cu06997 lecture 9-10_exercises
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Exercise 1
Clean and straight natural channel
Bed slope 1:2000, Length = 1000 m
Assuming steady uniform flow
1. Calculate the velocity and discharge using
Manning , assume n = 0,02 s/m1/3
2. Calculate the mean boundary shear stress
3. Is the flow turbulent?
4. Value specific energy?
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Open channel, with bed slope >0
2211 AuAuQ
Head loss
Reference line
𝑦1 + 𝑧1 +𝑢1
2
2𝑔= 𝑦2 + 𝑧2 +
𝑢22
2𝑔+ ∆𝐻1−2
4
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Manning’s formula
𝑉 =𝑅
23 ∙ 𝑆𝑓
12
𝑛
𝑉 = Mean Fluid Velocity [m/s]
R = Hydraulic Radius [m]
𝑆𝑓 = Slope Total head [1]
𝐴 = Wetted Area [m2]
𝑃 = Wetter Perimeter [m]
𝑛 = Mannings roughness coefficient [s/m1/3]
6
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Exercise 2
Clean and straight natural channel
Bed slope = 0 (horizontal), Length = 1000 m,
Water level downstream = +1,0 m N.A.P. ,
water depth downstream = 0,70 m.
Q = 1,5 m3/s, Assuming steady flow
1. Calculate water level upstream using Manning, ,
assume n = 0,02 s/m1/3
2. Calculate the mean boundary shear stress
3. Is the flow turbulent?
4. Uniform or non-uniform flow?
5. Value specific energy?
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u1
Reference [m]
Surfacelevel y +z [m]
Total Head H [m]
P1
z1
y1
u12/2g
P2 z2
y2
u22/2g
u2
21
2
222
2
111
22 H
g
uzy
g
uzy
Head loss [m] ΔH
Velocity Head [m]
Open channel, with bed slope <= 0
4
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Little errors or inaccuracies with calculation by hand.
1. Length between the calculation points.
2. Assume that between the calculation points ∆H = ∆y
+1,31 m
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Model in sobek
Waterdepth
Distance (m) Sobek (m) By Hand (m)
0 0.7 0.7
200 0.78 0.81
600 0.89 0.94
1000 0.96 1.01
+1 m NAP +1,26 m NAP