Opened 11 years ago

Closed 9 years ago

## #51 closed question (answered)

# fractional dimensions

Reported by: | André Hendriks | Owned by: | |
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Priority: | minor | Milestone: | |

Component: | Keywords: | dimension, fractional | |

Cc: |

### Description

How does the UCUM cope with fractional dimensions, like the much used Chezy coefficient (friction coefficient in hydraulic engineering), which has m^{½}/s as 'unit'?

### Change History (4)

### comment:1 Changed 11 years ago by

### comment:2 Changed 9 years ago by

Resolution: | → worksforme |
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Status: | new → closed |

This needs some resolution. There is no action proposed and I will resolve it as worksforme, because nothing is needed. Consider elevating this to a FAQ.

### comment:3 Changed 9 years ago by

Resolution: | worksforme |
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Status: | closed → reopened |

Type: | enhancement → question |

Actually, it wasn't a proposal, it was phrased as a question. So, not rejected but question answered. Thanks.

### comment:4 Changed 9 years ago by

Resolution: | → answered |
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Status: | reopened → closed |

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The answer is: we don't.

I have seen this, but I don't know enough of it to make sense of this. Obviously one can imagine to put any unit term under any root, but what does this mean? What is the square-root of a meter? Seem rather imaginary to me.

The formula is:

where C is this Chezy coefficient, R is radius, dimension L and i is dimensionless (a slope). So here we have a square root of a length. But what does this mean? I think the right way to write this formula would be:

and now your coefficient C

^{2}has the dimension L.T^{-2}, which looks much more reasonable.I always felt that this fractional dimensionality is arrived at by some nifty engineering trick, as factoring the coefficient before the square root, but really doesn't signify that dimensions can somehow be fractional. [Sounds a bit analogously esoteric as Cantor's continuum hypothesis.]