WaPUG USER NOTE No 27 MODELLING ANCILLARIES: WEIR COEFFICIENTS David Balmforth, MWH 1. SCOPE This user note gives advice on the choice of coefficient for overflo eirs and orifices hen modelling storm seage overflos and bifurcations. 2. BACKGROUND Before modelling any ancillary the user must understand: the hydraulic performance of the prototype; the orkings of the algorithm in the computer model. A combined seer overflo is typically represented as a small on-line tank ith a horizontal base, horizontal eir, and horizontal ater surface. Some softare can also accommodate an overflo as a hole in the all of a manhole chamber. In each case the flo in the chamber is assumed to be subcritical and the ater level regulated by a throttle on the continuation pipe (WaPUG User Note No 2). The discharge over the eir (Q ) is determined by the head above the crest (H ) using the equation: Q = C L gh (1) n here L length of eir (or eirs if more than one) (m) g gravitational acceleration (9.81 m/s 2 ) n index, normally 1.5 C eir coefficient Alternatively the user can specify an orifice overflo, such that the discharge through the orifice overflo (Q,) is determined by the equation: Q = (2) n 0 C 0A 0 gh 0 here A 0 area of orifice (m 2 ) H 0 head across the orifice (m) n index, normally 0.5 C 0 orifice coefficient The user also has the option to specify hether the overspill goes to aste, or to the head of a specified branch. Note 27 WaPUG Page 1 of 11 Version 2 March 2009
A bifurcation may be modelled as a special case of an overflo orifice, but ith the crest level of the overflo placed a small vertical distance above the chamber floor (e.g. 100 mm). 3. TRANSVERSE WEIRS 3.1 Introduction Five different flo cases can occur and it is important to establish hich case is appropriate in each ancillary. Sometimes the flo case ill change during the operation of an overflo and the flo case that occurs during a verification event may be different from that hich occurs in a more extreme event (e.g. a design storm). 3.2 Case 1: Free discharge over a eir Figure 1a Free discharge over a eir The discharge is solely dependent upon the head above the crest, and is calculated by Equation 1. The eir control should be selected and the eir coefficient C, depends on the geometry of the eir crest, and Table 1 gives suitable values. Table 1 Values of C for Case 1 flo Weir crest Sharp edged 0.60 Square crest 0.70 Round crest 0.80 C Note 27 WaPUG Page 2 of 11 Version 2 March 2009
3.3 Case 2: Freely discharging orifice Figure 1b Freely discharging orifice The discharge is unaffected by ater levels in the overflo pipe. The upper surface of the jet springs free from the upper edge of the pipe entry, and is vented to the atmosphere. H 0 is defined as the head above the vertex of the overflo orifice, and Q 0 is calculated from Equation 2. The orifice control should be selected and C 0 given a value of 0.85. 3.4 Case 3: Droned Overflo overflo pipe not specified in the data file Figure 1c Droned overflo ith overflo pipe not included in model In this case H 0 is taken as the head above the vertex of the overflo pipe, but energy losses in the overflo pipe (bends, flap valves etc.) can only be accounted for in the value C 0. In this case the orifice control should be selected and C 0 calculated from: 2 C 0 = (3) K here ΣK is the sum of the loss factors for fittings in the overflo pipe. Note 27 WaPUG Page 3 of 11 Version 2 March 2009
Values of appropriate loss factors may be taken from Table 2 hich is based on energy loss factors for fittings in ater mains. Note that if Equation 3 gives a value in excess of 0.85 then 0.85 should be used. Table 2 Energy loss factors for pipe fittings Fitting K Sharp entry 0.5 Sharp exit 1.0 90 o bend 1.0 Empty silt trap 3.0 Flap valve 3.0 to 6.0 3.5 Case 4: Droned orifice, overflo pipe specified in the data file Figure 1d Droned overflo ith overflo pipe included in model In recent softare the overflo pipe is normally included as a second control pipe. Where an orifice entry is assumed in place of the normal entry losses, the orifice equation 2 has to represent only the energy loss at entry, and C, should be specified as 2.0. In some early softare (e.g. WASSP) H as taken as the head above the vertex until the overflo pipe surcharged. Thereafter the difference as used. The sudden change in H, hen the pipe surcharged could lead to instabilities in computation if the vertex as lo (as in a bifurcation). To overcome such problems overflo pipes ere often oversized. 3.6 Case 5: Weir droned by flo backing up from overflo pipe This flo condition is quite common. Once the overflo operates and flo builds up in the overflo pipe the eir ceases to become the dominant control. The flo is effectively Case 3 or Case 4 and should be treated as such, but ith the invert level of the overflo pipe reset to the eir crest level to give the correct overflo setting. Note 27 WaPUG Page 4 of 11 Version 2 March 2009
