Methodology - Response of Flood Events to Land Use and Climate Change - page 71

o h þ z b ð Þ

þ o u ðÞ
ox

¼ 0 ð 3 : 20 Þ

ot

o u

ot þ u o u ox þ g o h þ z b

ð Þ u jj

h

þ c f ¼ 0 ð 3 : 21 Þ

ox

where:
x is the position along the channel axis (m); t is time (s), u is the velocity vector
in the x-direction (m/s), h is water depth (m), z b is the local bottom level above the
reference date, c f is the dimensionless bottom friction coefficient, and g is the
constant of gravity (9.81 m 2 /s).
The first equation represents the rate of volume stored over unit length of a
channel, and the discharge which changes along the channel per unit of time. The
second equation expresses the change of momentum in a controlled volume of unit
length of a channel and reflects the inertia of the water mass present in that
controlled volume [ 55 ].
In HEC-RAS, the total discharge is distributed to the channel and the floodplain
elements as per their conveyance. The governing equations for both the floodplain
and the channel grid elements are as follows:

DQ T þ DA c
Dt

Dx c þ DA f
Dt

Dx f þ DS

Dt Dx f ql ¼ 0

ð 3 : 22 Þ

¼ 0

D ð Q c Dx c þ Q f Dx f
DtDx e

DZ
Dx e

D bV T Q T ð Þ gA þ S f ð 3 : 23 Þ

where
Q is discharge (L 3 T -1 ); A is cross sectional area (L 2 ) = UK c /(K c ? K f ); K is
conveyance; V is vel ocity (L T - 1 ); Z is water level (L); S f is friction slope; S is
storage term (L 2 ); S l is average lateral inflow (L 3 T -1 ); b is coefficient and Dx e is
equation flow path (L). The parameters of C, f, and T are terms for channel,
floodplain, and combined channel and floodplain, respectively. In the second
equation, the friction slopes for both the channel and the floodplain are assumed to
equal zero.
As mentioned before to create all necessary input data for HEC-RAS modeling,
the extension of Hec-GeoRAS model in ArcGIS was applied. The process
modeling in HEC-GeoRAS and HEC-RAS modeling is presented in Fig. 3.8 .
Froude Number (Fr): In the HEC-RAS model (1D), the Froude number is an
important parameter which deals with the characteristics of the open channel flow.
The Froude number is defined as the ratio of flow velocity to the velocity of free
surface wave at a specific location. The Froude number in flood simulation models is
an important factor in both: (1) Understanding the flood wave movement and (2) The
numerical stability of the model. It could also be considered as a ratio of inertial
forces to the gravity forces, and is expressed in the following equation [ 60 - 63 ]: