![]() ![]() upstream and road crestDefault Max Submergence = 0.95 (95%) (see next slide)After max submergence reached, program reverts to energy equation for solution. High Flow - Weir FlowQ = Total flow over the weirC = Coefficient of discharge for weir flow (~2.5 to 3.1 for free flow)L = Effective length of the weirH = Difference between energy elev. High Flow Bridge ModelingWhen bridge deck is a small obstruction to the flow and not acting like a pressurized orifice, use energy method.When overtopped and tailwater is not submerging flow, use pressure/weir method.When overtopped and highly submerged, use energy method. Low Flow Bridge ModelingClass A Low Flow - SummaryEnergy & Momentum equations are appropriate for most bridgesYarnell should only be used when piers are the major obstacles to flowYarnell cannot be used when there are no piersConservative approach is to select all methods and use highest energy loss ![]() Low Flow Bridge ModelingClass A Low Flow - WSPROFederal Highway Administrations method of analyzing bridgesUses energy equation in an iterative procedure Low Flow Bridge ModelingYarnells Pier Coefficient, KSemi-circular nose and tail0.90Twin-cylinder piers with connecting diaphragm 0.95Twin-cylinder piers without diaphragm 1.0590 degree triangular nose and tail1.05Square nose and tail1.25Ten pile trestle bent2.50 Low Flow Bridge ModelingClass A Low Flow - Yarnell EquationBased on 2,600 lab experiments on different pier shapesRequires entering pier shape coefficient, KShould only be used where majority of losses are due to piers. Low Flow Bridge ModelingCD Coefficients for PiersCircular Pier1.20Elongated piers with semi circular ends 1.33Elliptical piers with 2:1 length to width0.60Elliptical piers with 4:1 length to width0.32Elliptical piers with 8:1 length to width0.29Square nose piers2.00Triangular nose with 30 degree angle1.00Triangular nose with 60 degree angle1.39Triangular nose with 90 degree angle1.60Triangular nose with 120 degree angle1.72 Low Flow Bridge ModelingClass A Low Flow - Momentum MethodFriction losses are external skin friction = wetted perimeter times length times shear stress.Requires entering coefficient of drag for piers, CDCheck Options menu under Bridge & Culvert Data window for momentum equation options. ![]() Low Flow Bridge ModelingClass A Low Flow - Energy MethodFriction losses are computed as length times average friction slope.Energy losses are empirical coefficient times change in velocity head (expansion and contraction losses).Does not account for pier drag forces. ![]() Low Flow Bridge HydraulicsAppropriate MethodsBridge piers are small obstruction to flow, friction losses predominate - Energy, Momentum, or WSPROPier and friction losses predominate - MomentumFlow passes through critical depth in vicinity of bridge - Energy or MomentumPier losses are dominant - YarnellSupercritical flow without piers - Energy or MomentumSupercritical flow with piers - Momentum Subcritical flow only.Yarnell - empirical formula developed to model effects of bridge piers. Developed for bridges that constrict wide floodplains with heavily vegetated overbank areas. Low Flow Bridge Hydraulics4 methods of modelingEnergy - physically based, accounts for friction losses and geometry changes through bridge, as well as losses due to flow transition & turbulence.Momentum - physically based, accounts for friction losses and geometry changes through bridge.FHWA WSPRO - energy based as well as some empirical attributes. Low Flow Bridge Modeling3 Types of FlowClass A Low Flow - SubcriticalClass B Low Flow - Passes through critical depthClass C Low Flow - Supercritical 2 Types of Flow BridgesLow Flow - Flow where the water surface does not reach the low beamHigh Flow - Flow where the water surface reaches the deck or higherThere are sub-types for both low and high flowOften both types of flow occur in single simulation with different profiles ![]()
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