1. Course CU06997 Fluid Dynamics
The 13 situations you are able to
calculate at the end of this course
1

2. Water
Stagnant
not flowing
u = 0 m/s
In motion
flowing
u > 0 m/s
Hydrostatics Fluid dynamics
Pipes Open channel
[Gesloten leidingen] [Open water]
1

3. Classification of flows.
1. Steady uniform flow [Eenparig uniform]
example: pipe with constant D and Q
example: channel with constant A and Q
2. Steady non-uniform flow
example: pipe with different D and constant Q
example: channel with different A and constant Q
3. Unsteady uniform flow[Niet eenparig , uni..]
example: pipe with constant D and different Q
example: channel with constant A and different Q
4. Unsteady non-uniform flow
example: pipe with different D and Q
example; channel with different A and Q1

4. Basics 𝑄 = 𝑢 ∙ 𝐴 P
A
R 
21
2
2
22
2
1
11
22
 H
g
u
zy
g
u
zy
u1
Reference /datum [m] [Referentie]
Surface level [m] [Waterstand]
Total head H [m] [Energiehoogte]
P1
z1
y1
u1
2/2g Velocity head [m] [Snelheidshoogte]
y = Pressure head [m] [drukhoogte]
z = Potential head [m] [plaatshoogte]
1

5. Turbulent or laminar flow
[Turbulente of laminaire stroming]
𝑅𝑒 =
𝑉. 4𝑅
𝜈
Subcritical or Supercritical flow
[Stromend of Schietend water]
𝑦𝑐 =
𝑄2
𝑔 ∙ 𝐵2
3
𝑉𝑐 = 𝑔 ∙ 𝑦𝑐
2
𝐹𝑟 =
𝑉
𝑉𝑐
1

6. Downstream
Upstream
Cross-section Culvert
HeadLoss
Length Culvert
Velocity
1. Discharge culvert [Debiet duiker]
2. Dimensions culvert
[Afmetingen duiker]
2

7. Downstream
Upstream
Cross-section Culvert
HeadLoss
Length Culvert
Velocity
Culvert,submerged [Duiker,volledig gevuld]
2
1
1








i
1o
R
L
f
4
 
[m]
2g
u
)ξξξ(ΔΗ
2
culvert
oficulvert 
2

8. DownstreamUpstream
Cross-section
Length Culvert
Flow velocity
3. Discharge partly submerged Culvert
[Debiet gedeeltelijk gevulde duiker]
2

9. DownstreamUpstream
Cross-section
Length Culvert
Flow velocity
Culvert, partly filled
[Duiker, gedeeltelijk gevuld]
Is a broad crested weir
[Is een lange overlaat]
2

10. Free flow broad crested weir
[Volkomen lange overlaat]
2
3
HBcq vv 
Total Head or Energy line H
Free flow broad crested weir
Super critical flow
Hydraulic Jump
2

11. Submerged broad crested weir flow
[Onvolkomen lange overlaat]
)(2 33 hHghBcq olv 
Total Head or Energy line H
Submerged broad crested weir
Bottom eddy
2

12. Bed Slope
Depth
HeadLoss
Cross-sectionProfile
4. Discharge open channel
5. Dimensions open channel
6. Equilibrium depth open channel
3

13. Bed Slope
Depth
HeadLoss
Cross-sectionProfile
Open channel, bed slope > 0
[Open watergang, bodemverhang > 0]
𝑉 =
𝑅
2
3 ∙ 𝑆 𝑏
1
2
𝑛
𝑉 = 𝐶 ∙ 𝑅 ∙ 𝑆 𝑏
𝑆 𝑏 = 𝑆𝑓
𝑦𝑛 =
𝑞2
𝑏2 ∙ 𝐶2 ∙ 𝑆 𝑏
3
3

14. Depth
Depth
HeadLoss
Hydraulic gradient
Horizontal bed
Cross-sectionProfile
7. Hydraulic Gradient open channel
[Energieverhang open watergang]
3

15. Depth
Depth
HeadLoss
Hydraulic gradient
Horizontal bed
Cross-sectionProfile
Open channel, bed slope <= 0
[Open watergang, bodemverhang <=0]
𝑉 =
𝑅
2
3 ∙ 𝑆𝑓
1
2
𝑛
𝑉 = 𝐶 ∙ 𝑅 ∙ 𝑆𝑓
3

16. SpecificHead
Width
Weir
Hydraulic Gradient
Cross-sectionProfile
8. Upstream water level Weir
9. Dimensions Weir [Afmetingen stuw]
3

17. SpecificHead
Width
Weir
Hydraulic Gradient
Cross-sectionProfile
Short crested weir [Korte overlaat, meetstuw]
𝑄 = 𝑚 ∙ 𝐵 ∙ 𝐻
3
2
3

18. Hydraulic Gradient
HeadLoss
Water level
Cross-sectionProfile
Submerged Pipe
10. Flow rate Pipe [Debiet buis]
11. Dimensions Pipe [Afmetingen buis]
4

19. Hydraulic Gradient
HeadLoss
Water level
Cross-sectionProfile
Submerged Pipe
Flow rate Pipe [Debiet buis]
𝑉 = 𝐶 ∙ 𝑅 ∙ 𝑆𝑓 𝐶 = 18 ∙ 𝑙𝑜𝑔
12𝑅
𝑘
𝑆𝑓 =
ΔH
𝐿
4

20. Waterdepth
W
aterpressure
Wall
Water level
Profile
12. Force by water [Kracht door water]
4

21. Waterdepth
W
aterpressure
Wall
Water level
Profile
Force by water [Kracht door water]
𝑝 = 𝜌 ∙ 𝑔 ∙ 𝑦 [𝑃𝑎] F = p ∙ A [N]
4

22. Culvert
Empty
Ground water level
Cross-section
13. Buoyancy [Opdrijving]
4

23. Culvert
Empty
Ground water level
Cross-section
Buoyancy, [Opdrijving]
Upward force = weight of fluid displaced by the body
4