not apply the Keulegan equation when relative roughness is less than 3. Instead,
the Strickler equation is automatically substituted.
Keulegan equations, rigid bed
The relative roughness approach based on the Keulegan (1938) equations for
velocity distribution is still the state-of-the-art for rigid boundary channel design.
Keulegan classified flow types as hydraulically smooth, hydraulically rough, or
transitional. His equations can be combined with the Chezy equation to obtain a
Chezy roughness coefficient. The equations are written in terms of the Chezy
coefficient, C, because the powers are simpler than when the Manning's equation
is employed. Chezy's C may then be converted directly to a Manning's n-value.
(1)
The equation for fully rough flow is
12.2 R
C = 32.6 log10
Equation 2-3
ks
(2)
For smooth flow the equation is
5.2 Rn
C = 32.6 log10
Equation 2-4
C
The smooth flow equation is a trial and error solution, best accomplished using a
computer program such as SAM.
(3)
The equation for transitional flow is
C
ks
+
C = - 32.6 log10
Equation 2-5
12.2 R
5.2 R n
(4)
The equation showing the relationship of n-value and Chezy C is
1.486 1/6
n=
Equation 2-6
R
C
where
Rn = Reynolds number
= 4RV/υ
v = kinematic viscosity of water
11
Chapter 2
Theoretical Basis for SAM.hyd Calculations
Previous Page
