Download CE 150 - CSU, Chico

Selected Topic: Open
Channel Flow
Reading: Munson, et al.,
Chapter 10
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Introduction
• Open channel flow - flow of a liquid
in a channel (or conduit) that is not
completely filled
• Main driving force is gravity;
pressure force is only hydrostatic
• Applications
–
–
–
–
river/stream flow
flow in canals, ditches, gutters, sewers
ocean waves, tidal effects
roadway, parking lot runoff
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General Characteristics
• Free surface represents an additional
degree of freedom (and complexity)
compared to pipe flows
• New parameter: fluid depth (y)
which may vary with time (t) and
distance along channel (x)
• Classifications based on depth
– Uniform flow (UF): constant depth, or
dy/dx = 0
– Gradually varying flow (GVF), dy/dx
<< 1
– Rapidly varying flow (RVF), dy/dx  1
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General Characteristics
• Classification based on flow
condition
–
–
–
–
Laminar: Re  500
Transitional: 500  Re  12,500
Turbulent: Re  12,500
where
Re 
VRh
,

A
Rh 
P
(hydraulic radius)
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Surface Waves
• Waves can occur when the channel
boundaries are suddenly perturbed
• Waves travel due to hydrostatic
pressures differences
• Small amplitude wave speed
– Solitary waves: c  gy
– Sinusoidal waves:
 g 
 2y 
c 
 tanh 

 2 
  
shallow wa ves ( y   ), c  gy
g
deep waves ( y   ), c 
2
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Froude Number
• Froude number is the ratio of fluid
speed to wave speed:
Fr 
V
V

c
gy
– Froude number determines the surface
characteristics of open channel flow
• Subcritical flow: Fr < 1
• Critical flow: Fr = 1
• Supercritical flow: Fr > 1
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Channel Depth for
GVF
• Channel depth variation for steady,
gradually varying flow (GVF):
dy S f  S 0

dx 1  Fr 2
dhL
dz
where S f 
, S0 
dx
dx
– If Sf > S0 and Fr < 1, channel depth
will increase
– If Sf < S0 and Fr < 1, channel depth
will decrease
– See Table 10.2 for all possibilities and
classifications
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Manning Equation
• For uniform channel flow (UF), the
average velocity is given by the
Manning equation:
V

n
Rh2 / 3 S 0
– where
 = unit conversion constant
n = Manning resistance coefficient
(see Table 10.1)
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Hydraulic Jump
• The hydraulic jump is an example of
a rapidly varying flow (RVF), where
a shallow high-speed flow suddenly
changes to a deeper, low-speed flow
• The jump occurs due to a conflict
between upstream influences
(supercritical flow, Fr > 1) and
downstream influences (subcritical
flow, Fr < 1)
• The energy loss of a hydraulic jump
is useful in spillway design
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