CE 3372 Water systems design

1. CE 3372 Water systems design Lecture 12: Introduction to Open Channel Hydraulics

2. Outline • Flow Terminology • Energy Equation • Critical Depth/Flow • Flow Profiles for GVF • Manning’s Equation

3. Open Channel Design Concepts • Interest to engineers: • Water surface elevation (WSE)(minimize impact/reduce floods) • Discharge –Depth relationships • Channel design

4. Open Channels • Conduits whose upper boundary of flow is the liquid surface.

5. TYPES OF FLOW • Steady Flow – flow, depth and velocity may differ from point to point but remain constant over time • Unsteady Flow – flow, depth, and velocity is a function of time • Uniform Flow – occurs in prismatic channels when flow depths are equal no change in velocity within the channel: Q, y, A, S are all constant • Non-uniform Flow – velocity is not the same at every point Temporal Spatial

7. Open Channel Nomenclature • Flow depth is the depth of flow at a cross-section measured from the channel bottom. y

8. Open Channel Nomenclature • Elevation of the channel bottom is the elevation at a cross-section measured from a reference datum (typically MSL). y z Datum

9. Open Channel Nomenclature • Slope of the channel bottom, So, is called the topographic slope or channel slope. y z So 1 Datum

10. Open Channel Nomenclature • Slope of the water surface is the slope of the HGL, or slope of WSE (water surface elevation). HGL Swse y 1 z So 1 Datum

11. Open Channel Nomenclature • Slope of the energy grade line (EGL) is called the energy or friction slope. EGL Sf HGL V2/2g 1 Q=VA Swse y 1 z So 1 Datum

12. Steady NON-uniform Flow Sketch of steady flow in a channel Based on cross-sections: Section 1 is upstream Section 2 is downstream

13. Steady Flow The energy grade line (EGL) is: z_head + P_head + v_head Sketch of steady flow in a channel The hydraulic grade line (HGL) is at the water surface Energy grade line (EGL) Profile grade line is the channel bottom velocity Hydraulic grade line (HGL) pressure (depth) The head loss is depicted as the difference between a horizontal zero-loss energy grade line and the energy grade line elevation

15. Energy relationships • Energy equation for closed conduits • Energy equation for open conduits

16. Specific energy • The sum of the depth of flow + velocity head (Head relative to the channel bottom) • For a given discharge, the SE can be calculated for various flow depths including critical depth

17. Critical depth • Depth of flow for a given discharge, where the specific energy is at a minimum • Occurs when dE/dy = 0 and Fr = 1 • It is important to calculate yc in order to determine if the flow in the channel will be subcritical or supercritical • Can be found through Specific Energy Diagram

18. Alternate Depths: Plug & chug. Solve for y3 roots –1 negative = 2 depths A = By y Q=qywhere q is the discharge/unit width of channel B

19. Open channel flows • Critical depth, yc occurs at Fr = 1 • Open channel flow is also classified by the Froude number

20. Open channel flows Subcritical flow • Low velocities, Fr < 1 • Disturbance travels upstream • y > yc Supercritical flow • High velocities, Fr > 1 • Disturbances travel downstream • y < yc

21. Arbitrary cross-section Critical Flow T dy Has a minimum at yc A y dA P More general definition of Fr

22. Critical Flow – Rectangular channel T yc Ac Only for rectangular channels! Given the depth we can find the flow!

23. Critical Flow: Rectangular Channels velocity head = 0.5 (depth)

24. Open channel flows • Similar to pipe flow, open channel flow can be classified into which is dependent on Reynolds number

25. Open channel flows Where V = average velocity Rh = hydraulic radius v = kinematic viscosity

26. Area represents cross sectional area of the fluid Wetted perimeter does not include the free surface

27. Rectangular Conduit

28. Trapezoidal Channel • common geometry • Engineered (improved) natural channels are reasonably well approximated by trapezoidal equations • the geometry is important in drainage engineering

29. Circular Conduit • Sweep angle definition matters, book uses 2a.

30. Varied Flow • Gradually varied flow – change in flow depth moving upstream or downstream is gradual • Rapidly varied flow – change in flow depth occurs over a very short distance • Ex: waterfall, hydraulic jumps, etc. • RVF is outside the scope of this course.

31. Gradually Varied Flow • Equation relating slope of water surface, channel slope, and energy slope: Discharge and Section Geometry Variation of Water Surface Elevation Discharge and Section Geometry

32. Gradually Varied Flow • Procedure to find water surface profile is to integrate the depth taper with distance:

33. Flow profiles

35. MANning equation (1891) • Depth-Discharge Calculator for any open channel implements Manning's equation • The equation is the U.S. customary version • A drainage engineer in the US should memorize this equation!

36. Values of Manning n n = f(surface roughness, channel irregularity, stage...) d = median size of bed material d in ft

37. All the complications of pipe flow plus ______________________ Importance of Froude Number Fr>1 decrease in E gives increase in y Fr<1 decrease in E gives decrease in y Fr=1 standing waves (also min E given Q) Summary of open channels free surface location

38. NEXT TIME • Introduction to Storm Water Management Model • Introduction to SWMM software • Workshop for an uncomplicated open channel (bring your computer!)