Solution 10.37
For corrugated metal, take n = 0.022. From Ex. 10.5, for a vee-channel, recall that
2
h
tan( /2); 2 sec( /2);
0.5 sin( /2)
A y P y
Ry
==
=
Manning’s formula (10.19) predicts that:
2/3
3
2/3 1/2 2
1 m 1
8 tan sin 0.005
s 0.022 2 2 2
o
hy
Q AR S y
n
= = =
(a) Eliminate y in terms of P and set dP/d
= 0. The algebra is not too bad, and the result is:
Minimum perimeter occurs for a given flow rate at . (a)P Ans
=90
(b) Insert
= 90 in the formula for Q = 8 m3/s above and solve for:
. (b) and . (c)Ans Ans.
min
1.83m 5.16m==yP