53.
A comparison of the relative values of n, in the formula v = n (r s)^{1/2},
for the foregoing ditch, flume, and pipe will be instructive. The ditch
has a width on the bottom of 3 feet, on the top of 6 feet, with a depth of
3 feet, and an inclination of 20 feet per mile; its sides are rough, being
cut in part through the rock and with sharp curves, although fairly
regular; with a flow of about 1,300 miner's inches (32.8 cubic feet per
second) the ditch runs about full.
Therefore:
6 + 3
a = ----- x 3 = 13.5 ;
2
[TEX: a = \frac{6+3}{2} \times 3 = 13.5;]
a
r = ------------- = 1.41 ;
3.3 + 3 + 3.3
[TEX: r = \frac{a}{3.3 + 3 + 3.3} = 1.41;]
20 1
s = ------ = ----- ;
5280 264
[TEX: s = \frac{20}{5280} = \frac{1}{264};]
Q = 32.8, hence
Q
v = --- = 2.43;
a
[TEX: v = \frac{Q}{a} = 2.43;]
and
/ {1/2} \
n ( in v = n (r s)^ ) = 33.
\ /
[TEX: n\ (\text{in}\ v = n (r s)^\frac{1}{2}) = 33.]
The flume is of unplaned boards, rectangular, 2.67 wide x 2.83 deep, with
an inclination of 32 feet per mile. There are sharp curves, although these
were made as regular as practicable; the boiling action of the water
passing around these curves brought the flow line (Q = 32.
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