53:071 Principles of Hydraulics
Laboratory Experiment #4
Weir Calibration
Li-Chuan Chen, Marian Muste, and
Larry Weber
Objective
To determine the head-discharge
relationship of three different shapes of
weirs, and to compare the experimental
results with their corresponding
analytical expressions.
Principle
U
pstreamlevel
h
H
dh
V= 2gh
N
appe
W
eir
crest
P
W
eir
V  h  2 gh
Principle
H
Q   V (h)dA  2 g  b(h) hdh  kh
n
A
0
log( Q)  log( kh )  n log( h)  log( k )
n
Slope
Intercept
Apparatus — Flume
Q  2.04 h
Apparatus — Weirs
W
E
I
R
E
X
P
E
R
I
M
E
N
T

=
1
'
0
"
9
0
.0
°
1
0
3
/4
"
6
"
2
'
0
"
2
'
0
"
R
e
c
ta
n
g
u
la
r
C
o
n
tr
a
c
te
d
W
e
ir
o
9
0T
r
ia
n
g
u
la
rW
e
ir
Procedures
1.
2.
3.
4.
Insert the weir of the desired shape.
Record the reference point of the weir.
Set the appropriate discharge in the flume.
Record the water surface elevation upstream
of the weir
5. Repeat Steps 3 and 4 for four more
discharges.
6. Repeat Steps 1 to 5 for two more weir
shapes.
Data Sheet
Triangular 60
Discharge
h
(ft)
Q
(cfs)
Ref. Point
(ft)
W.S.
Elev.
(ft)
Weir
Head
(ft)
Analysis
Determine the discharge Q in the flume
(using the side-contraction meter) and the
head H on the weirs.
Using several measured Q-H pairs, plot log Q
versus log H.
From the best-fit line to the experimental
points, determine the kexp (the intercept) and
nexp (the slope).
Compare kexp and nexp with values indicated in
the literature.
Sample Result
Further Considerations
Derive, analytically, the head-discharge
relationship for each of the weir shapes.
If data seem to imply nexp  ntheory, why?