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ppt_file_mannings_equation.v2.pptx
- 1. This work is supported by the National Science Foundation’s Directorate for Education and Human Resources (TUES-1245025, IUSE- 1612248, IUSE-1725347). Questions, contact education-AT-unavco.org CHANNEL CAPACITY AND FLOODS Manning’s Equation
- 2. FLOODS, CHANNEL CAPACITY TOPOGRAPHY The shape of the channel and adjacent terrain are simultaneously sculpted by water, and determine how much water the channel can carry
- 3. PREDICTING FLOOD RISK REQUIRES … 1. Measurements of channel and floodplain topography Geodesy!! 2. Physics-based calculations of channel capacity. How much water can a channel carry. Manning’s Equation 𝑸 = 𝒄 𝒏 𝑹𝟐 𝟑𝑺𝟏 𝟐𝑨
- 4. MANNING’S EQUATION 𝑸 = 𝒄 𝒏 𝑹𝟐 𝟑 𝑺𝟏 𝟐 𝑨 𝑅 = 𝐻𝑦𝑑𝑟𝑎𝑢𝑙𝑖𝑐 𝑅𝑎𝑑𝑖𝑢𝑠 = 𝐴 𝑃 𝐴 = 𝐶𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 𝑎𝑟𝑒𝑎 𝑃 = 𝑤𝑒𝑡𝑡𝑒𝑑 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑆 = 𝑐ℎ𝑎𝑛𝑛𝑒𝑙 𝑠𝑙𝑜𝑝𝑒 𝑛 = 𝑀𝑎𝑛𝑛𝑖𝑛𝑔′𝑠 𝑅𝑜𝑢𝑔ℎ𝑛𝑒𝑠𝑠 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑐 = 1 𝑖𝑓 𝑙𝑒𝑛𝑔𝑡ℎ 𝑢𝑛𝑖𝑡𝑠 𝑖𝑛 𝑚𝑒𝑡𝑒𝑟𝑠 1.42 if length units in feet
- 5. BASIC PHYSICS OF FLOW IN CHANNELS 1. Water flows downhill 2. Conservation of mass, energy, and momentum are obeyed 3. Channel properties provide resistance to flow 4. Properties of flow (depth and velocity) emerge as points 1, 2, and 3 find balance
- 6. MANNING’S EQUATION BASIC CONCEPTS 1. Water flows down hill (slope) along a potential energy gradient Assumption: The potential energy gradient equals bed slope, S z u x 𝑆 = 𝑑𝑧 𝑑𝑥
- 7. MANNING’S EQUATION BASIC CONCEPTS 2. Mass, energy, and momentum are conserved leading to flow at the “normal depth” under steady state, uniform conditions z u x Steady-state: Velocity (u) and depth (z) do not change in time Uniform: Velocity (u) and depth (h) do not change in space 𝑑𝑧 𝑑𝑡 = 0, 𝑑𝑢 𝑑𝑡 = 0 𝑑𝑧 𝑑𝑥 = 0, 𝑑𝑢 𝑑𝑥 = 0
- 8. MANNING’S EQUATION BASIC CONCEPTS 3. Channel properties impose resistance to flow Channel shape Sinuosity Bed roughness Turbulence …act together to impose an upstream resisting force
- 9. MANNING’S EQUATION BASIC CONCEPTS 4. Depth and Velocity of flow in a channel adjust themselves is response to input flow rate, Q, energy gradient, S, and channel properties that cause resistance— all expressed in Manning’s equation z u x 𝑢 = 𝑄 𝐴 = 𝑐 𝑛 𝑅2 3 𝑆1 2 Energy gradient driving flow. Note, the square root on the energy gradient is caused by turbulence Channel properties providing resistance
- 10. MANNING’S N
- 11. MANNING’S EQUATION PROBLEM Determine the bankfull discharge, Q, of a mountain stream with a channel shape that can be approximated by a trapezoid shown below. The stream bed has a slope of 0.003, and is composed of gravels, cobbles, and a few boulders. Depth = 0.5 Bottom width = 4m 2m 2m (not to scale)
Notes de l'éditeur
- DO REMEMBER to include attribution information for all the figures you include. Even if you took the picture or made the diagram, it will make it easier later if we just have that recorded. ALSO – it is much easier to make notes (at least preliminary ones) for each slide NOW compared to several months later. Think about the information that future instructors using this materials will need to know in order to understand what the point of the different slides are. If all the relevant text is on the slide, notes may not be necessary, BUT if there are images, most likely some notes will be needed for future users.
- Intstructor Notes: Emphasize that river channels and floodplains are naturally adjusted to accommodate moderate high flows that occur every couple of years. Higher flows spill onto floodplains. Topography determines the extent of flooding for any given flow.
- Instructor Notes: These concepts define the learning objectives of this unit. Students will be introduced to basic topographic measurement techniques with and emphasis on channel form, and use Manning’s equation to compute flow rates for specified channel depths. Variables in Manning’s Equation are explained later Credit: Steve Holnbeck, Wyoming-Montana Water Science Center. Public domain. https://www.usgs.gov/media/images/ground-point-survey-total-station-measure-depth-streambed
- Instructor Notes: Manning’s equation can simply be presented as is, or be developed with a few slides about open channel flow physics.
- Instructors notes: Explain that the physics of open channel flow are quite complicated, Manning’s equation is an example of how these principles come together. Full development of open channel flow physics is beyond the slope of this Unit Photo by James McNamara
- In these slides
- In these slides
- Instructors Note: Force balance is a critical concept in geomorphology.