VIEWS: 318 PAGES: 75 CATEGORY: Education POSTED ON: 7/20/2010 Public Domain
FLOWING WATER: HYDRAULICS AND OPEN CHANNEL FLOW FLOW SETTINGS OF INTEREST: •Overland flow, interflow throughflow •Groundwater flow •Open channel flow (rivers, canals etc) •Pipe flow Flow •Flow through lakes •Flow through wetlands •Tidal flow (wetlands) flow (c rrents a es •Ocean flo (currents, waves etc) Each of these are complex physical settings, and prediction of the flow regime will be equally complex. We use the laws of physics, along with simplifications, to make estimates of the flow regime. VELOCITY SCALES There fl i fi t t f diff t Th are many flow regimes of interest for different purposes. In this class we will focus on flow in river channels. OPEN CHANNEL FLOW: How deep and how fast water will flow in an open channel Basic question: how deep and fast will the river flow at your point of interest in the watershed for various recurrence interval storms [ie, Q(100); Q (2)]? Point of interest Open Channel Flow y p 1. Why is it important? 2. Some definitions 3. Hydraulic processes: “types of flow” 1 Steady vs unsteady 1. 2. Uniform vs nonuniform 3. Laminar vs turbulent flow (vertical velocity profile) 4. Sub-critical i i l fl 4 S b i i l vs super-critical flow Specific energy p - critical depth - froude number 4. Flow in Actual Channels 5 Estimating flow velocity, depth: Manning s equation 5. velocity Manning’s 6. Beyond Manning’s Equation: Backwater programs (HEC-RAS) 7. Hydrodynamic modeling: 1-d, 2-d, 3-d: unsteady flow models Principle of “Continuity” Applied to rivers: Flow rate (cfs) is the same at each cross- section Open Channel Flow y p 1. Why is it important? 2. Some definitions 3. Hydraulic processes: “types of flow” 1 Steady vs unsteady 1. 2. Uniform vs nonuniform 3. Laminar vs turbulent flow (vertical velocity profile) 4. Sub-critical i i l fl 4 S b i i l vs super-critical flow Specific energy p - critical depth - froude number 4. Flow in Actual Channels 5 Estimating flow velocity, depth: Manning s equation 5. velocity Manning’s 6. Beyond Manning’s Equation: Backwater programs (HEC-RAS) 7. Hydrodynamic modeling: 1-d, 2-d, 3-d: unsteady flow models Steady vs Unsteady flow: does the flow rate (at a specific location g ) change over time?) But we often assume a steady rate of flow to analyse a specific example 100-year problem: For example, we know that the 100 year flow event will include a complete hydrograph (ie, flow changes over time) but we may only be interested in the flow properties at the peak (maximum flow t ) f th t t fl rate) of that event. During this rain event, the flow in the river will vary over the duration of the storm (unsteady). However, we may choose to just determine hat flo elocit what the flow depth and velocity will be in the channel for the Peak flow rate Open Channel Flow y p 1. Why is it important? 2. Some definitions 3. Hydraulic processes: “types of flow” 1. 1 Steady vs unsteady 2. Uniform vs nonuniform 3. Laminar vs turbulent flow (vertical velocity profile) 4 S b i i l vs super-critical flow 4. Sub-critical i i l fl Specific energy p - critical depth - froude number 4. Flow in Actual Channels 5. velocity 5 Estimating flow velocity, depth: Manning equation Uniform vs Non-uniform: Variation of Flow along the Channel Uniform flow: constant depth along the channel Non-uniform flow: water is deeper in the pool, and shallow in the rapid Open Channel Flow y p 1. Why is it important? 2. Some definitions 3. Hydraulic processes: “types of flow” 1. 1 Steady vs unsteady 2. Uniform vs nonuniform 3. Laminar vs turbulent flow i l l i fil vertical velocity profile 4. Flow in real rivers Bernoulli equation Specific energy - critical depth - froude number Flow equation, Manning equation Laminar flow virtually never occurs in nature. Only a lab phenomenon Because of the inherent “roughness of natural channels, virtually all rivers experience “turbulent” flow Open Channel Flow y p 1. Why is it important? 2. Some definitions 3. Hydraulic processes: “types of flow” 1. 1 Steady vs unsteady 2. Uniform vs nonuniform 3. Laminar vs turbulent flow (vertical velocity profile) 4 S b i i l vs super-critical flow 4. Sub-critical i i l fl Specific energy p - critical depth - froude number 4. Flow in Actual Channels 5. velocity 5 Estimating flow velocity, depth: Manning equation Energy Concepts in flowing water: • The water at any location in the watershed has a fixed amount of “energy” associated with it. Potential i t d ith th f t th t h • P t ti l energy: energy associated with the fact that it has been raised (by evaporation) to a point above MSL (think of a ball at the top, vs bottom of a set of stairs). • Energy based on the depth of water in the channel (higher depth has more energy. • Energy based on the fact that it is flowing (just like a moving car has energy, since it takes counter energy to stop it. • Energy is neither created or destroyed as the water moves down the channel. Some of the energy forms described above are converted to heat (very slight, and hardly measurable) as a result of friction on the channel banks and bed, and by internal turbulence (as the water molecules rub past each other) How is energy lost in streamflow? Subcritical Super-critical Subcritical Hydraulic jump Most of the flow in rivers is “subcritical” flow, again because of the roughness of the channels. • We do see supercritical flow in some concrete channels •We see it in natural rivers in flow over drops, boulders etc. Open Channel Flow y p 1. Why is it important? 