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# Fluvial Hydraulics

Fluvial Hydraulics. Channel Dimensions Velocity Discharge Hydrographs Types of Streamflow Streamflow and Energy. A = (w x d). P w (w + 2d). Channel Dimensions. w = width d = depth P w = wetted perimeter A = X-sec area. w. Hydraulic Radius (R) Defined as R = A/P w

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## Fluvial Hydraulics

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1. FluvialHydraulics • Channel Dimensions • Velocity • Discharge • Hydrographs • Types of Streamflow • Streamflow and Energy

2. A = (w x d) Pw (w + 2d) Channel Dimensions w = width d = depth Pw = wetted perimeter A = X-sec area w Hydraulic Radius (R) Defined as R = A/Pw Approximated w/ R = (w*d)/(2d+w) d Channel Cross-section

3. Velocity • The velocity profile of the section is usually measured at a particular fraction of the depth (h) of x-sec. • For streams with depth < 2.5 feet, the velocity is usually measured at the 60% depth (0.6 method) and this measurement is taken to be the average velocity in the individual section (vi): vi = vi measured @ 0.6depth • For depths > 2.5 feet, then measurements are taken at the 80% and 20% depths and the two measurements are averaged: vi = (vi measured @ 0.8depth + vi measured @ 0.2depth)/2 • Alternatively, velocities can be measured at all three depths and averaged : vi = [vi measured @ 0.6depth + (vi measured @ 0.8depth + vi measured @ 0.2depth)/2]/2 HOp. 5

4. Velocity • Robert Manning (1889) related velocity to depth as well as to the surface slope and bed roughness v = (C/n) R0.667s0.5 v = velocity C = constant  1.49 in English and 1.00 in metric n = hydraulic roughness  turbulence introduced by vegetation, rocks or seds. R = hydraulic radius s = slope or gradient of the channel

5. Discharge (Q) • Equation of Continuity Q = wdv or Q = vA w = width d = depth v = velocity A = cross-sectional area (w x d)

6. Discharge (Q) • Slope-area method using the Manning equation Q = (C/n) (AR0.667s0.5) C = constant  1.49 in English and 1.00 in metric n = hydraulic roughness A = cross sectional area R = hydraulic radius s = slope or gradient of the channel

7. Hydrograph

8. Hydrograph

9. Stormflow Hydrograph

10. Types of Streamflow • Laminar vs. Turbulent • Determination of whether flow is turbulent or laminar • Reynolds Number (Re) Re = (VR)/v V = velocity R = hydraulic radius v = 0.0000121 kinematic viscosity Re <500 = Laminar Flow Re >750 = Turbulent Flow

11. Types of Streamflow • Laminar vs. Turbulent • Determination of whether flow is turbulent or laminar • Froude Number (Fr) Fr = v/(dg)0.5 v = velocity d = depth g = acceleration due to gravity Fr <1 = streaming or subcritical Fr >1 = shooting or supercritical

12. Friction and Streamflow • Darcy-Weisback Frictional Coefficient ( ff ) ff = (gRs)/v2 g = acceleration due to gravity R = hydraulic radius s = slope or gradient of the channel v = velocity

13. Streamflow and Energy • Bed shear stress = entrainment and subsequent transport (movement) • Bed shear stress is exerted by moving water parallel to the bed surface and exerting frictional drag on the particle. • The frictional drag that sets the particles in motion is referred to as tractive force and can be measured by the DuBoys equation: to= yRS to = tractive force (Nm2) y = unit weight of water (9799 Nm-3) R = hydraulic radius S = slope or gradient of the channel when to is high, there is the potential to move large particles when to is low there only the movement of smaller caliber particles

14. Streamflow and Energy • Stream Power W = yRSV W = unit stream power (Wm2) y = unit weight of water (9799Nm-3) R = hydraulic radius S = slope or gradient of the channel V = velocity If more power is being expanded than is needed to move the sediments in the stream then there will be erosion (degradation). If too much sediment is being supplied than the river aggrades.

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