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Cwiczenie na laborki z hydrologii
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OPEN CHANNEL
FLOW
PART 1
There are two main types of open channels:
- Natural
- Regular/ Artificial
Types of open channel flows :
Steady flow – when discharge Q does not change with time
Uniform flow – when depth of fluid does not change for a selected length or section
of the channel
Uniform steady flow – when discharge does not change with time and depth
remains constant for a selected section dv/dx = constant
Varied steady flow – when depth changes but discharge remains the same (how it
is possible?) dv/dx ǂ constant
Varied unsteady flow – when both depth and discharge change along a channel
length of interest.
Rapidly varying flow – depth change is rapid
Gradually varying flow – depth change is gradual
Hydraulic radius of open channel flow is a parameter that is defined as:
R = A/ WP
cross sectional area (A)
wetted perimeter (WP)
Hydraulic radius R for various channel shapes
Reynolds number for channel flow
NR= ρ v R/ μ
For channel flow
NR < 500 – laminar flow
NR > 2000 – turbulent flow
Froude Number
NF witch is gravity versus inertial forces:
NF= v/ (g* H)^1/2
Where H is referred as the hydraulic depth and given by
H = A/B
where A is the area and B is the top width of the channel.
NF = 1.0 or when v = (H)1/2 - critical flow
NF < 1.0 – subcritical flow
NF > 1.0 – super critical flow
A combination of both the numbers is used to describe channel flow conditions.
Uniform steady flow and Manning’s Equation
When discharge remains the same and depth does not change then we have
uniform steady flow.
In this condition the surface of water is parallel to the bed of the channel.
The slope of the channel can be expressed as :
• an angle = 1 degrees
• percent = 1%
Velocity of flow in a channel can be calculated many empirical equations.
One of them is
Manning’s equation:
Q = Flow Rate, (ft3/s)
v = Velocity, (ft/s)
A = Flow Area, (ft2)
n = Manning’s Roughness Coefficient
R = Hydraulic Radius, (ft)
S = Channel Slope, (ft/ft)
This is the SI units form of the equation with v (meters/sec) and R (meters).
The Manning’s coefficient (dimensionless) values are developed through experimentation.
Manning’s coefficient table example.
Task 1
Determine normal discharge for a 200 mm inside diameter
common clay drainage tile running half-full if the slope drops 1m over 1000 m.
S= 1/1000 = 0.001
A = (1/2) * (π D2 /4) = 0.5*π*(0.2)2 /4 = 0.0157 m2
WP = (1/2) * (π D) = 0.5*π*0.2 = 0.3141 m
R = 0.05 m
From Table n for clay tile = 0.013
Substitute these values in the equation:
Thus
Q = 5.18 x 10-3 m3/s
Task 2
Calculate slope of formed unfinished concrete channel, if Q = 50 ft3 /s.
Solution:
Transform the equation in terms of S
Compute
A = 12 ft2
WP = 9.66 ft
R = A/WP = 12/9.66 = 1.24 ft
Manning’s n for unfinished concrete channel = 0.017
Substitute
And S = 0.00169
Drop 1.69 ft for every 1000 ft.
Task 3
Design rectangular channel in formed unfinished concrete
Q = 5.75 m3 /s
S = 1.2%
Normal depth H = ½ of the width of the channel B
Use formula:
A*R2/3 = (n* Q)/ S1/2
Express Area and the hydraulic radius in terms of B.
A = B*H = B2 /2
WP = B+ 2H = 2B
R = A/WP = B/4
Back to the equation:
Therefore,
B = 1.76 m
H = 1.76/2 m