Reynolds Number Determination for All Channel (Hydraulic diameter, Wetted Perimeter)

Reynolds number (Re) is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions.

In pipe flow, Re is defined as: Re = rho.V.D/miu

where:
rho = density of the fluid
V = velocity of the fluid
D = pipe diameter
miu = dynamic viscosity of the fluid

How to determine the Reynolds number in square pipe?

actually, Re is defined as = rho.V.L/miu

where L is characteristic of length . The characteristics of length and is different based on the flow. For the flow pipe with square, rectangular and annular, the pipe flow is determined by hydraulic diameter:

Dh = 4A/P

where:
A = cross sectional area
P = wetted perimeter

Wetted perimeter is the perimeter of the cross sectional area that is "wet."
For example in round pipe flow the wetted perimeter is the circumference of the pipe. So the hydraulic diameter for flow in round pipe flow is:
Dh = 4.phi.R**2/2.phi.R = 2R = D (the dimeter of the pipe).

So for square pipe flow, the hydraulic diameter is:
assume that the rib of the square is a
Dh = 4.a**2/4a = a

for rectangular pipe flow then (if the rectangular has size: p x l):
Dh = 4pxl/2(p+l) = 2xpxl/(p+l)

For you who will solve the problem for flow of flood. You may use the open channel. Flow in an open channel is a flow liquid with a free surface, the hydraulic radius must be determined. This is the cross-sectional area of the channel divided by the wetted perimeter, i.e.:

R = A/P

Let's assume that the cross sectional area of the channel is trapezoidal. So that the hidraulic diameter is:
Dh = trapezoidal area / (circumference of the trapezoidal - length of the upper side of the trapezoidal)

Please send me your comment if there are mistakes of my understanding. Thank you.

Reff. :
S. Inamdar, Open Channel, http://udel.edu, accessed on April 13rd 2013.
Anonym, Reynolds Number, http://wikipedia.org/, accessed on April 13rd 2013.