Course CU06997 Fluid Dynamics The 13 situations you are able to calculate at the end of this course 1
Aug 20, 2015
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 π = π’ β π΄ 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]
π π =π. 4π
π
Subcritical or Supercritical flow
[Stromend of Schietend water]
π¦π =π2
π β π΅2
3
ππ = π β π¦π2
πΉπ =π
ππ
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)ΞΎΞΎΞΎ(ΞΞ
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]
π =π
23 β ππ
12
π
π = πΆ β π β ππ
ππ = ππ
π¦π =π2
π2 β πΆ2 β ππ
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]
π =π
23 β ππ
12
π
π = πΆ β π β ππ
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]
π = π β π΅ β π»32
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]
π = πΆ β π β ππ πΆ = 18 β πππ12π
π ππ =
ΞH
πΏ
4
Wate
r depth
Wate
r pre
ssure
Wall
Water level
Profile
Force by water [Kracht door water]
π = π β π β π¦ [ππ] F = p β A [N]
4