Cu06997 lecture 9-10_exercises

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?

Open channel, with bed slope >0

2211 AuAuQ

Head loss

Reference line

𝑦1 + 𝑧1 +𝑢1

2

2𝑔= 𝑦2 + 𝑧2 +

𝑢22

2𝑔+ ∆𝐻1−2

4

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

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?

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

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

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