critical submergence depth

71Dam Engineering Vol XIX Issue 2

Critical submergence for horizontal intakes inopen channel flows

Z Ahmad, Associate ProfessorK V Rao, Former Post Graduate StudentM K Mittal, Emeritus FellowDepartment of Civil EngineeringIndian Institute of Technology RoorkeeRoorkee 247667UttarakhandIndia

AbstractAn analytical and experimental study regarding critical submergence for a 90° horizon-tal intake in an open channel flow, is presented in this paper. Based on the potentialflow and critical spherical sink surface theories, an analytical equation for the criticalsubmergence for this type of intake is derived using two different locations of intakefrom the channel bed - one with clearance from the bottom equal to zero and the otherhaving half the intake diameter. Experiments were performed in a concrete flume 10min length, 0.37m wide, and 0.6m deep, using intake pipes with diameters equal to4.25mm, 6.25mm and 10.16mm for collecting data for critical submergence under awide range of flow conditions. Analysis of this data reveals that the critical submer-gence depends on the Froude number, ratio of intake velocity and channel velocity,Reynolds number, and Weber number. However, the effect of the Froude number andthe ratio of intake velocity and channel velocity is more pronounced in comparison tothe other parameters. Based on the statistical analysis, predictors for critical submer-gence for bottom clearance equal to zero, and half of the diameter, are proposed andvalidated with the unused data. The proposed predictors produce satisfactory results.However, the analytical equation does not produce satisfactory results due to largeboundary effects. It also does not take into account the effect of viscosity, surface ten-sion, and circulation, in its derivation. The predictors available in the literature whenexamined using these data were found to overestimate the value of critical submer-gence.

IntroductionWater is drawn from water bodies like rivers, lakes, and reservoirs, through intakes for

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its different uses, e.g. irrigation, domestic and industrial supply, and power generation.Intakes are more economical, easier to operate, and draw less sediment, when they arelocated near the water surface. However, if the water depth above an intake is insuffi-cient, strong vortices are formed which may lead to air entrainment. Vortices have beenobserved frequently at many installations such as the Hirfanli Dam in Turkey, theHarspranget Dam in Sweden, and the Kariba Dam in Zambia. Such vortices not onlycause appreciable loss in the efficiency of hydraulic machinery, and corrosion in thewater conducting system, but also produce vibrations and noise. Denny [3] has reportedthat a vortex entraining one percent (by volume) of air can cause as much as a 15 per-cent reduction in the efficiency of a centrifugal pump. Air entraining is more severe intropical climates where the water demand is high and the reservoir level is low. Thus, asufficient cover of water is required at the intake, to avoid the formation of these vor-tices.Several empirical relationships and charts are available in literature (Gordon [5],

Reddy & Pickford [17], Swaroop [18], Prosser [16], Jain [9], Jain et al [10], Gulliver etal [6], Odgaard [14], Knauss [12], Gulliver & Arndt [7], ASCE [1], IS 9761 [8], Jiminget al [11], Yildirim & Kocabas [19, 20, 21, 22], and Yildrim [23]) for the prediction ofcritical submergence for intakes. These relationships relate the critical submergence as afunction of the Froude number, Reynolds number, the vertical height of intake, Webernumber, circulation, and other additional parameters. Recently, Durai et al [4] reportedthat the Froude number is the predominant parameter which affects critical submer-gence. For the same Froude number, the values of critical submergence for flat and bellmouth vertical intakes are different. Circulation in flows increases the critical submer-gence for both flat and bell mouth vertical intake. Durai et al [4] also proposed the pre-dictors for the critical submergence for both flat and bell mouth vertical intakes.Yildrim & Kocabas [19, 20, 21, 22] have shown that critical submergence can be pre-dicted by means of potential flow solution for intakes in open channel flow, still waterreservoir, and for rectangular intakes.In most projects, a series of intakes are provided along the river, like the Sakarya

River Valley Irrigation Project in Turkey, in which a forward flow along the riveroccurs near the intakes. Critical submergence in such a case would obviously be differ-ent on account of forward flow in the channel. Yildrim & Kocabas [19] undertook sucha study for the vertical intake using potential theory and dimensional analysis. The pre-sent study, however, deals with the determination of critical submergence for a lateral(90°) horizontal intake from an open channel flow.