3.7 Alloance for velocity of approach Alloance for the velocity energy in flo approaching a transverse eir may be made by multiplying the eir coefficient by a factor F, here F 2 2 1 + 1 2C r = (5) 2 C r 2 H here r = H + P P height of eir crest above the chamber floor Similarly for an orifice overflo: 1 F = (6) 1 2 2 1 C 0 r 2 A 0 here r = A u A u cross sectional area of flo approaching the orifice These corrections should only be used here there is an appreciable velocity of flo directly approaching the overflo. 4. MODELLING SIDE WEIRS 4.1 Introduction With side eirs the main issue that arises is the potential variation in ater level along the length of the eir due to the reduction in flo in the channel. With lo side eirs and here the incoming flo is supercritical there can also be a hydraulic jump in the channel leading to a large and unpredictable change in ater level. Lo side eirs normally have a crest belo the centre line level of the upstream seer, and this flo type occurs hen the energy at inlet exceeds tice the eir height. 2 V1 1 2C1 d + (7) 2g here d 1 = depth at the upstream end of the eir V 1 = velocity at the upstream end of the eir C 1 = height of eir crest at the upstream end of the eir Fraser (Ref 2) identified five possible flo types of side eir flo, as illustrated in Figure 2. Note 27 WaPUG Page 5 of 11 Version 2 March 2009
Type I Flo: Occurs ith lo side eirs in mild sloping seers. A mild sloping seer is defined as a seer here uniform flo is subcritical. Figure 2a Lo side eir The head over the eir decreases along the length of the chamber and ater levels (and hence eir discharge) are governed by conditions at inlet to the chamber, here the depth ill be beteen 0.85 and 0.90 of the critical depth. When this flo type occurs, conditions in the donstream seer have no influence on the eir discharge nor on the level of the hydraulic gradient in the upstream seer. Flo in the chamber is supercritical. Type II Flo: Occurs ith high eirs, hich usually have their crest above the centreline level of the upstream seer. Water levels in the chamber, and the eir discharge, are determined by the throttle at entry to the donstream seer, and the discharge and level of the hydraulic gradient in that seer. In this case the head on the eir increases along the length of the chamber. Flo in the chamber is subcritical. Figure 2b High side eir ith throttle Note 27 WaPUG Page 6 of 11 Version 2 March 2009
Type III Flo: Occurs in mild sloping seers ith lo side eirs fitted ith a throttle at the donstream end of the chamber, or ith lo side eirs here the donstream seer is surcharged. Conditions in the donstream seer influence the eir discharge but do not determine the ater level in the upstream seer. Flo in the chamber is a combination of Type I and II ith a hydraulic jump forming. Figure 2c Lo side eir on steep slope Type IV Flo: Occurs ith lo eirs in steep seers. It is similar to Type I flo but the approaching flo is uniform and d 1 approximates to the depth of uniform flo in the upstream seer. Figure 2d Lo side eir ith throttle, on steep slope Type V Flo: Occurs ith lo side eirs in steep seers here the chamber has a throttle at outlet, or here the donstream seer is surcharged. It is a combination of Types IV and II and is similar in character to Type III. A number of alternative methods exist for analysing side eir flo and calculating eir discharges. Balmforth and Sarginson (Ref 1) have revieed the various methods and explain ho the discharge capacity of side eirs can be calculated. Note 27 WaPUG Page 7 of 11 Version 2 March 2009
4.2 Modelling requirements - High Side Weirs Where the user is confident that the flo in the chamber is subcritical, the folloing approach is recommended. Where there is a significant variation in the head above the crest of a eir, along its length, then an alloance for this should be made in the value of the eir coefficient C. For a particular head at the donstream end of the eir the discharge over the eir should be calculated (Ref 1) or measured in situ. Denoting this head by H, and the corresponding eir discharge Q, these values should be substituted into Equation 1 and the corresponding value of C calculated. Where the flo in the chamber can be supercritical (i.e for lo side eirs). The method belo should be used. 4.3 Modelling requirements - Lo Side Weirs In models it is assumed that the flo in the chamber is governed by the continuation throttle and conditions in the donstream seer. Hoever, ith lo side eirs, ater levels and eir discharges, are governed by conditions in the upstream seer at entry to the chamber. If the actual chamber dimensions and eir coefficients are used directly in the model then the model ill over-predict the eir discharge and the ater levels in the upstream seer, as Figure 3 demonstrates. Figure 3 Model For a particular inflo, the correct eir discharge can be simulated simply by reducing the eir coefficient to give the desired result. Hoever, the ater level in the upstream seer ill be over-predicted and this can affect the discharge capability of the upstream system and flooding may be predicted here it does not occur in practice. Over-prediction of upstream ater levels can be avoided by artificially over-sizing the first seer length immediately donstream of the chamber, and if necessary reducing its gradient to maintain the correct first spill value. For Type I and IV flos the procedure is best summarised as follos: Note 27 WaPUG Page 8 of 11 Version 2 March 2009
