Sediment Transport Concepts - Sediment Transport in Irrigation Canals: A New Approach - page 109

the method by replacing the hydraulic radius R by an equivalent hydraulic
radius R e , which is given by:

N 3 / 5

P i R 5 / 3
i
P

R e = (5.27)

i = 1

i = 1

N

P i R 5 / 3

i

n e = (5.28)

P i R 5 / 3
i
n i

i = 1

N

Method 4. Krishnamurthy and Christensen (1972) proposed that the
summation of the discharges in subsections with roughness coefficient
k s,i (i subscript for the subsection) is equal to the summation of the
discharges of all the subsections with an equivalent roughness k se . The
flow in each section is assumed to be turbulent and the velocity distribution
is described by the logarithmic law. The hydraulic roughness is related
to Manning's roughness coefficient by (Henderson, 1966):

0 . 034 k 1 / 6
s

=

n (5.29)

The equivalent roughness value is given by:

i = 1 P i R 3 / 2

N

ln n i

i

ln n e = (5.30)

i = 1

N

P i R 3 / 2

i

where:
n e =

equivalent Manning's roughness coefficient for the whole cross
section;

n i =

Manning's roughness coefficient in subsection i;

u ∗ i =

shear velocity in subsection i;

v i = mean velocity in subsection i;

A = area of the entire cross section;

A i = area of subsection i;

S = energy gradient;

q i = discharge in subsection i;

τ e = shear stress for the whole cross section;

τ i = shear stress in subsection i;

P = wetted perimeter of the whole cross section;

P i = wetted perimeter of the subsection i;

R = hydraulic radius for the whole cross section;