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Unformatted text preview: proof, that the flow over the crest draws down to hmin H/3,
the volume flow q Q/b over the crest is approximately
H q
crest  v v 2
3  eText Main Menu  V2 dh
2g H V2)1/2 dh
1 (2gh
H/3 V2
1
2g 3/2 Textbook Table of Contents H
3  V2
1
2g 3/2 Study Guide (10.52) 690 Chapter 10 OpenChannel Flow Normally the upstream velocity head V 2/(2g) is neglected, so this expression reduces to
1
Sharpcrested theory: 0.81( 2 )(2g)1/2H3/2
3 q (10.53) This formula is functionally correct, but the coefficient 0.81 is too high and should be
replaced by an experimentally determined discharge coefficient. Analysis of BroadCrested Weirs The broadcrested weir of Fig. 10.16b can be analyzed more accurately because it creates a short run of nearly onedimensional critical flow, as shown. Bernoulli’s equation
from upstream to the weir crest yields
V2
1
2g Y 2
Vc
2g H 2
If the crest is very wide into the paper, Vc yc gyc from Eq. (10.33). Thus we can solve for
V2
1
3g 2H
3 yc Y 2H
3 This result was used without proof to derive Eq. (10.53...
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 Spring '08
 Sakar

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