91
Theory
For uniform flow over a gravel bed, the Manning formula states that:
2
1
3
2
S
R
n
1
v
=
where:
n
= Coefficient of roughness
(Dimensionless)
v
= mean fluid velocity
(m/s)
R
= Hydraulic mean radius
(m)
= Flow area A / Wetted perimeter P
S
= Slope of energy line
(m)
= sin
θ
= (y
0
– y
1
) / x
where
x = distance between level measurements
y
0
= upstream flow depth
y
1
= downstream flow depth
Note:
For simplicity the slope S can be assumed to be the slope of the water surface, if the small
change in velocity head between inlet and outlet is ignored. When using the flume with
the bed inclined, the slope of the bed must be added to calculations of S, when using the
hook and point gauges with the bed as a datum.
The actual fluid velocity can be calculated as:
v = Q / A
where
v
= mean fluid velocity
(m/s)
Q
= Volume flow rate
(m³/s)
h
= Average depth of flow above gravel bed
(m)
= (y
0
+ y
1
) / 2
A
= Area of flow
= Breadth of channel b x Depth of flow h
(m²)
