Environmental Engineering Reference
In-Depth Information
The cross-section is generally defined by the following geometrical
measures.
Water
depth y :
vertical
distance
from
the
bottom
to
the
water
surface
Section depth d : normal (perpendicular) distance from the bottom to
the water surface
Surface or top width B s : length of the channel width at the water
surface
Wetted area A : area normal to the flow direction
Wetted perimeter P : length of the wetted line of intersection
Hydraulic radius R : wetted area A /wetted perimeter P
Hydraulic depth D : wetted area A /top width B s
Bottom width b : length of the bottom
Side slope m : 1 vertical: m horizontal
Some other quantities that are related to a cross-section include:
Discharge Q which is the total amount of water flowing through a
cross-section during the unit of time t ; the unit of discharge is m 3 /s
The average velocity is by definition: v
=
Q / A
αv 2 /2 g ( y
Total energy: E
=
z
+
d cos
+
=
d cos ; is the bottom
slope in radian)
αv 2 /2 g (for small slopes cos
Specific energy: E s =
y
+
=
1)
Velocity head: αv 2 /2 g ( α is the Coriolis coefficient)
Froude number: Fr 2
αQ 2 B s / gA 3
=
2.4 BASIC HYDRAULIC PRINCIPLES
The motion of water can be described by considering the conservation
of mass (continuity) and the conservation of momentum as expressed by
Newton's second law. Sometimes the energy equation can also be helpful
to describe the motion of water, especially when all the energy losses are
known.
Continuity principle
The continuity equation is applicable for all flow types without any restric-
tion. By using an x -, y -, z -coordinate system that is fixed in space and
the velocity components u , v and w , respectively, the continuity equation
is obtained by considering a small fluid element and the net rate of mass
entering that element. The continuity equation for unsteady, compressible,
real (with friction) or ideal (no friction) fluids reads:
δρv
δy +
δρw
δz +
δρ
δt =
δρu
δx +
0
(2.6)
 
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