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Various

"Scientific American Supplement, No. 455, September 20, 1884"

8) nearly up to
the top of the sides; with a straight flume of the same size, the water
would have doubtless stood several inches lower.
Therefore:
a = 2.67 x 2.83 = 7.56 ;
a
r = -------------------- = 0.908 ;
2.83 + 2.67 + 2.83
[TEX: r = \frac{a}{2.83 + 2.67 + 2.83} = 0.908;]
32 1
s = ------ = ----- ;
5280 165
[TEX: s = \frac{32}{5280} = \frac{1}{165};]
Q = 32.8, hence
Q
v = --- = 4.34;
a
[TEX: v = \frac{Q}{a} = 4.34;]
and n = 59.
With the pipe,[6] 1.416 diameter,
d
r = --- = 0.354; Q = 31.69; v = 20.13.
4
[TEX: r = \frac{d}{4} = 0.354;\ Q = 31.69;\ v = 20.13.]
[Footnote 6: _Vide_ pages 120-122, Transactions American Society of Civil
Engineers for 1883.]
Allowing for loss of head due to imparting velocity to water, and for
contraction,
296.1
s= --------; and n = 131.
4438.7
[TEX: s = \frac{296.1}{4438.7};\ \text{and}\ n = 131.]
We hence have the following values of n, in v = n (r s)^{1/2}, Q being
constant:
Rough ditch, with sharp curves. 33
Rectangular flume, with sharp curves. 59
Wrought-iron pipe, with easy curves, coated with
asphalt, but with rivet-heads forming noteworthy
obstructions (m = 65.


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