Course CU06997 Fluid Dynamics

The 13 situations you are able to

calculate at the end of this course

1

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

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 Q 1

Basics 𝑄 = 𝑢 ∙ 𝐴 P

AR

21

2

222

2

111

22 H

g

uzy

g

uzy

u1

Reference /datum [m] [Referentie]

Surface level [m] [Waterstand]

Total head H [m] [Energiehoogte]

P1

z1

y1

u12/2g Velocity head [m] [Snelheidshoogte]

y = Pressure head [m] [drukhoogte]

z = Potential head [m] [plaatshoogte]

1

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 ∙ 𝑦𝑐2

𝐹𝑟 =𝑉

𝑉𝑐

1

Downstream

Upstream

Cross-section Culvert

Head L

oss

Length Culvert

Velocity

1. Discharge culvert [Debiet duiker]

2. Dimensions culvert

[Afmetingen duiker]

2

Downstream

Upstream

Cross-section Culvert

Head L

oss

Length Culvert

Velocity

Culvert,submerged [Duiker,volledig gevuld] 2

11

i

1oR

Lf

4

[m] 2g

u)ξξξ(ΔΗ

2

culvertoficulvert

2

DownstreamUpstream

Cross-section

Length Culvert

Flow velocity

3. Discharge partly submerged Culvert

[Debiet gedeeltelijk gevulde duiker]

2

DownstreamUpstream

Cross-section

Length Culvert

Flow velocity

Culvert, partly filled

[Duiker, gedeeltelijk gevuld]

Is a broad crested weir

[Is een lange overlaat]

2

Free flow broad crested weir

[Volkomen lange overlaat]

23

HBcq vv

Total Head or Energy line H

Free flow broad crested weir

Super critical flow

Hydraulic Jump

2

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

Bed Slope

Depth

Head L

oss

Cross-sectionProfile

4. Discharge open channel

5. Dimensions open channel

6. Equilibrium depth open channel

3

Bed Slope

Depth

Head L

oss

Cross-sectionProfile

Open channel, bed slope > 0

[Open watergang, bodemverhang > 0]

𝑉 =𝑅

23 ∙ 𝑆𝑏

12

𝑛

𝑉 = 𝐶 ∙ 𝑅 ∙ 𝑆𝑏

𝑆𝑏 = 𝑆𝑓

𝑦𝑛 =𝑞2

𝑏2 ∙ 𝐶2 ∙ 𝑆𝑏

3

3

Depth

Depth

Head L

oss

Hydraulic gradientHorizontal bed

Cross-sectionProfile

7. Hydraulic Gradient open channel

[Energieverhang open watergang]

3

Depth

Depth

Head L

oss

Hydraulic gradientHorizontal bed

Cross-sectionProfile

Open channel, bed slope <= 0

[Open watergang, bodemverhang <=0]

𝑉 =𝑅

23 ∙ 𝑆𝑓

12

𝑛

𝑉 = 𝐶 ∙ 𝑅 ∙ 𝑆𝑓

3

Specific

Head

Width

Weir

Hydraulic Gradient

Cross-sectionProfile

8. Upstream water level Weir

9. Dimensions Weir [Afmetingen stuw]

3

Specific

Head

Width

Weir

Hydraulic Gradient

Cross-sectionProfile

Short crested weir [Korte overlaat, meetstuw]

𝑄 = 𝑚 ∙ 𝐵 ∙ 𝐻32

3

Hydraulic Gradient

Head L

oss

Water level

Cross-sectionProfile

Submerged Pipe

10. Flow rate Pipe [Debiet buis]

11. Dimensions Pipe [Afmetingen buis]

4

Hydraulic Gradient

Head L

oss

Water level

Cross-sectionProfile

Submerged Pipe

Flow rate Pipe [Debiet buis]

𝑉 = 𝐶 ∙ 𝑅 ∙ 𝑆𝑓 𝐶 = 18 ∙ 𝑙𝑜𝑔12𝑅

𝑘 𝑆𝑓 =

ΔH

𝐿

4

Wate

r depth

Wate

r pre

ssure

Wall

Water level

Profile

12. Force by water [Kracht door water]

4

Wate

r depth

Wate

r pre

ssure

Wall

Water level

Profile

Force by water [Kracht door water]

𝑝 = 𝜌 ∙ 𝑔 ∙ 𝑦 [𝑃𝑎] F = p ∙ A [N]

4

CulvertEmpty

Ground water level

Cross-section

13. Buoyancy [Opdrijving]

4

CulvertEmpty

Ground water level

Cross-section

Buoyancy, [Opdrijving]

Upward force = weight of fluid displaced by the body

4