The first impression of the studies in this paper is that the results of tests in the high-speed flume present errors of an order unhelpful for calibrating a flow measuring device. The results of the Thames Water Utilities (TWU) prototype stick testing using the 200 mm diameter stick seem to be more favourable.
From the tests I conducted in 1996 in the 100 mm conduit model, I feel those results are equally satisfactory if not better, despite the concern about the repeatability of the correlation of the gap-meter readings of flow and the corresponding depths of flow. This can be overcome by arranging to measure the head in the feeder tank with respective depths of flow. When the appropriate corrections for the cross-sectional area occupied by the stick are made, the errors in these experimental results in general reduce to between zero to mostly around 10%.
A further correction is required because the inclined flow-stick is not subjected to the exact velocity profile of the pipe cross-section. It registers the velocities and hence drag forces around the mid-section of the pipe and misses the low velocities near the bottom wall. This registers upwards of 0·65 to 0·75 ratio of the maximum velocity at the centre (K factors of equation (4)), constantly missing the 0·5 to 0·6 ratios near the sill wall. This concerns equation (11) of the theory. An important difference is that the errors in TWU stick tests for the 200 mm pipe are mostly negative which would be exacerbated when the above corrections were incorporated. The 200 mm pipe is more representative of a prototype sewer than the 100 mm pipe.
I am disconcerted by the authors’ approach of substituting drag coefficient denoted by, say, CD, with a coefficient of discharge, Cd, as defined in equation (13). These are two completely different parameters. The former is dependent on the shape of the body and the Reynolds or Froude number; the latter is based merely on a ratio of experimental and theoretical error in results. It is the wrong argument to the plausible end. The Hoerner's Froude number approach to determine the drag coefficient associated with a surface-piercing cylinder in water is an interesting departure. From the Hoerner's chart reproduced in Fig. 9, a drag coefficient, CD, of 0·8 seems to fit some of the test results in the uniform velocity flume. For a few results, CD, down to 0·6 can be deduced. This seems to make a general improvement as well as odd exacerbation. The Froude numbers in these tests are mostly less than 4 and, particularly the Froude numbers less than 1 in conjunction with the parameter h/d, are difficult to reliably correlate to Fig. 9. Moreover, I presume that in general the Froude numbers above 1 and the corresponding velocities are higher than realistic velocities found in sewers. I suppose the values of Cd in Fig. 10 are deduced from equation (13).
Authors’ reply
The authors wish to thank Ananda Moonasingha, their former student, for his contribution to the discussion. He spent some time working on the flow-stick studies at Liverpool for his MSc(Eng) dissertation in 1996. His various points will be addressed in the following paragraphs.
Firstly, the usefulness of the high-speed (unsheared) flow tests is questioned in relation to the calibration of the flow measuring device. This is indeed the case and the results arising were not incorporated in the final phase of the discussion leading to the recommendations for the ‘fitting coefficient’ Cd. The main value of these tests was to observe the behaviour of such flow-stick assemblies under extreme full-scale flow conditions and to evaluate that element of the theoretical modelling focused on the validity of the drag-type hydrodynamic loading imposed on the basis of the cross-flow principle. The positive outcome of these ‘proving trials’ was sufficient to justify the later pipe flow tests. A further benefit of these data was that they could be subject to loose comparison to the earlier work of Hoerner, illustrated in the paper.
Ananda strongly supports the smaller-scale 100 mm pipe tests used in his study, though the flow circuit did exhibit some shortcomings. Nevertheless, valuable data were collected and some of his results were presented in Fig. 8. The drawback was largely one of scale, principally in respect of measurement accuracies but to a lesser extent in respect of Reynolds numbers of the flow regimes generated. He also moves on to discuss the blockage effect of the stick and suggests that allowance should be made for this in the velocity computations. In terms of the area projected into the approaching flow, such allowance is made, as might be appreciated from the illustrations of Fig. 3. The suggestion of taking this further by attempting the synthesis from other than the assumed undisturbed approaching flow field would lead to further unjustified complexity in the analytical result. It is fully acknowledged that the theoretical approach adopted is a simplification of reality but is nonetheless a physically justifiable treatment of a highly complex flow problem.
