Open Channel Flow. Ch 10 Young, Handouts

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1 Open Channel Flow Ch 10 Young, Handouts

2 Introduction Many Civil & Environmental engineering flows have a free surface open to the atmosphere Rivers, streams and reservoirs Flow in partially filled pipes Storm surge and tides Pollutant transport Wetland transport Floods Gravity is the major driving force Bottom friction is usually the major dissipative force (and sometimes internal turbulence)

3 Topics Speed of Small Disturbances and Froude Number Specific Energy for Open Channels Weirs and Gates Hydraulic Jump Manning s Equation Uniform Flow Channel Design Gradually Varying Flow

4 Types of Flow Uniform Flow Gradually varying flow Rapidly varying flow May require somewhat different approaches

5 Examples Hydraulic Jump rapidly varying (link) Uniform channel flow (link) V-notch weir (rapidly varying) (link)

6 Speed of Small Disturbances for Open Channel Flow Consider a small disturbance in a flow with a free surface Hydrostatic pressure Atmospheric pressure at free surface Mass and momentum conservation over a control volume Long waves assumed (like shallow water waves)

7 Stationary Reference Frame Moving Reference Frame

8 Froude Number Most important parameter to determine overall flow characteristics Fr<1 Subcritical flow Fr = 1 Critical flow Fr > 1 Supercritical flow Similar to ratio of momentum to gravitational forces Depending on Froude number, information may propagate either upstream or downstream, with entirely different behavior

9 Slowly moving current (Fr<1, subcritical) Disturbances propagate both upstream and downstream Fast moving current (Fr>1, supercritical) Disturbances try to propagate both upstream and downstream but current is too strong Disturbances only propagate downstream Analogous situation for a moving object in still water Fr<1 has disturbances forward and back of object Fr>1 only has disturbances back of object

10 Apply Bernoulli s Equation at Bed or Surface

11 Specific Energy Useful to look at total energy above bed per unit weight (units length) Simplifies considerably Bernoulli equation Energy increases if dissipation is less than energy added by elevation change Energy decreases if dissipation is greater than energy added by elevation change For constant flow, usually two different water depths that can carry the same flow with the same energy Minimum energy below which it is impossible to transport a given quantity of flow

12 Changes in Specific Energy Increase in specific energy for subcritical flow Depth Increases

13 Changes in Specific Energy (II) Increase in specific energy for supercritical flow Depth Decreases

14 Changes in Flow Rate q Increase in flow rate q (e.g. from change in channel width) for supercritical flow Specific Energy is same Depth Increases

15 At lowest possible energy, we have critical flow (Fr=1) If greater energy, one subcritical solution, one supercritical solution Example 10.1, Young

16 Laboratory Flow over Weir Subcritical Critical Supercritical

17 More Specific Energy Examples Water flowing down slope to lower elevation Water flowing over bump and down slope Concept of Hydraulic control, weir Jump to

18 Specific Energy Summary 1. Your intuition is almost always wrong! 2. Specific Energy changes are governed by Bernoulli s equation adapted for open channel flow 3. You must follow along the curve for a channel of constant cross-section Only exception is for hydraulic jumps 4. When channel width decreases, curve moves right and upwards, and vice versa

19 Broad-Crested Weirs The critical depth concept can be used to determine and control flowrates Broad-crested weir Wide, flat, shallower section

flow Real world apply experimentally-based discharge coefficient If

20 Investigate using Bernoulli, critical depth concept Upstream velocity head often negligible Simple relationship between depth, flow Real world apply experimentally-based discharge coefficient If depths are too great, will not achieve critical flow drowned weir be careful

21 Behavior of C wb with H/P w Coefficient Cp varies with height of weir compared to head height over weir Accounts for upstream velocity head and losses See Eq. (10.29)

22 Sharp Crested Weir Often, flow goes past a sharp obstruction and falls into a lower body of water Quite complex, but can approximate

23 Pressure in nappe is atmospheric Use Bernoulli eqn

24 Results for rectangular, triangular, etc weirs Semi-Empirical Coefficients Fundamental behavior is different for rectangular, triangular (v-notch) weirs For all, need to make sure of scour protection at downstream end

25 Labyrinth Weir Like sharp-crested weir, but maximize the length of crest for more flow

10.6.4 Underflow Gates Sometimes have flow exit from bottom of a weir underflow gates Flow is designed to be supercritical for large heads Will be subcritical for lower head

26 Underflow Gates Sometimes have flow exit from bottom of a weir underflow gates Flow is designed to be supercritical for large heads Will be subcritical for lower head flows: depends on downstream water level Coefficient depends on: Upstream water level Gate opening height Downstream water level Flow does not change quickly with upstream depth

10.6.1 Hydraulic Jump The hydraulic jump is one of the most arresting phenomena in fluid mechanics Rivers, ocean, atmosphere

27 Hydraulic Jump The hydraulic jump is one of the most arresting phenomena in fluid mechanics Rivers, ocean, atmosphere Nonlinear transition from supercritical to subcritical flow (link, link2 ) Strong Energy Dissipator Hydraulic Jump Subcritical Supercritical

Perform momentum balance between inflow and outflow sides of hydraulic jump From this can infer what goes on in middle which is difficult to treat analytically

28 Perform momentum balance between inflow and outflow sides of hydraulic jump From this can infer what goes on in middle which is difficult to treat analytically Ignore bottom friction over a short distance Ratio of upstream, downstream water levels only corresponding to upstream Froude number Corresponding energy dissipation

29 Hydraulic Jump acts as energy dissipator Higher to lower energy Higher to lower velocity Reduces scour downstream because velocities are lower Will scour strongly at hydraulic jump unless bed is armoured in some way Often used in hydraulic structures Very small hydraulic jumps will not break: undular bore for approximately Fr<1.7

30 Tiny Undular Bore Still Water Advancing Bore Giant Hydraulic Jump and Kayak (link)

31 Hydraulic Jump Existence Need certain conditions Upstream supercritical Downstream subcritical Need to be in balance according to results derived here If not in balance Downstream level too small: jump swept downstream Downstream level too deep: jump moves upstream Friction, elevation changes determine where jump is located NOTE: Sometimes existence of jump depends on previous conditions

32 Severn River Tidal Bore (Undular) Very large tides in Severn River Incoming tide creates weak hydraulic jump (undular bore) Very predictable arrival with spring tides QOIck

CE Hydraulics. Andrew Kennedy 168 Fitzpatrick

CE Hydraulics. Andrew Kennedy 168 Fitzpatrick CE 40450 Hydraulics Andrew Kennedy 168 Fitzpatrick Andrew.kennedy@nd.edu Final Exam, 8AM May 7, Will cover entire course 155 Fitzpatrick Around half on material since last midterm Like 1.5 midterms in