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Area-velocity method (direct method)


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5 TOPIC Grounding of statistical research methods of river flow

4.4 Area-velocity method (direct method)

  • Figure 4.14 and Example 4.1
  • Velocity is measured at 0.6 of the depth
  • For the first and last sections
  • For the rest of segment

4.8 indirect method

  • Make use of the relation between the discharge and the flow discharge and the depths at specified locations.
  • Flow measuring structures (weirs, flume…etc)
  • Slope area methods
  • For flow measuring structures the discharge Q is a function of the water-surface elevation measured at specified location
  • Q=f(H)

4.8 indirect method Slope- Area method

  • The Manning equation
  • Where
  • Q = discharge (m3/s)
  • n = Manning’s roughness coefficient (range between 0.01 and 0.75)
  • A = cross-section area (m2)
  • R = the hydraulic radius, equal to the area divided by the wetted perimeter (m)
  • S = the head loss per unit length of the channel, approximated by the channel slope
  • R=A/P
  • P = witted parameter

See Figure 4.21

  • See Figure 4.21
  • Applying energy equation to section 1 and 2
  • Z1+Y1+V12/(2g)= Z2+Y2+V22/(2g)+hl
  • h1 = Z1+Y1
  • h2 = Z2+Y2
  • hl (head losses) = he + hf
  • he = eddy loss
  • hf = frictional losses
  •  h1+ V12/(2g)= h2+ V22/(2g)+ he + hf
  • he = ke|V12/(2g)-V22/(2g)|
  • ke = eddy loss coefficient
  • hf = (h1- h2)+(V12/(2g)- V22/(2g)-he
  •  
  •  

4.8 indirect method Slope- Area method

  • For uniform coefficient
  • L= length of the section
  • hf/L = Sf = energy slope = Q2/k2
  • k = conveyance of the channel = 1/n A R2/3
  • where n is manning roughness coefficient
  • K = (K1K2)0.5 for different cross sections A1 and A2
  • For non-uniform flow
  • an average conveyance is used for hf/L = Sf = energy slope = Q2/k2
  • where previous equation and continuity equation can be used to estimate discharge Q (known value of h, cross-section properties and n)
  • Q=A1V1=A2V2

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