Finally, concern is raised about the interpretation of the parameter Cd. This is first defined as a conventional ‘drag’ coefficient, it being an integral element in the theoretical approach (see equation (1)). Simplifying assumptions in the theoretical development, not least the neglect of wave drag arising from the disturbance of the water surface and assumed cross-sectional velocity profiles in the approaching flow, were outlined in the subsequent derivation leading to equation (11), which enables the flow rate computation. By this point, the value of Cd arising from a calibration based on this equation becomes the required ‘fitting’ coefficient. It should then no longer be interpreted as a drag coefficient. In conventional analysis, the right-hand-side (rhs) of equation (11) excluding the Cd term might be interpreted as the ‘theoretical discharge’, being formed by the known parameters of the problem. In this case a coefficient of discharge, or discharge coefficient (C) would be the multiplier which best converts this theoretical value to the observed flows. It follows, therefore, that the discharge coefficient C is equivalent to (1/Cd)1/2. In the analysis and presentation of results it was convenient to consider the theoretical result as the functional form of the rhs of equation (11) with unknown coefficient Cd defaulting to unity and to compare this with the observed flow rates. It is convenient but coincidental that the drag coefficient on an infinite cylinder in a uniform flow stream at high Reynolds number takes this unit value. The values of the fitting coefficient Cd presented in Fig. 10 arise from the solution of equation (11) using all the measured parameters of the problem.
1. INTRODUCTION
The authors studied a flow-stick for discharge measurement in sewers. Devices for such purposes are widely sought because maintenance and extension of an underdesigned sewer reach depend on this information. One may basically differentiate between permanent and mobile discharge measurement, the latter being of considerable interest with regard to the paper. In the following, two alternative devices are first introduced, and questions relating to the authors’ devices are then posed.
2. MOBILE VENTURI FLAME
The discusser has proposed an alternative method of discharge measurement with the so-called Mobile Venturi Flume (MVF), based on the critical flow principle.12 The device consists of a circular cylinder of diameter d finished at its bottom such as to be positioned in a circular sewer upstream from a manhole. The optimum ratio of device diameter d to sewer diameter D is 0·25 to 0·35. For a smaller ratio the backwater effect is too small to produce critical flow, whereas the discharge capacity is too small for larger-diameter ratio. The device was extensively tested in the laboratory and also inserted in a prototype sewer. For a combined sewer, one may recommend only a limited time usage, typically smaller than one day, because of the danger of the sewer clogging due mainly to paper, cloth and small pieces of wood. Compared to the authors’ device, the MVF has some significant features, namely
robustness
simple reading of stagnation depth H
ease in mounting into the sewer
principle of critical flow with Q ∼ H5/2
independence of sewer slope up to about 3%
accuracy ±5% in lab and ±10% in prototype (estimated).
The disadvantages of MVF are: mainly poorer clogging characteristics than the flow-stick; and the fact that a separate device is required for each sewer diameter range—that is, higher costs for a set of flumes. For 0·25 m < D < 1·50 m, a minimum of five MVFs would be required.
3. HINGED FLAP GATE
The discusser also recently investigated the Hinged Flap Gate (HFG) that bears some similarity to the authors’ flow-stick.13 An HFG is used in storage sewers to control the upstream water level. For discharges up to the design discharge, the surface elevation may be kept constant with a hinged gate that is extended by a counterweight not attached perpendicularly to the gate. This device may be considered a two-dimensional abstraction of the flow-stick, except that the downstream flow is supercritical.
The optimum design is much related to the gate stability. The stability was poor either for very small angles θ because minute discharge or turbulence variations induce large oscillations, or for large angles θ > 45° because of the surfing effect. A rational approach for both optimum arrangement and discharge capacity are provided in Reference 13.
4. AUTHORS’ DEVICE
The authors made a detailed hydraulic study of their flow-stick, yet without taking account of the relevant literature. They also did not specify the optimum stick weight nor its geometry relative to the sewer diameter. How would the stick be placed in the manhole? What is the fixation and how does a sensitive meter behave in typical sewer conditions? Are the authors aware of normally handmade manhole transition sections (U-shaped), whose cross-sectional shape may significantly deviate from the assumption of an exact U? The authors have assumed flow conditions around their stick close to uniform flow. What is the performance for transitional flow both from sub- to supercritical, and vice versa? What is the prototype behaviour in combined sewers?
Authors’ reply
The authors wish to thank Dr Hager for his comments and for advising of his own very recent work on related matters. His papers arising were probably in the review/publication process at the same time as the present contribution.
