need to design one. So I think: what parameters influence the lifting power of a wing? I do a little tinkering and thinking and I conclude that the lift of a wing depends on 1) it's span, 2) its camber, 3) its angle of attack 4) airspeed, 4) viscosity of air, and so on (I'm just using lift as an example).
So, I have LIFT as a function of N variables. Note that lift is a kind of force and that a force is measured in pounds and that a pound is a derived quantity composed of M=3 fundamental quantities: length (feet), time (seconds), mass (slugs). You still with me?
So it turns out there is something called the Buckingham Pi theorem. This theorem basically says that if I have a quantity involving M physical dimensions that is a function of N variables, then I can find ANOTHER function that involves P=N-M terms called pi terms. There are a couple methods to find pi terms, see https://en.wikipedia.org/wiki/Rayleigh%27s_method_of_dimensional_analysis for example. Once you have pi terms, it is much, much easier to perform experiments and find empirical, quantitative relationships between them. Reynold's number is an example of a pi term. So is the Froude number, Mach number, etc. Any decent fluid mech text should have a section on dimensional analysis.

hmm?
[eqn]\mathcal{L}/b=-\rho_\infty U_\infty\Gamma[/eqn] where
[eqn]\Gamma=\oint\mathbf{V}\cdot\text{d}\mathbf{s}[/eqn]