3 ms·
IIRC fluid mechanics is where this turns up most obviously. So the issue here is you don't quite know how certain shape of boat/airplane will behave in a flow
by lordnacho 4y ago
IIRC fluid mechanics is where this turns up most obviously.
So the issue here is you don't quite know how certain shape of boat/airplane will behave in a flow of water/air.
But you do know that whatever the relationships are, they have to be dimensionally consistent. You then work out a dimensionless version of force or whatever your interested in, and that tells you how it scales since you have a bunch of square, cube, root, etc terms.
So now you can build a little model, measure the real force you're interested in, and make a guess about what the force would be on the actual size version.
- HPsquared 4y agoThe key here is to have all the relevant dimensionless numbers (e.g. Reynolds number, perhaps Mach number, Froude number, etc.) as well as the geometry (which is also dimensionless: it's a set of angles and ratios), of your wind tunnel model consistent with the real-world situation you're testing. Then you measure other dimensionless quantities (e.g. drag coefficient). The tests give a correlation from one dimensionless quantity to another. That can mean, counter-intuitively, that a wind tunnel model needs to have a higher wind speed than the full-size object - so that the Reynolds number is correct.
- hgsgm 4y agoAngle is a dimension, and not equivalent to length. Fight me (and Matlab).
- HPsquared 4y agoAngle in radians is just (length of arc) / (radius). That is length/length, which cancel out - so angle is dimensionless. Solid angle is area/area.
- nh23423fefe 4y agoanother way: if exp(x) implies x dimensionless then by euler identity sin and cos parameters are dimensionless as well.