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Centrifugal Decanter (Pieralisi)Logic inverse

Trapezoidal channel: uniform flow

Input data

Flow

Inferior length (b)

Z1

Z2

Slope

Roughness coefficient (n)

Output data

Flow normal depth

Superior width (B)

Velocity

U²/2g

Description

Given the basic characteristics of a trapezoidal channel in uniform flow, calculate:

  • Normal flow depth
  • Flow
  • Roughness coefficient ($$n$$)
  • Slope

Trapezoidal Channel DiagramTrapezoidal Channel Diagram

Calculation Methods

  1. Depth

    • Inputs

      Parameter
      Default Unit
      Description
      Flow ($$Q$$)
      $$m^3/s$$
      Volumetric flow rate
      Inferior width ($$b$$)
      $$m$$
      Base width of the channel
      $$Z1$$
      -
      Left side slope
      $$Z2$$
      -
      Right side slope
      Slope ($$I$$)
      -
      Channel slope
      Roughness coefficient ($$n$$)
      -
      Channel roughness

    • Outputs

      Parameter
      Default Unit
      Description
      Normal flow depth ($$y$$)
      $$m$$
      Computed flow depth
      Superior width ($$B$$)
      $$m$$
      Total width at the top of the channel
      Velocity ($$U$$)
      $$m/s$$
      Average flow velocity
      $$U^2/2g$$
      -
      Energy term per unit mass

  2. Flow

    • Inputs

      Parameter
      Default Unit
      Description
      Depth ($$y$$)
      $$m$$
      Flow depth
      Inferior width ($$b$$)
      $$m$$
      Base width of the channel
      $$Z1$$
      -
      Left side slope
      $$Z2$$
      -
      Right side slope
      Slope ($$I$$)
      -
      Channel slope
      Roughness coefficient ($$n$$)
      -
      Channel roughness

    • Outputs

      Parameter
      Default Unit
      Description
      Flow ($$Q$$)
      $$m^3/s$$
      Computed flow rate
      Superior width ($$B$$)
      $$m$$
      Total width at the top of the channel
      Velocity ($$U$$)
      $$m/s$$
      Average flow velocity
      $$U^2/2g$$
      -
      Energy term per unit mass

  3. Inferior width ($$b$$)

    • Inputs

      Parameter
      Default Unit
      Description
      Depth ($$y$$)
      $$m$$
      Flow depth
      Flow ($$Q$$)
      $$m^3/s$$
      Volumetric flow rate
      $$Z1$$
      -
      Left side slope
      $$Z2$$
      -
      Right side slope
      Slope ($$I$$)
      -
      Channel slope
      Roughness coefficient ($$n$$)
      -
      Channel roughness

    • Outputs

      Parameter
      Default Unit
      Description
      Inferior width ($$b$$)
      $$m$$
      Base width of the channel
      Superior width ($$B$$)
      $$m$$
      Total width at the top of the channel
      Velocity ($$U$$)
      $$m/s$$
      Average flow velocity
      $$U^2/2g$$
      -
      Energy term per unit mass

  4. Roughness coefficient ($$n$$)

    • Inputs

      Parameter
      Default Unit
      Description
      Depth ($$y$$)
      $$m$$
      Flow depth
      Flow ($$Q$$)
      $$m^3/s$$
      Volumetric flow rate
      Inferior width ($$b$$)
      $$m$$
      Base width of the channel
      $$Z1$$
      -
      Left side slope
      $$Z2$$
      -
      Right side slope
      Slope ($$I$$)
      -
      Channel slope

    • Outputs

      Parameter
      Default Unit
      Description
      Roughness coefficient ($$n$$)
      -
      Computed channel roughness
      Superior width ($$B$$)
      $$m$$
      Total width at the top of the channel
      Velocity ($$U$$)
      $$m/s$$
      Average flow velocity
      $$U^2/2g$$
      -
      Energy term per unit mass

  5. Slope ($$I$$)

    • Inputs

      Parameter
      Default Unit
      Description
      Depth ($$y$$)
      $$m$$
      Flow depth
      Flow ($$Q$$)
      $$m^3/s$$
      Volumetric flow rate
      Inferior width ($$b$$)
      $$m$$
      Base width of the channel
      $$Z1$$
      -
      Left side slope
      $$Z2$$
      -
      Right side slope
      Roughness coefficient ($$n$$)
      -
      Channel roughness

    • Outputs

      Parameter
      Default Unit
      Description
      Slope ($$I$$)
      -
      Computed channel slope
      Superior width ($$B$$)
      $$m$$
      Total width at the top of the channel
      Velocity ($$U$$)
      $$m/s$$
      Average flow velocity
      $$U^2/2g$$
      -
      Energy term per unit mass

References

  • SILVESTRE, Paschoal. Hidráulica geral. Rio de Janeiro, LTC, 1979.