A study of boundary shear stress, flow resistance and the free overfall in open channels with a circular cross section
PhD thesis by Sterling M., 1998

Mainly experimental work in a specialist pipe rig built within a 22 m long flume to simulate flow in circular pipes running part full. Complementary work was undertaken in a small wind tunnel with a circular segment built within it. The 244 mm diameter pipe was studied with various flat rigid beds inserted into the base, to mimic a pipe with different depths of a deposited sediment bed.

The work was aimed at obtaining very detailed velocity and boundary shear stress data in fully developed turbulent flow, for use in drainage and sewerage systems. The flat and curved boundary surface elements make the prediction of these basic parameters problematic in such geometries when secondary flows are present. Attempts were made to simulate the boundary shear stress using the entropy principle. In addition to these studies, measurements were also made of the end depth ratio, h b/h c, for circular pipes running part full, with deposited sediment beds.

Abstract

The characteristics of fully developed turbulent flow in smooth open channels of circular cross section (with and without a flat bed) have been examined experimentally in the range 0.375 < Fr < 1.96, 6.5 x104 < Re < 3.42 x105. A pipe of internal diameter 244mm, mounted in a 22m long tilting flume, was used for all the experiments. The depth of water in the channel was varied to produce cross sectional shapes with relative depths (h+t)/D =0.333, 0.399, 0.500, 0.666, 0.750 and 0.800 (where h and t are the depth of water and bed thickness respectively, both parameters are measured above the invert of the channel. Five different bed levels were investigated, i.e. t/D=0.0, 0.25, 0.332, 0.504 and 0.664. For each depth of water the boundary shear stress was measured using a Preston tube of internal diameter 4.8mm. The Preston tube readings were converted to shear stresses by use of Patel's calibration. In order to check the accuracy, the boundary shear stress data were numerically integrated along the wetted perimeter and compared to the frictional slope value, (i.e. t = pgRSf). The boundary shear stress distributions have been correlated with the geometry parameter Pb/Pw, and were shown to compare favourably with Knight's empirical equation which gives the percentage of total shear force carried by the wall. Ancillary equations are presented giving the correlation between the geometric parameters and the mean and maximum boundary shear stresses. Attention is also focused on the effect of the hydraulic parameters on flow resistance.

The distribution of velocity within the channel has been measured for a number of relative depths by means of a Pitot tube, (external diameter = 3.96mm). The data from the Pitot tube were used to calculate the discharge, and checked against the true value (obtained from a calibrated orifice plate). The velocity data have been used to produce isovels, from which secondary flow patterns have been inferred and the influence of the side walls on the flow has been examined. The use of the side wall correction procedure has been verified for the current cross sectional shape

The characteristics of fully developed turbulent flow in smooth ducts have been examined experimentally in the range 2.9 x l04 < Re < 8.3 x104, using a 9.2m long wind tunnel. The cross sectional shape of the duct was similar to that of the open channel. Bed levels of t/D=0.737, 0.800 and 0.900 were investigated. For each cross sectional shape the boundary shear stresses and point velocities were measured using the Preston and Pitot tube techniques described earlier. In order to fully explore the limits of the wind tunnel, pressure gradient versus discharge curves have been obtained. Such curves allowed the variation of global friction factor with Reynolds number to be investigated. The velocity data were used to determine the discharge, (which was numerically integrated and compared to the orifice plate value), and isovels. Using the isovels, a plane of zero shear was inferred for each of the tests which enable local resistance parameters to be investigated.

In order to check their accuracy, the boundary shear stress data were numerically integrated along the boundary of the channel, and compared to the average value, (i.e. x =R.dP/dx). The boundary shear stress distributions were used to examine the various prediction methods outlined by Lundgren and Johnson. These distributions have also been correlated with the geometry parameter Pb/Pw and compared to Knight's empirical equation.

A method to predict the transverse distribution of boundary shear stress based upon the entropy concept has been developed. The data obtained in the current study and that of Yuen (1989) have been used to test the applicability of the new method.

Publications

  • Knight, D.W. and Sterling, M.S., 2000, Boundary shear in circular pipes running partially full, Journal of Hydraulic Engineering, ASCE, Vol. 126, No. 4, April, 263-275. [J]
  • Sterling, M.S. and Knight, D.W., 2000, Resistance and boundary shear in circular conduits with flat beds running part full, Proc. Instn. of Civil Engineers, Water and Maritime Engineering, London, Vol. 142, Issue 4, Dec., 229-240. [J]
  • Sterling, M.S. and Knight, D.W., 2001, The free overfall as a flow measuring device in a circular channel, Proc. Instn. of Civil Engineers, Water and Maritime Engineering, London, 148, December, Issue 4, 235-243. [J]
  • Sterling, M.S. and Knight, D.W., 2002, An attempt at using the entropy approach to predict the transverse distribution of boundary shear stress in open channel flow, Journal of Stochastic Environmental research and Risk Assessment, Vol. 16, Spinger-Verlag, 127-142. [J]