Flow resistance, discharge capacity and momentum transfer in smooth compound closed ducts
PhD thesis by Lai, C.J., 1986

Mainly experimental work in a small wind tunnel with rectangular compound section and variable ‘floodplain’ widths, aimed at obtaining velocity and boundary shear stress data, using air as the medium. Contains some very high quality data on ducts of varying sizes, as may be seen in the ‘Pictures’ file. Also a considerable of time was spent on numerical work, solving Poisson’s equation for laminar flow in similar shaped ducts. Interesting comparisons are made between flow parameters (velocity distributions, kinetic energy correction factors, etc.) between turbulent (experimental) and laminar (analytical) flow results.


The characteristics of laminar and turbulent flow in smooth compound ducts with rectangular main channels are examined by numerical and experimental studies. Methods for estimating the overall friction factors and discharge capacities of compound ducts or channels are assessed.

The numerical model used for laminar flow simulation is based on a finite difference formulation of the Poisson equation and is solved by an over-relaxation factor iteration scheme. A series of "numerical experiments" were performed over a wide range of symmetric and asymmetric compound duct geometries in the range of relative depth: 0.04 to 0.75, relative width: 2.0 to 5.0 and main channel aspect ratio: 0.2 to 5.0. The turbulent flow experiments were carried out in a 17 metres long T-shaped or cross-shaped 480mm x 300mm air flow duct over a range of Reynolds numbers between 104 -105.

Empirical functions for certain hydraulic parameters are derived. Particular attention is paid to the percentages of the total shear force which act on, and the overall discharge which occurs in, the main channel. Some consideration is also given to the friction factors in the main channel and the floodplain, the apparent shear stresses on various internal interfaces, the kinetic energy and momentum correction factors and flow structures.

The results show that the relative depth and the aspect ratio of the main channel are the most important geometric parameters. A relative depth value of 0.3 is suggested as a suitable division between the different hydraulic conditions which occur at high and low stage. The variation of certain hydraulic parameters with relative depth in laminar and turbulent flow are found to be very similar at high stages but less similar at low stages, due to the strong lateral shear layers that develop. The momentum transfer is the strongest at a relative depth of around 0.1. The results will be useful in verifying numerical models.


  • Knight, D.W. and Lai, C.J., 1985, Turbulent flow in compound channels and ducts, Proc. 2nd Int. Symposium on Refined Flow Modelling and Turbulence Measurements, Iowa, USA, Sept., Hemisphere Publishing Co., I21-1 to I21-10. [C]
  • Knight, D.W. and Patel, H.S., 1985, Boundary shear stress distributions in rectangular duct flow, Proc. 2nd Int. Symposium on Refined Flow Modelling and Turbulence Measurements, Iowa, USA, Sept., Hemisphere Publishing Co., I22-1 to I22-10. [C]
  • Lai, C.J. and Knight, D.W., 1988, Distributions of streamwise velocity and boundary shear stress in compound ducts, Proc. 3rd Int. Symposium on Refined Flow Modelling and Turbulence Measurements, Tokyo, Japan, July, 527-536. [C]