Analytical solutionAn analytical equation for the critical submergence can be obtained by considering theflow as potential flow, with pipe intake as point sink, and superposition of point sinkand uniform flow (Yildirim & Kocabas [19]). The Rankine half-body of revolution

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divides the flow into two regions, i.e. the flow area entering, and not entering, theintake. Unless the upper boundary of the Rankine half-body of revolution reaches thefree surface, the surface water just above the centre of the intake cannot enter the intake.At critical condition, water surface level above the intake almost matches the upper

surface of the Rankine half-body of revolution, which is also called the CriticalSpherical Sink Surface (CSSS). Thus, the vertical distance between any point on theupper portion of the Rankine half-body of revolution and the intake level may be takenas approximately equal to the critical submergence.

Assuming the radius of CSSS, r is less than the channel width. The surface area ofCSSS Ac is equal to the surface area of sector OAB, plus the surface area of sectorOBC, as shown in Figure 1.

Surface area of sector OAB = (1)

Surface area of sector OBC = (2)

Here, c = bottom clearance, and di = diameter of intake pipe.

Figure 1. Critical spherical sink surface for a horizontal intake


Thus:

(3)

Assuming critical radial velocity Us entering the CSSS, the intake discharge is:

(4)

Yildirim & Kocabas [19] showed that the critical submergence for an intake, in a for-ward flow for a vertical intake, is equal to the radius of an imaginary spherical sink sur-face, where the radial velocity Us is equal to half of the velocity of the forward flow, i.e.

. Thus:

(5)

Also, the intake discharge:

(6)

Here Ui = velocity in the intake pipe. From Equations 3, 5 and 6, one obtains:

(7)

This can be solved for critical submergence Sc as

(8)

Equation 8 can be used for the calculation of critical submergence for c = 0 andc = di / 2. A close examination of Equation 8 reveals that the critical submergenceincreases with an increase in intake velocity and intake diameter. However, it decreas-es with an increase in velocity in the channel. Thus, the water cover required for avoid-ing the air entrainment in a lateral intake from a channel flow is less than that requiredif the intake is from a stagnant pool of water. Furthermore, critical submergenceincreases with a decrease of bottom clearance, due to an increase of blockage from thebottom boundary.

Dimensional analysisFunctional relationship for the critical submergence can also be obtained by dimensional


analysis of variables affecting it. Various pertinent variables influencing the criticalityat a horizontal intake pipe are di, Ui, U∞, c, width of the channel b, circulation �, massdensity �, dynamic viscosity �, surface tension �, and acceleration due to gravity g. Thefunctional relationship for the critical submergence Sc can be written as:

(9)

Using �, di, and Vi as repeating variables, the dimensional analysis of variables ofEquation 9 yields:

(10)

where F = intake Froude number, R = intake Reynolds number, andW = Weber number.The effect of the width of the channel may be neglected for critical submergence

Sc < b. Previous studies reveal that the critical submergence mainly depends on theFroude number (Gordon [5], Reddy & Pickford [17], Prosser [16], and Gulliver et al[6]). Dagget & Keulgan [2] reported that the Weber number, W, in the range 615 to9000, has no effect on the critical submergence. Based on the experimental study, Jainet al [10] concluded that there is no influence of surface tension on the critical submer-gence when W > 120. Odgaard [14] has shown that in the case of air entraining vorticesin a still water body, for W > 720 and Reynolds number, R, greater than 1.1 x 105, theeffects of surface tension and viscosity can be neglected. Padmanabhan & Hecker [15]proposed that for W > 600 and R > 7.7 x 104, the effects of surface tension and viscositycould be neglected. Based on the experimental results for a bell mouth vertical pipeintake, Jain [9], and Jain et al [10], concluded that the critical submergence increaseswith circulation. The data collected in the present study have been analysed for obtain-ing the relationship for Sc / di.

