3 Ss. YOKOTA: A METIIOD OF DETERMINING THE CROSS-SECTION 
000281 1811 
eared ATC + ave ee 
e 1 
O-O0Z81 
1+(41:64 — Wares 
\ e v 
416+ 
7 Ress 
— 
ri 
SE: 
a 
Il 
in which 
v==the mean velocity of water in feet per second, 
%=the hydrauhe mean depth in feet, 
J ==the slope of the water surface, 
and n ==coeflieient of roughness of the wetted perimeter. 
Hence, it has been my aim to avoid this repetitive process and to 
determine the cross section at once, when the quantity of discharge is 
given, 
(a) The Cross Section of Minimum Wetted Perimeter. 
If we introduce a relation between the bottom breadth b and the 
depth d so as to ignore one variable, the problem becomes far simpler 
and the cross section may be determined once for all. For this relation 
we may assume a cross section of minimum wetted perimeter, as causing 
the least frictional resistance or, in other words, as giving the maximum 
discharge for a given cross sectional area. This relation is given by 
ed 
(2) d=jot,, 
where @ is the angle of inclination of the sides to a horizontal plane. 
So that 
1 0 
(3) R= un b cot-5-. 
The quantity of discharge Q per second is equal to the sectional 
area A multiplied by the mean velocity per second. Therefore, from 
(1) and (3), 
kk’ I (kr ot ps 
(4) Ql 
in which 
N 
3-+ cot? 
. . 5) 
ENORMEN, Kat NER k’=k'x zu 
J 4 2 2 ie 
Using this notation, we have (\.. 
(2)’ ih Sat 
(3) R=k’b, 