The Mobile Venturi Flume (MVF) outlined by Dr Hager appears to be a promising alternative to the conventional ultrasonic ‘wedge’ or ‘mouse’ transducers which have been extensively used, in the UK at least, for short-term flow surveys over the past decade or so. Being inserted on the sewer invert, these devices also suffer occasionally from the ragging problem, which apparently afflicts the MVF also.
The Hinged Flap Gate (HFG), described by Dr Hager in respect of its application, within sewer, as an upstream water level control device, also has potential for flow rate estimation. The authors make reference to their own work in the Introduction section of the paper, citing Reference 2 which is now available in the technical literature.14 Unfortunately, by oversight, this latest reference was not substituted for Reference 2 in the final version of the paper. This work on flap valves was an extension of earlier work focused on the upstream surcharge implications.15
The authors would concur that performance of devices such as the HFG (or flow-stick) is dependent upon the range of angular movement induced by the flow. The authors also experienced 'stability/accuracy’ problems at very low angles or at high angles when surfing effects were experienced. Addressing a later query by Dr Hager, in the case of both the HFG and the flow-stick, ‘optimal’ design can be achieved by careful choice of the device's weight to ensure suitable angular movements over the range of flows to be experienced. For the flow-stick, a specific procedure has been developed,7 but with space limitations it was not possible to include this in the paper.
Turning attention now to Dr Hager's further comments, firstly, it should be clarified that the flow-stick (and HFG) monitoring systems presented are intended for long-term (permanent) monitoring of the sewer flows, rather than the ‘mobile’ discharge measurement which his comment implies.
The context of the work is laid out in the Introduction section of the paper, but the following additional comments may be helpful. The Research and Development section at Thames Water Utilities (TWU) first conceived the use of flap gates for monitoring of combined sewer overflow (CSO) and storm sewer overflow (SSO) discharges. In a joint venture with Simon Hartley Ltd, a leading UK manufacturer of high-quality precision-engineered equipment for the water industry, they developed the Total Event Monitoring System (TEMS). This aims to ‘provide reliable, low-cost, local or remote management and monitoring of combined sewer overflows, emergency overflows, or other key discharge points, to comply with international environmental regulations.16 The Flap Valve Monitor was marketed first and the Flowstick followed, for application where outfalls require no flap gate provision. Initially, the system provided only qualitative information, the angular sensor (accurate to ±1°) indicating time, duration, scale and, in the case of the flow-stick, the direction of the discharge so identifying tailwater intrusion. The laboratory studies described in the paper, and in Reference 14 for the HFG, enable the quantification of discharge.
TWU has completed extended and successful field trials of the flow-stick, paying special attention to surface coatings (including the ‘nylatron’ tested in the laboratory) to address the fat/ grease deposition and ragging issue. The flow-stick is suspended at the pipe soffit from a metal band forming a ring-clamp, a similar fixing to that used for conventional invert-positioned ultrasonic ‘wedge’ flow transducers. Ideally, this should be placed at a reasonable distance upstream from the outfall or the access manhole to avoid flow disturbance or drawdown effects. It would not be recommended that the flow-stick be positioned in the manhole itself because of the potential adverse effects on flow of sectional discontinuities arising from the benching transitions.
While all laboratory tests, and most intended applications, are to pipes of circular section, the paper provides the basis for application of the methodology developed to non-circular flow sections. There is no assumption that the flow at the measuring section is uniform, though this is advisable, so long as the velocity field in the longitudinal direction does not vary significantly over the reach contacted by the inclined stick. As might be clear from Fig. 3 and the Appendix, cross-sectional velocity profiles are taken to follow the normal logarithmic law from the wall boundaries.
In the paper it is suggested that the blockage created by the stick in the pipe section should be minimised (by choice of stick diameter) to reduce localised disturbance to the flow profile. As a consequence, it is not anticipated that the stick will be subject to local transitions from sub- to supercritical flow or vice versa (i.e. at the location of either a hydraulic drop or a hydraulic jump). The phase 1 laboratory studies subjected 300 mm and 900 mm prototype stick assemblies to flow velocities up to 3 m/s over a full range of water depths, so spanning a range of sub- and supercritical flows. No notable transitional effects were apparent in the prediction errors (or Cd) arising.
Finally, the operational performance of both the stick/hinge mechanism (together with its fixing) and the angular transducer (with associated logger systems) in extended deployment within real sewers has been successfully proven. Field-scale flow calibration studies, to supplement the smaller-scale laboratory tests, were in process (by TWU) at the time of writing.
