1. Basic Hydraulics: Open Channel Flow – II

2. Steady Uniform Flow
Steady flow means that the discharge at a point does not change with time.
Uniform flow means that there no change in the magnitude or direction of velocity with distance, that the depth of flow does not change with distance along a channel.
This uniform flow definition implies constant channel geometry – more importantly, geometry and flow are related.

3. Steady Uniform Flow
Steady uniform flow is an idealized concept of open channel flow that seldom occurs in natural channels and is difficult to obtain even in model channels.
However, in many practical highway applications, the flow is assumed to be reasonably steady, and changes in width, depth, or direction (resulting in non-uniform flow) are assumed to be sufficiently small so that flow can be considered uniform.
Examples: Short sections of drainage infrastructure, bridge deck drainage, etc.

4. Steady Non-Uniform Flow
Steady non-uniform flow is flow that is steady (no change in Q with time), but the flow geometry can (and does) change in space.
Two kinds of non-uniform, steady flow are:
Rapidly varied flow:
the changes take place abruptly over short distances. (Typically as flow changes between super- and sub-critical)
Gradually varied flow:
the changes take place over long distances, and occurs within one flow regime (sub- or super-critical)

5. Gradually Varied Flow
Gradually varied flow (GVF) is important in drainage engineering to account for:
Backwater effects (flow draining into a “pool” situation)
Frontwater effects (flow accelerating over or under a structure).
GVF conditions are characterized by relationships of normal and critical depths, slope designations, and water surface profile “shapes”

6. Slope Designation Relations
Critical to Normal Relationship
Remarks
Steep – S
Critical – C
Mild – M
Horizontal – H
Adverse – A

7. Profile-Type Relationships
Logic
Type – 1
.AND.
Type – 2
.OR.
Type – 3

8. Slope/Profile Sketches
The GVF slope and profile designations convey information on control (of flow) and are useful for:
Selecting control sections for measurements
Selecting geometries to produce desired flow depths near infrastructure

9. M1 water surface profile
Indicative of downstream control
Flow into a “pool” or forebay, flow approaching a weir.

10. M2 water surface profile
Indicative of downstream control
Flow accelerating over a weir, waterfall, or contraction but otherwise sub-critical

11. M3 water surface profile
Indicative of upstream control
Flow under a sluice gate, a jet from a culvert

12. S1 water surface profile
Indicative of downstream control

13. S2 water surface profile
Indicative of upstream control
Acceleration of flow just past a submerged weir on a steep slope

14. S3 water surface profile
Indicative of upstream control
Flow under a sluice gate on an OGEE spillway

15. Froude Number
Recall the specific energy diagram, the energy minimum for a given discharge occurs when the dimensionless Froude number (Fr) is unity
The Froude number is the ratio of inertial to gravitational forces in flow. In a wide channel or rectangular channel the number is well approximated by

16. Froude Number
The Froude number also classifies the flow.

17. Energy and Momentum
The short segment of open channel between two sections is called a reach.
The momentum change in a reach is related to the frictional forces of the channel on the water in the reach, the gravitational force on the water in the reach, and the difference in pressure forces at the upstream and downstream sections.
Momentum change is important in computing forces of water on structures as well as determining the location of abrubt changes in flow regime.

18. Energy and Momentum
Momentum equation for steady open channel flow is (after considerable algebraic simplification)

19. Example – Hydraulic jump
A hydraulic jump occurs as an abrupt transition from supercritical to subcritical flow. There are significant changes in depth and velocity in the jump and energy is dissipated.
Specific energy changes across a jump.
Momentum however is nearly conserved, hence computations would use the momentum equation

20. Example – Hydraulic jump
The potential for a hydraulic jump to occur should be considered in all cases where the Froude number is close to one (1.0) and/or where the slope of the channel bottom changes abruptly from steep to mild.

21. Basic Hydraulics: Open Channel Flow – II

22. Steady Uniform Flow
Steady flow means that the discharge at a point does not change with time.
Uniform flow means that there no change in the magnitude or direction of velocity with distance, that the depth of flow does not change with distance along a channel.
This uniform flow definition implies constant channel geometry – more importantly, geometry and flow are related.

23. Steady Uniform Flow
Steady uniform flow is an idealized concept of open channel flow that seldom occurs in natural channels and is difficult to obtain even in model channels.
However, in many practical highway applications, the flow is assumed to be reasonably steady, and changes in width, depth, or direction (resulting in non-uniform flow) are assumed to be sufficiently small so that flow can be considered uniform.
Examples: Short sections of drainage infrastructure, bridge deck drainage, etc.

24. Steady Non-Uniform Flow
Steady non-uniform flow is flow that is steady (no change in Q with time), but the flow geometry can (and does) change in space.
Two kinds of non-uniform, steady flow are:
Rapidly varied flow:
the changes take place abruptly over short distances. (Typically as flow changes between super- and sub-critical)
Gradually varied flow:
the changes take place over long distances, and occurs within one flow regime (sub- or super-critical)

25. Gradually Varied Flow
Gradually varied flow (GVF) is important in drainage engineering to account for:
Backwater effects (flow draining into a “pool” situation)
Frontwater effects (flow accelerating over or under a structure).
GVF conditions are characterized by relationships of normal and critical depths, slope designations, and water surface profile “shapes”

26. Slope Designation Relations
Critical to Normal Relationship
Remarks
Steep – S
Critical – C
Mild – M
Horizontal – H
Adverse – A

27. Profile-Type Relationships
Logic
Type – 1
.AND.
Type – 2
.OR.
Type – 3

28. Slope/Profile Sketches
The GVF slope and profile designations convey information on control (of flow) and are useful for:
Selecting control sections for measurements
Selecting geometries to produce desired flow depths near infrastructure

29. M1 water surface profile
Indicative of downstream control
Flow into a “pool” or forebay, flow approaching a weir.

30. M2 water surface profile
Indicative of downstream control
Flow accelerating over a weir, waterfall, or contraction but otherwise sub-critical

31. M3 water surface profile
Indicative of upstream control
Flow under a sluice gate, a jet from a culvert

32. S1 water surface profile
Indicative of downstream control

33. S2 water surface profile
Indicative of upstream control
Acceleration of flow just past a submerged weir on a steep slope

34. S3 water surface profile
Indicative of upstream control
Flow under a sluice gate on an OGEE spillway

35. Froude Number
Recall the specific energy diagram, the energy minimum for a given discharge occurs when the dimensionless Froude number (Fr) is unity
The Froude number is the ratio of inertial to gravitational forces in flow. In a wide channel or rectangular channel the number is well approximated by

36. Froude Number
The Froude number also classifies the flow.

37. Energy and Momentum
The short segment of open channel between two sections is called a reach.
The momentum change in a reach is related to the frictional forces of the channel on the water in the reach, the gravitational force on the water in the reach, and the difference in pressure forces at the upstream and downstream sections.
Momentum change is important in computing forces of water on structures as well as determining the location of abrubt changes in flow regime.

38. Energy and Momentum
Momentum equation for steady open channel flow is (after considerable algebraic simplification)

39. Example – Hydraulic jump
A hydraulic jump occurs as an abrupt transition from supercritical to subcritical flow. There are significant changes in depth and velocity in the jump and energy is dissipated.
Specific energy changes across a jump.
Momentum however is nearly conserved, hence computations would use the momentum equation

40. Example – Hydraulic jump
The potential for a hydraulic jump to occur should be considered in all cases where the Froude number is close to one (1.0) and/or where the slope of the channel bottom changes abruptly from steep to mild.