Open Channel Flow Ch 10 Young, Handouts
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)
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
Types of Flow Uniform Flow Gradually varying flow Rapidly varying flow May require somewhat different approaches
Examples Hydraulic Jump rapidly varying (link) Uniform channel flow (link) V-notch weir (rapidly varying) (link)
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)
Stationary Reference Frame Moving Reference Frame
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
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
Apply Bernoulli s Equation at Bed or Surface
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
Changes in Specific Energy Increase in specific energy for subcritical flow Depth Increases
Changes in Specific Energy (II) Increase in specific energy for supercritical flow Depth Decreases
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
At lowest possible energy, we have critical flow (Fr=1) If greater energy, one subcritical solution, one supercritical solution Example 10.1, Young
Laboratory Flow over Weir Subcritical Critical Supercritical
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 10.6.3
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
Broad-Crested Weirs The critical depth concept can be used to determine and control flowrates Broad-crested weir Wide, flat, shallower section
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
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)
Sharp Crested Weir Often, flow goes past a sharp obstruction and falls into a lower body of water Quite complex, but can approximate
Pressure in nappe is atmospheric Use Bernoulli eqn
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
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 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 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 Ignore bottom friction over a short distance Ratio of upstream, downstream water levels only corresponding to upstream Froude number Corresponding energy dissipation
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
Tiny Undular Bore Still Water Advancing Bore Giant Hydraulic Jump and Kayak (link)
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
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 http://www.youtube.com/watch?v=ika39l QOIck