Floodplain Hydraulics 1. Uniform flow - Mannings Eqn in a prismatic channel - Q, V, y, A, P, B, S and roughness are all constant 2. Critical flow - Specific Energy Eqn (Froude No.) 3. Non-uniform flow - gradually varied flow (steady flow) - determination of floodplains 4. Unsteady and Non-uniform flow - flood wavesUniform Open Channel Flow Chezy and Mannings Eqn. 1. Must use results from Fluid Mechanics 2. Derivation of these equations requires a force balance (x) 3. Actual forces (F = hydrostatic) are summed across C.V. Fx = Q[V2 V1 ]= 0 [F1 F2 ] wPl +W sin = 0Chezy and Mannings Eqn. 1. Since hydrostatic forces are equal, and sin = S0 w = W sin /Pl = WS0 /Pl 2. Define R = A/P, the hydraulic radius Now w = K V^2/2 for turbulent flows

Chezy and Mannings Eqn. Finally, we can equate the two eqns for shear stress RS0 = K V^2/2 ,solving for V = C(RS0) C = Chezy Coefficient (1768) in Paris Manning was an Irish Eng and 1889 developed his EQN.Uniform Open Channel Flow Mannings Eqn for velocity or peak flow rate v = 1/n R^2/3 xS S.I. units v = 1.4/n x R^2/ x S English units where: n = Mannings roughness coefficient R = hydraulic radius = A/P S = channel slope Q = V A = flow rate (cfs)Energydepth relationship in a rectangular channelFrom Wikipedia, the free encyclopediaInopen channel flow,specific energy(E) is the energy length, or head, relative to the channel bottom. Specific energy is expressed in terms ofkinetic energy, andpotential energy, andinternal energy. TheBernoulli equation, which originates from a control volume analysis, is used to describe specific energy relationships influid dynamics. The form of Bernoullis equation discussed here assumes the flow is incompressible and steady. The three energy components in Bernoulli's equation are elevation,pressureandvelocity. However, since with open channel flow, the water surface is open to theatmosphere, the pressure term between two points has the same value and is therefore ignored. Thus, if the specific energy and the velocity of the flow in the channel are known, the depth of flow can be determined. This relationship can be used to calculate changes in depth upstream or downstream of changes in the channel such as steps, constrictions, or control structures. It is also the fundamental relationship used in theStandard Step Methodto calculate how the depth of a flow changes over a reach from the energy gained or lost due to the slope of the channel.IntroductionWith the pressure term neglected, energy exists in two forms,potentialandkinetic. Assuming all the fluid particles are moving at the same velocity, the general expression for kinetic energy applies (KE=mv2). This general expression can be written in terms of kinetic energy perunit weightof fluid,

(1)Where:m= mass

v= fluid velocity (length/time)

V= volume (length3)

= fluid density (mass/volume)

=specific weightof water (weight/unit volume)

g=accelerationdue togravity(length/time2)

The kinetic energy, in feet, is represented as thevelocity head,

The fluid particles also have potential energy, which is associated with the fluid elevation above an arbitrary datum. For a fluid of weight (g) at a heightyabove the established datum, the potential energy iswy. Thus, the potential energy per unit weight of fluid can be expressed as simply the height above the datum,

Combining the energy terms for kinetic and potential energies along with influences due to pressure and headloss, results in the following equation:

Where:y= the vertical distance from the datum (length)

P= pressure (weight/volume)

hf= headloss due to friction (length)

As the fluid moves downstream, energy is lost due to friction. These losses can be due to channel bed roughness, channel constrictions, and other flow structures. Energy loss due to friction is neglected in this analysis.Equation 4 evaluates the flow at two locations: point 1 (upstream) and point 2 (downstream). As mentioned previously, the pressure at locations 1 and 2 both equalatmospheric pressurein open-channel flow, therefore the pressure terms cancel out. Headloss due to friction is also neglected when determining specific energy; therefore this term disappears as well. After these cancelations, the equation becomes,

and the total specific energy at any point in the system is,

Volumetric dischargeTo evaluate the kinetic-energy term, the fluid velocity is needed. The volumetric discharge,Qis typically used in open channel flow calculations. For rectangular channels, the unit discharge is also used, and many alternative formulas for rectangular channels use this term instead ofvorQ. In US customary units,Qis in ft3/sec. andqis in ft2/sec.

Where:q= unit discharge (length2/time)

Q= volumetric discharge (length3/time)

b= base width of rectangular channel (length)

Equation 6 can then be rewritten for rectangular channels as,

The Ey diagram[edit]For a given discharge, the specific energy can be calculated for various flow depths and plotted on an Ey diagram. A typical Ey diagram is shown below.

Three differentqvalues are plotted on the specific energy diagram above. The unit discharges increase from left to right, meaning thatq1