Experimental workExperiments were performed in the Hydraulics Laboratory of the Department of CivilEngineering, at the Indian Institute of Technology in Roorkee, India, in a concreteflume 10m in length, 0.37m wide and 0.6m deep (Figure 2). Flow straighteners andwave suppressors were provided at the entrance of the flume to align the flow, and toprevent the surface disturbances, respectively. A tailgate was provided at the end, and atank at the inlet of the flume. Water was supplied from an overhead tank through a sup-ply pipe, which was fitted with a valve for the regulation of discharge. A sluice gate wasprovided in the tank to regulate the water level in the flume. Experiments were per-formed with three horizontally oriented intake pipes of diameter di = 4.25mm, 6.25mm,and 10.16mm, provided with bottom clearance c = 0 and di / 2.


The intake was placed on a horizontal plane, in a lateral direction, at a distance of 5mfrom the inlet of the flume, and connected to a pump which discharges water from theintake into the sump. Discharge through the intake was measured via an ultrasonic flowmeter, while the remaining discharge in the downstream of the flume was measured bya weir. A pitot tube was used to measure the velocity, while depth of flow was mea-sured using a pointer gauge of accuracy 0.01mm.

Water was allowed to flow into the flume, and the pump was started to draw thewater from the intake. Flow near the intake was observed for air entrainment. Thewater surface level in the flume near the intake was varied using the sluice gate of theinlet tank, until the critical submergence condition was obtained. Once the air entrain-ment started, intake discharge Qi, flow velocity in the flume U∞, and the depth of flowD, were measured. Figure 3 shows the formation of a typical air entraining vortex atthe intake.For each intake pipe the experiment was conducted for six different intake dis-

charges, Qi, and for each intake discharge the velocity of flow in the flume was variednine times, which gave 54 runs for each intake pipe. A total of 324 runs were conductedfor the three intakes for c = 0 and di / 2.

Figure 2. Experimental setup


Validation of analytical equation for critical submergenceAnalytical Equation 8, for the critical submergence with bottom clearance c = 0 and di / 2,is validated with the data collected in the present study. The calculated values of Sc arecompared with those observed. Figure 4 shows the variation of calculated Sc with thoseobserved for c = 0, and Figure 5 for c = di / 2. Figure 4 and Figure 5 show that theobserved values of Sc do not match the values obtained using an analytical solution.This could be due to (a) effects of bed and side wall boundaries, which are more domi-nant in the case of lateral horizontal intake than vertical intake, in which completeRankin half-body is formed, (b) neglecting viscosity, surface tension, and circulation inderiving the analytical equation, and (c) assuming intake as a point sink. Thus, the ana-lytical equation based on potential theory may not provide the solution for the criticalsubmergence for horizontal intakes in view of the reasons mentioned above.

Figure 3. Formation of air entraining vortex


Figure 4. Validation of analytical equation for critical submergence

Figure 5. Variation of Sc / di with (a) F; (b) Ui / di; (c) R; and (d) W for c = 0


Proposed predictors for the critical submergenceFunctional relationship, i.e. Equation 10 for the critical submergence, is used along withthe data collected in the present study, to propose a predictor for Sc for c = 0 and di / 2.Analysis of data showed that except for F, Ui / U∞, R, and W, other dimensionless para-meters listed in Equation 10 do not affect the values of Sc / di. Variation of Sc / di with F,Ui / U∞, R, andW, for c = 0, is shown in Figure 5, which depicts that Sc / di increases withan increase in F, Ui / U∞, R, and W. However, there is strong correlation between Sc / diand Ui / U∞. Similarly, variation of Sc / di with F, Ui / U∞, R, and W, is also observed forc = di / 2. From the total data collected in the present study, 90 percent is used to pro-pose the predictors, and the remaining 10 percent for their validation.

(a) Predictor for Sc / di for c = 0Dominancy of F, Ui / U∞, R, and W, on Sc / di, is also studied by calculating the partialcorrelation coefficients. The partial correlation coefficients for Sc / di with F, R, W, andUi / U∞, are 0.715, 0.713, 0.678 and 0.949, respectively. Such high values of correlationcoefficient reflect that all parameters affect the critical submergence. Thus, the func-tional relationship may be written as:

(11)

Using 90 percent of the collected data, the values of constants a1, a2, a3, a4, and a5,are obtained using least square technique. These values are a1 = 0.042, a2 = -0.49,a3 = 0, a4 = 0.31, and a5 = 0.90, with R2 = 0.93. Neglecting R and W, the relationshipfor Sc / di with F and Ui / U∞ is:

(12)

with R2 = 0.92, which is close to R2 of Equation 11 and, therefore, Equation 12 is pro-posed as a predictor for Sc / di. With slight adjustment of the parameters, Equation 12may be written as:

(13)

Equation 13 reveals that critical submergence increases with Froude number, butdecreases with increases of velocity in the channel.