(i) using proportional depth-discharge calculations for the upstream and donstream seers, determine the setting of the overflo; (ii) (iii) (iv) (v) (vi) (vii) upsize the donstream seer. An increase to tice the actual diameter is normally sufficient, though both higher and loer multiples have proved necessary at times. adjust the gradient of the oversize pipe to give the correct overflo setting by raising the donstream invert level (the ground level at this point may also have to be raised); for the upstream seer running approximately three-quarters full, calculate the eir discharge and continuation discharge using an established method of calculating side eir flo (Ref 1). Scumboards fitted to the eir reduce the discharge by 10-20%, and this should be alloed for in estimating the eir flo; using proportional depth discharge calculations, determine the depth of flo in the oversize donstream seer at the calculated continuation discharge. Calculate the drop in the level of the hydraulic gradient at the throttle using the softare's orifice equation. Add this drop to the depth in the oversize seer to give the depth at the donstream end of the chamber; the softare typically assumes a horizontal ater level and eir crest in the chamber, so that the donstream depth may no be used to determine the head on the eir and the ater level in the upstream seer. Use the former, together ith the actual eir length and the calculated eir discharge, in the softare's eir equation to obtain an equivalent eir coefficient for use in the model. This may be much smaller than traditional values; revie the calculated ater level in the upstream seer and if it is significantly higher or loer than that hich actually occurs, after the diameter of the oversize donstream seer and adjust the other parameters accordingly. When test running the model, particular attention should be paid to the conditions adjacent to the lo side eir overflo. In particular, the seer immediately donstream of the oversize pipe surcharges to any extent then Type III or V flo conditions ill probably occur in practice. In this case the donstream seer should not be oversized. For Type III and V flo the folloing procedure should be adopted: (i) (ii) (iii) model the donstream seer as built; assume the hydraulic jump forms half ay along the eir that the head along the donstream half of the eir is constant, and that the discharge over the upstream half of the eir is negligible; model the eir as a transverse eir. Use the actual eir length. If there is only one side eir, take the transverse eir coefficient (reduced by 10-20% if a scumboard is fitted), and halve it. If there are to eirs, do not halve the coefficient. With smaller side eir chambers in particular it is possible that the hole chamber becomes droned so that the eir has little effect, and the eir discharge and Note 27 WaPUG Page 9 of 11 Version 2 March 2009
continuation flo are determined by the size of their respective outlets. In this case it is better to model the chamber as a hole-in-manhole overflo, but ith the invert of the overflo orifice set level ith the crest of the actual eir. Note: Adoption of the above procedures ill greatly improve the simulation of the seer system containing a number of lo side eir overflos. During verification, it is permissible to make minor changes to the ancillary data provided they can be justified in the ay the ancillary has been modelled, and not purely as a means of force fitting the data. Care should be taken to identify possible Type III and V flo conditions. This is particularly true hen running a verified model ith design storms here greater surcharging may cause the flo case to change from I to II or IV to V in practice. It may be necessary therefore to amend ancillary data beteen verification and running ith design storms. Time-series rainfall should be in ith the verification data hoever. Often the data used to model lo side eirs appears strange, bearing little resemblance to actual values. This is because the on-line tank model in the softare behaves differently from the physical performance of lo side eirs, and this has to be compensated for hen specifying the ancillary data. 5. OTHER ALLOWANCES 5.1 Alloance for scumboards Where fitted, scumboards tend to reduce the discharge capacity of eirs. They can have little or no effect, or here their supports are eak they can distort and press against the eir shutting off the flo almost completely. In most cases the vertical distance beteen the underside of the scumboard and the floor of the chamber ill be much greater than the horizontal opening beteen the scumboard and the face of the eir. It is therefore the latter that usually determines ho much the flo is restricted. If the horizontal opening is greater than the maximum head on the eir then no alloance for the scumboard is needed. At other times a reduction in C, of 10% to 20% is recommended. Where ragging around scumboard supports is excessive a greater reduction should be made. 5.2 Alloance for screens Screens fitted to the crest of the eirs also tend to reduce the discharge capacity. In this situation it is better to use an equivalent eir length, shorter than the actual eir length rather than adjusting the eir coefficient. L = Actual eir length h b h b + t b here h b is the clear spacing beteen the bars (mm) t b the bar thickness (mm) If the screens are not mechanically raked, a further alloance may be necessary for ragging. For idely spaced bars rags tend to accumulate around the bars, reducing the effective dimension h b. For finer screens, rags ill completely obstruct the openings Note 27 WaPUG Page 10 of 11 Version 2 March 2009
beteen the bars immediately above the eir crest. The eir crest height should therefore be increased to allo for this. 6. REFERENCES 1. Balmforth D J and Sarginson E J; A comparison of methods of analysis of side eir flo, Chartered Municipal Engineer, Vol 105, No 10 pp 273-279, October 1978. 2. Fraser W, The Behaviour of Side Weirs in Prismatic Rectangular Channels, proceedings of the Institution of Civil Engineers, Vol 6, February 1957. AMENDMENTS Ver Description Date 1. First Published August 1993 2. Revision incorporating material from user note 14 March 2009 Note 27 WaPUG Page 11 of 11 Version 2 March 2009