2. Some definitions 3. Hydraulic processes: “types of flow” 1. 1 Steady vs unsteady 2. Uniform vs nonuniform 3. Laminar vs turbulent flow (vertical velocity profile) 4 S b i i l vs super-critical flow 4. Sub-critical i i l fl Specific energy p - critical depth - froude number 4. Flow in Actual Channels 5. velocity 5 Estimating flow velocity, depth: Manning equation Flow in Natural Channels Spiral or helical flow occurs at river bends/meanders. bends/meanders The centrifugal force pushes the water out and down, d h f and creates somewhat of a “corkscrew” motion. This y creates additional velocity and scour on the outside of the meander bend, and causes the meander to grow over time. Open Channel Flow y p 1. Why is it important? 2. Some definitions 3. Hydraulic processes: “types of flow” 1. 1 Steady vs unsteady 2. Uniform vs nonuniform 3. Laminar vs turbulent flow (vertical velocity profile) 4 S b i i l vs super-critical flow 4. Sub-critical i i l fl Specific energy p - critical depth - froude number 4. Flow in Actual Channels 5. velocity 5 Estimating flow velocity, depth: Manning equation One-dimensional (downstream) flow: For steady, uniform flow, we assume that the forces pushing the water downhill (gravity) are balanced by the resistance to flow (shear stress) exerted by the ( ) y channel bed and banks and the internal shear of the water flowing past itself. We can assume that the flow velocity (V) will be directly ti l t th l proportional to the slope andd hydraulic radius, and inversely to the roughness Manning’s equation is applicable to steady, uniform flow conditions Estimating values of Manning’s “n”: roughness coefficient Open Channel Flow y p 1. Why is it important? 2. Some definitions 3. Hydraulic processes: “types of flow” 1 Steady vs unsteady 1. 2. Uniform vs nonuniform 3. Laminar vs turbulent flow (vertical velocity profile) 4. Sub-critical i i l fl 4 S b i i l vs super-critical flow Specific energy p - critical depth - froude number 4. Flow in Actual Channels 5 Estimating flow velocity, depth: Manning s equation 5. velocity Manning’s 6. Beyond Manning’s Equation: Backwater programs (HEC-RAS) 7. Hydrodynamic modeling: 1-d, 2-d, 3-d: unsteady flow models Open Channel Flow: how do we do this in real life? 1. Not surprisingly, we have computer programs that help us do this. There are a companies number available from different software companies, but the most common one is produced by the US Army COE in the Davis HEC center. 2. It is called HEC-RAS (for River Analysis System). It used to be called HEC-2. 3. It is often used in conjunction with HEC-HMS (old HEC-1): j ( ) 1. We first use HEC-HMS to tell us what the flow RATE will be at a given location along a river, in response to a certain rainfall event. 2. Then we use HEC-HMS to tell us how deep and how fast the water will be flowing at our “point of interest” 4. We have to provide the computer program with information about our river channel system (just like we did for our watershed in HEC-HMS). We need to i i hi f i give it enough information to solve M i l Mannings equation: channel area (A), wetted i h l (A) d perimeter (P), slope (S) and roughness (n) and the flow rate (Q): 1. Channel cross-section data: we used surveyed cross section data to tell the P). program what our river looks like at a specific location (A and P) We provide multiple cross-sections along a river reach to characterize changes in the channel shape at various locations. 2 cross-section 2. The model computes channel slope (S) by comparing one cross section with the ones above and below it. 3. We tell the program how “rough” the channel is (with Mannings “n”) 5. Using this data, the program computes the depth and velocity of flow at each XS. Open Channel Flow y p 1. Why is it important? 2. Some definitions 3. Hydraulic processes: “types of flow” 1 Steady vs unsteady 1. 2. Uniform vs nonuniform 3. Laminar vs turbulent flow (vertical velocity profile) 4. Sub-critical i i l fl 4 S b i i l vs super-critical flow Specific energy p - critical depth - froude number 4. Flow in Actual Channels 5 Estimating flow velocity, depth: Manning s equation 5. velocity Manning’s 6. Beyond Manning’s Equation: Backwater programs (HEC-RAS) 7. Hydrodynamic modeling: 1-d, 2-d, 3-d: unsteady flow models