(b) Predictor for Sc / di for c = di / 2Partial correlation coefficients for Sc / di, with F, R, W, and Ui / U∞, are 0.873, 0.865,0.879, and 0.967, respectively. Thus, for the functional relationships of Equation 11, thevalues of different parameters a1 = 0.068, a2 = -0.211, a3 = 1.0, a4 = 0, and a5 = 0.206,are obtained using the least square technique. After neglecting R and W, the relationshipfor Sc / di with F and Ui / U∞ is:

(14)

The multiple correlation coefficient of the above equation is 0.935, which is compara-ble to R2 = 0.936, obtained after including R and W. Therefore, Equation 14 is proposedfor the estimation of critical submergence for c = di / 2. However, Equation 14 may besimplified as:

(15)

Equation 15 also reveals that critical submergence increases with Froude number, butdecreases with increases of velocity in the channel.


(c) Validation of proposed predictorsThe proposed relationships for Sc / di, i.e. Equation 13 for c = 0, and Equation 15, arevalidated with the unused data, which is about 10 percent of the total data. The variationof predicted Sc / di, and observed ones for c = 0 and c = di / 2, are shown in Figure 6aand Figure 6b, respectively. It is clear from these figures that the proposed predictorsproduce satisfactory prediction of Sc / di. For c = 0 predictions are within a �20 percenterror of those observed, and for c = di / 2 within�15 percent error of those observed.The adequacy of predictors proposed by Swaroop [18], i.e. Sc / di = 1.5+F, and Reddy

& Pickford [17], i.e. Sc / di = 1+F, has also been checked with the data collected in thepresent study. The values of Sc / di predicted by these two predictors are much greaterthan the observed ones, as shown in Figure 7. This is due to the fact that these predic-tors do not consider the approach velocity, and relate the critical submergence only withthe Froude number of the intake.

Figure 6. Validation of proposed predictors for (a) c = 0, and (b) c = di / 2


Figure 7. Validation of Reddy & Pickford [17] and Swaroop [18] equations for (a) c = 0, and(b) c = di / 2


Table 1. Range of data collected in the present study


Table 2a. Details of data collected in the present study for c = 0


Table 2a (cont). Details of data collected in the present study for c = 0


Table 2b. Details of data collected in the present study for c = di / 2


Table 2b (cont). Details of data collected in the present study for c = di / 2


ConclusionsThe critical submergence for the horizontal intake in an open channel flow is studied inthis paper. Based on the analytical considerations, and the analysis of experimental datacollected in the present study, the following conclusions are drawn:1. Analytical equation derived on the basis of potential flow and CSSS theories for thecritical submergence, for bottom clearance equal to zero, and di / 2, do not produce sat-isfactory results. This could be due to large boundary effects and neglecting viscosity,surface tension, and circulation affects, in the derivation of analytical equation.2. Analysis of data reveals that Sc / di increases with an increase in F, Ui / U∞, R, and W,for both c = 0 and di / 2. However, the effect of F and Ui / U∞ on Sc / di dominates theother parameters.3. The proposed relationships for Sc / di, for c = 0 and di / 2, produce satisfactory predic-tion of Sc / di. For c = 0 prediction is within �20 percent error of the observed values,and for c = di / 2 they are within�15 percent.4. A check on the adequacy of predictors proposed by both Swaroop [18] and Reddy &Pickford [17], using data collected in the present study, shows that the predicted valuesof Sc are much greater than the observed values.

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NotationsAc = surface area of CSSSb = width of the channelc = bottom clearancedi = intake pipe diameterD = depth of flow in the channelF = Froude numberg = acceleration due to gravityQi = intake discharger = radius of CSSSR = Reynolds numberSc = critical submergenceU∞ = velocity of cross flowUi = velocity in the intake pipeUs = radial velocityW = Weber number� = circulation� = mass density of liquid used� = surface tension� = dynamic viscosity

critical submergence depth

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