FLOOD07520

• County: Statewide
• Basin: Statewide
• Title: Roughness Coefficients for Densely Vegetated Flood Plains
• Date: 1/1/1987
• Prepared By: USGS
• Floodplain - Doc Type: Floodplain Report/Masterplan

1
I
I

The pressure forces in the x-direction cancel, and the remaining forces
are gravity, shear forces in the boundary caused by viscosity and wall
roughness, and drag forces on the plants.

Equation 3 is expanded to

where: y
A
L
S
Ioi
~w

p

YALS - rDi - ~wPL = 0

(4)

specific weight of liquid, in pounds per cubic foot;
cross-sectional area of flow, in square feet:
length of channel reach being considered, in feet;
bed slope of the channel, in feet per feet;
summation of drag forces on all plants, in pounds;
the shear force on the channel boundary per unit area,
in pounds per square foot; and
wetted perimeter of channel, in feet.

The drag force on each plant may be described by

C.1Vi 2Ai

Di =

(5)

2g

where: C. drag coefficient for the vegetation;
Vi average approach velocity to the ith plant, in feet per
second;
Ai projected area of the ith plant in the flow direction,
in square feet; and
g gravitational constant, in feet per second squared.

The average boundary shear stress, twr is conventionally derived in the
form

where: Se

~w = Y (~) Se

( 6)

energy gradient due to the average shear stress on
the boundary, in feet per feet.

By rewriting the Manning's formula (eq. 1) in terms of velocity and
wetted perimeter, and substituting the results into equation 6, the following
result is obtained for shear stress:

or

where: V
no

() ( n )2 (f.A) 4/3
~w Y ~ v2 1. ~ 9

(.2.:.2...)2
1w = yv2 1. 49

average velocity, in feet per
Manning's boundary roughness,
vegetation.

(~) 1/3

(7)

second; and
excluding the effect of

4