Case Study

ESRU Energy Systems Research Unit

University of Strathclyde


Resource: Velocity Distributions

    Velocity Profile    Model     Effects of Roughness    Flow Characteristics     Tool     References
von Karman BL Calculation

Modelling the Flow characteristics of a channel

This method above is implemented in a Matlab script, with input being provided in the form of a coloured bitmap image constructed using Autocad. The bitmap is of a cross section of interest, and is created by using the mapping technique described here. It is then coloured using a specific key so as areas of differing bottom roughness are distinguishable.

The overall channel Manning number and velocity is input along with various terms to aid the program in finding points of inflection. The program runs under the assumption that the velocity at a given point is influenced by that points proximity to the wall: the interaction between the fluid at one point and that at another is not modelled.

This drastically simplifies the calculation and has a profound effect on calculation time over more complete finite difference methods (the disadvantage is that this is another assumption to add to a growing list of other ad hoc assumptions made during Cole’s derivation).

The channel area is used (along with an assumption of rectilinear flow) to calculate a bulk flow rate, and the program then runs and attempts to match a velocity distribution by Cole’s with the Bernoulli distribution (velocity, not probability) by Manning.

The program uses values of dx and dy to discretise the geometry of the channel section, and then calculates a velocity profile in the vertical and horizontal directions at each station based on the slope of the element. The profile is first generated for the overall channel mannings number, and the results of this are then used as the freestream velocities for the caclulations which include roughness effects. In all, the boundary layer calculation module is called three times:

The output is a computed value of velocity at every point in the channel in the channels axial direction.




The Velocity Distribution tool can be accessed by clicking on the tool icon.

The tool consists of Matlab Programme and instructions are contained within the file.

  1. Inputs: coloured (16 Windows Cols) bitmap .bmp file; dx, dy; tolerance for finding turning pts.; Manning number; Slope; bulk flow velocity
  2. Outputs: velocity distribution

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von Karman BL Calculation

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