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Dimensional Analysis

I got asked this quiz question and worked it out to be True but the answer is False and I can’t see why?

The nondimensional Froude number πΉπ‘Ÿ=π‘ˆ^2/(𝑔h) where π‘ˆ is a speed, h is a length scale and 𝑔
acceleration due to gravity is calculated in a paper with π‘ˆ given in feet/sec and h in feet. If π‘ˆ
were to be calculated in metres/sec and h
in metres, one would get a different answer for πΉπ‘Ÿ? True or False



40500074-A23B-4C1E-8C4D-4C73655B57E9.jpg.jpeg
Original post by Y2_UniMaths
I got asked this quiz question and worked it out to be True but the answer is False and I can’t see why?

The nondimensional Froude number πΉπ‘Ÿ=π‘ˆ^2/(𝑔h) where π‘ˆ is a speed, h is a length scale and 𝑔
acceleration due to gravity is calculated in a paper with π‘ˆ given in feet/sec and h in feet. If π‘ˆ
were to be calculated in metres/sec and h
in metres, one would get a different answer for πΉπ‘Ÿ? True or False



40500074-A23B-4C1E-8C4D-4C73655B57E9.jpg.jpeg

What about g ?
Original post by RDKGames
What about g ?


Tbh I did think the only way this could work was if g was also converted as then all multipliers would cancel out. Since the question only stated U and h were measured in feet/sec I presumed g was irrelevant :frown:
Original post by Y2_UniMaths
Tbh I did think the only way this could work was if g was also converted as then all multipliers would cancel out. Since the question only stated U and h were measured in feet/sec I presumed g was irrelevant :frown:

It’s relevant. You divide speed by time. If your speed is all of a sudden measured in feet/sec then your g should be expressed as feet/sec^2. Otherwise, you are multiplying different units together and that is meaningless.

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