3 Hydrodynamics
213
Fig. 3.42 Free flow over the broad crested weir
is located in the curved region of the streamline (which belongs to the rapid
flow) and the piezometric head on 1-1 section is not constant. So the average
piezometric head value on 1-1 section is used. The resulting energy equation
is
H 0 = H +
α 0 V 2
0
2g
=
z +
p
γ
+ (α 1 + ξ )
V 2
1
2g
where H 0 is the total head of weir crest (including the head of approaching
velocity); α 0 and α 1 are the kinetic energy correction coefficients at corresponding sections; ξ is the local head loss coefficient. Let us assume
z +
p
γ
= λH 0
where λ is the correction coefficient. From the energy equation, the velocity
at 1-1 section can be shown to be
V 1 =
√ (1 − λ)
√ α 1 + ξ
2g H 0
where the width of the weir crest is b. The thickness of weir crest water nappe
is μH 0 in which μ is the vertical contraction coefficient reflecting the water
nappe at the crest. In this way, the discharge Q over the weir crest is
Q = bμH 0 V 1 = μ
√ (1 − λ)
√ α 1 + ξ
b
2g H
3/2
0
= mb
2g H
3/2
0
m = μ
√ (1 − λ)
√ α 1 + ξ
where m is the discharge coefficient over the weir. The above formula is the
standard weir flow formula, which shows that the discharge over the weir