048586a3-770f-4ecb-a884-6d8827a784ca 31 overlord 4 5 false false 0 decimal

&[DATE] &[TIME] - &[FILENAME]

Problem:

A rectangular channel (bottom width \[REGION[76b2e5f2b6a74b8f9ba6b2baea150ca7]]\, Manning's roughness coefficient \[REGION[b366c6b7a42a4ed7a9bcc651a73b560b]]\) flows \[REGION[54494ab45c704b7997207d52fdabc8c8]]\ deep on a slope \[REGION[1966fbcaf60f4031a4bae853bb6d7c65]]\.

b

n

y.norm

s

A suppressed weir (height \[REGION[006d7faf1d5d429eb25a6b57cb35f3fa]]\, weir coefficient \[REGION[b1867bdafbf84674a5057c29d9d03696]]\) is built across the channel.

h.weir

C.weir

Taking the elevation of the bottom of the channel just upstream from the weir to be \[REGION[a934d0f2ad7442789db1f8ca16bf88e7]]\, estimate (using one reach) the elevation of the water surface at a point "A", \[REGION[60f393394bec4144832c6fad9140ed0b]]\, which is\[REGION[bab5927c59ab4b0d980da0a58338b3be]]\ upstream from the weir. (See figure.)

z.B

H.A

L

Given:

n 0.025 s m 3 nthroot / * :

b 20 ft * :

s 14.7 10000 / :

y.norm 5 ft * :

z.B 100 ft * :

L 1000 ft * :

h.weir 2.45 ft * :

C.weir 3.45 ft sqrt s / * :

Solution:

A b y.norm * : ft 2^100

p.w b 2 y.norm * + : ft 30

R A p.w / : ft 3.3333

v 1 n / R 23 /^* s 12 /^* : ft s / 5.0851

Q A v * : ft 3^s / 508.51

y.weir y.B h.weir - :

v.B Q b y.B * / :

Flow over weir is given with following equation:

Q.weir C.weir b * y.weir v.B 2^2 g.e * / + (32 /^v.B 2^2 g.e * / (32 /^- (* :

y.B Q Q.weir - y.B 2 ft * ≡ FindRoot Re eval :

ΔQ Q Q.weir - :

must be equal to zero

satifactory enough, \[REGION[7eb025afd4804862802dffe2f78eb4cc]]\

y.B ft 6.0089

z.A z.B s L * + : ft 101.47

A.A b y.A * :

v.A Q A.A / :

v.average 12 / v.A v.B + (* :

R.average 12 / y.A b * y.B b * + (* 12 / b 2 y.A * + b + 2 y.B * + (* / :

h.lost v.average n * R.average 23 /^/ (2^L * :

Check Bernoulli's equation:

H.A z.A y.A + :

H.B z.B y.B + : ft 106.0089

y.A H.A H.B - h.lost - y.A 2 ft * ≡ FindRoot Re eval : ft 5.52

H.A H.B - h.lost -

must be equal to zero

satifactory enough, \[REGION[4ada7347241243f292f985ef2aad1b8d]]\

y.A ft 5.52

Thus: \[REGION[29232d729fa741e4a9011028c8221d02]]\

H.A ft 106.99