Deane Yang wrote:
Noah Roberts wrote:
There's just plain going to be times when you have to break out of the dim/unit analysis model. For instance, in fluid flow analysis, what I do, you often have empirical functions...guesswork...it is not at all uncommon to take a quantity to some variable power that might itself be a quantity. There's no way to enforce dimensions on this.
Is this really right? Are you sure there isn't a constant lurking around that resolves all the dimensions properly? Surely, these formulas have to be adjusted appropriately if you use different units.
Can you provide a concrete example?
Formula for Fluid Compressibility through a Venturi Tube: Y = {[kt^(2/k)/(k-1)][(1-b^4)/(1-b^4t^(2/k))][(1-t^((k-1)/k)/(1-t)]}^.5 With k being the SP heat ratio of the fluid passing through the venturi. Static dimensional analysis is impossible here. In fact dimensional analysis at all just isn't appropriate in these odd cases.