A study of boundary shear stress, flow resistance and momentum transfer in open channels with simple and compound trapezoidal cross section
PhD thesis by Yuen, K. W. H., 1989

Mainly experimental work in a 22m long flume in which smooth trapezoidal channels of various widths were constructed, aimed at obtaining detailed velocity and boundary shear stress data in both sub-critical and super-critical flows.

The side slopes were fixed at 1:1, and the base width of the channel varied to obtain a wide range of breadth/depth ratios. The brink depth was monitored so that the end depth ration, h b/h c, could be investigated over a wide range of Froude numbers. The same flume was later used to investigate sub-critical flow in one particular trapezoidal compound channel, over a wide range of relative depths. Finally, one series of experiments was conducted to investigate the meaning and significance of ‘critical flow’ in a compound channel. 


The characteristics of fully developed turbulent flow in smooth open channels of simple trapezoidal cross-section have been examined experimentally in the range 0.5 < Fr < 3.5, 1.9 x 104 < Re < 6.2 x 105 and 0.3 < 2b/H < 15.0. Subcritical flow in a compound trapezoidal channel has also been studied for relative depths between 0.05 < Dr < 0.5. The effect of secondary flows and the interaction between the main channel and the flood plain flows have been shown to influence the boundary shear stress and velocity distributions significantly.

For simple channels, the boundary shear stress distributions have been correlated with the geometry parameters 2b/H or Pb/Pw, and empirically derived equations are presented giving the percentage of the total shear force carried by the wall. Ancillary equations are also presented giving the correlation between the geometry parameters and the mean and maximum shear stresses. Attention is also focussed on the effect of the hydraulic parameters on flow resistance. A comparison is made between the data and traditional formulations for smooth pipes and rectangular channels. The Froude number effect is also examined and found to be important.

For compound channels, the transfer of momentum between the main channel and the flood plain has been studied in detail. Boundary shear force results have been used to calculate the apparent shear forces on vertical, horizontal and inclined interfaces. An empirically derived equation relating the geometry parameters and the boundary shear force on the flood plain bed and walls is presented. In order to quantify the momentum transfer within the whole section, the Navier-Stokes equation for steady uniform flow is used, and an analytical solution to the depth averaged form of the equation compared with the experimental results. A comparison of the depth-averaged values of flow resistance with those values obtained from a one-dimensional formulation is also made, and distinct differences noted. Improvement may be made by using the resistance radius in place of the traditional hydraulic radius. Use is made of the apparent shear force results in assessing channel discharge calculation methods which are based on sub-dividing the flow area. Equations are presented giving the main channel discharge for both vertical and horizontal division planes.

The methods for evaluating the critical depth in a compound channel are also reviewed and assessed against experimental data. The free overfall for simple trapezoidal channels has been studied and an analytical relationship obtained between the ratio of brink depth to critical depth and the channel bed slope. Experimental data confirm this relationship.


Two types of channel were used in these experiments. Initially simple trapezoidal channels were used, constructed in such a way that allowed the aspect ratio (2b/h) to be varied from 0.3 to 15. Detailed measurements were made of boundary shear stress distributions, with corresponding velocity distributions only measured for some specific cases. Five series of tests were undertaken at 5 different bed slopes (nominally set close to 1, 4, 9, 16 & 25 (x10^-3), so that the discharges would be in the approximate ratios of 1:2:3:4:5. In effect the bed slopes were 1.000, 3.969, 8.706, 14.52 & 23.37 (x10^-3), as shown in the accompanying Table. This meant that data were obtained for both sub-critical and super-critical flow conditions (0.39 < Fr < 3.59). Later some brink depth measurements were made to check theoretical BDRs (brink depth ratios, hb/hc)

Two further series of experiments were undertaken later in a compound trapezoidal channel of a fixed geometry (2b = 150 mm, h = 75 mm, s = 1.0, B = 225 mm), giving Wr = B/b = 3.0. Measurements of flow parameters U and tb were undertaken at different bed slopes, one fixed at 1.000 (x10^-3) to give sub-critical flow conditions, and the other at slopes between 2.043 – 3.010 (x10^-3) to investigate ‘critical flow’. This meant that experiments were conducted for both sub-critical (Fr ~ 0.63) and super-critical flow (Fr ~ 1.0). Only overbank flow conditions were investigated, since one series from the simple channel experiments complemented these and gave the corresponding inbank flow data.

Tables are shown below that summarise the various results, details of which may be found in the appropriate data file, each with a unique reference number. The individual files are organised like the others in this data base, with a one page Summary files (1 page), Results files (all data, both before and after adjustment) and Data files (raw data).

Data file links

Simple trapezoidal channels

Compound trapezoidal channels

  • data files (raw data)
  • summary files (summary data)
  • results files (all data, both before and after adjustment)


  • Yuen, K.W.H. and Knight, D.W., 1990, Critical flow in a two stage channel, Proc. Int. Conf. on River Flood Hydraulics, (Ed. W.R. White), Wallingford, September, J. Wiley & Sons, Paper G4, 267-276. [C]
  • Knight, D.W., Al-Hamid, A.A.I. andYuen, K.W.H., 1992, Boundary shear in differentially roughened trapezoidal channels, In Hydraulic andEnvironmental Modelling : Estuarine and River Waters (Eds R.A. Falconer, K. Shiono & R.G.S. Matthew), Ashgate Press, 3-14. [C]
  • Knight, D.W., Yuen, K.W.H. and Alhamid, A.A.I., 1994, Boundary shear stress distributions in open channel flow, in Physical Mechanisms of Mixing and Transport in the Environment, (Eds K. Beven, P. Chatwin & J. Millbank), J. Wiley, Chapter 4, 51-87. [B]