Journal of Power and Energy Engineering, 2014, 2, 53-57
Published Online April 2014 in SciRes. http://www.scirp.org/journal/jpee
http://dx.doi.org/10.4236/jpee.2014.24008
How to cite this paper: Dhatrak, A.I. and Tatewar, S.P. (2014) Air Entrainment and Pressure Fields over Stepped Spillway in
Skimming Flow Regime. Journal of Power and Energy Engineering, 2, 53-57. http://dx.doi.org/10.4236/jpee.2014.24008
Air Entrainment and Pressure Fields over
Stepped Spillway in Skimming Flow Regime
Anant I. Dhatrak, Sandip P. Tatewar
Department of Civil Engineering, Government College of Engineering, Amravati, India
Received December 2013
Abstract
This paper deals with some aspects of the air entrainment process along the chute of spillway and
study of pressure fluctuations. The experimental study has been carried out using stepped spill-
way model located in the campus of Government College of Engineering, Amravati (India). It is
observed that air concentration is increasin g with discharge as well as with number of step. Air
concentration is increasing along the length of spillway. It is also observed that the bottom mean
air concentration increases with step height in the upstream reach of stepped spillway, which is
prone to cavitation. The pressure profiles exhibit a wavy pattern down the stepped chute and
pressure on each step increases with ratio of critical depth to step height (yc/h).
Keywords
Stepped Spillway; Air Entrainment; Skimming Flow Regime; Pressure Fluctuations
1. Introduction
Stepped spillways have been used for many centuries. The stepped spillway consists of series of steps provided
from just below the crest to the toe of spillway. The stepped design increases the rate of energy dissipation on
the surface of spillway and there by reduces the size of stilling basin generally provided at the toe of spillway.
The flow over stepped spillway is broadly classified into two types: 1) Nappe flow and 2) Skimming flow. In
case of nappe flow, the flow from each step hits the step below as a falling jet. In case of skimming flow regime,
the water flows down the stepped face as a coherent stream, skimming over the steps and cushioned by the re-
circulating fluid trapped between them. Along the upstream steps, the flow is smooth and no air entrainment
occurs. Downstream the flow is characterized by a large amount of flow aeration. The air entrainment starts
where the boundary layer reaches the outer edge of the free surface and this point is called point of inception.
Downstream of the point of inception, the flow becomes rapidly aerated and presents a typical white surface.
This paper deals with some aspects of the air entrainment process along the chute of spillway and study of pres-
sure fluctuations.
2. Experimental Test
A model of stepped spillway has been constructed in the premises of Government College of Engineering,

A. I. Dhatrak, S. P. Tatewar
54
Amravati (India). The stepped spillway model, 0.59 m wide, 2.46 m high, has 34 steps with step height 0.08 m,
and slope angle equal to 51.34˚. The pressure values have been recorded by means of piezometers connected to
middle of the tread of step numbers 5, 7, 9, 14, 19, 24, 29, and 32. Air concentration is measured by means of air
concentration V-probe. In the model setup, V-probes are placed on the step numbers 9, 16, 23, and 27 for the
measurement of air concentration.
3. Measurement of Air Concentration
The average air concentration (c) is measured for two values of discharge 0.040 m3/s·m and 0.0545 m3/s·m.
Buwa and Ranade [1] have given the details of the V-probe used in experimental setup. The trend of average air
concentration with aerated flow depth (ya) in Figures 1 and 2 which is found to be similar with the trend pre-
sented in the paper of Boes and Hager [2]. Further it shows that air concentration increases with discharge as
well as with number of step. Air concentration increases along the length of spillway.
3.1. Study of Uniform Bottom Air Concentration on Stepped Spillway
Pfister, M., Hager, W. H., and Minor, H. E. [3] investigated the uniform bottom air concentration on stepped
spillway with experimental approach. They suggested Equation (1) for calculation of Cbu,
3*
bu
C0.2685.6910Ffor α50
−
= −×=

(1)
Boes [4] suggested Equation (2) for calculation of Cbu,
()
23* 00
0.75sin 0.31.810sin 8.110for2655
bu
CF
−−
=∝−−×∝−×<∝<
(2)
Figure 1. Air concentration profiles on stepped spillway mod-
el (q = 0.0400 m3/s·m).
Figure 2. Air concentration profiles on stepped spillway mod-
el (q = 0.0545 m3/s·m).

A. I. Dhatrak, S. P. Tatewar
55
where
( )
*
3
sin
s
q
Fgk =× ∝×
( )
cos
s
kh =×∝
where α is downstream slope/chute angle of spillway. Figure 3 compares Cbu calculated from Equations (1) and
(2). Both the equations show the good agreement with observed values of Boes.
3.2. Effect of Step Height on Mean Bottom Air Concentration
The effect of step height on mean bottom air concentration is studied by using Equation (3) [4] for minimum
discharge of 0.109 m3/s·m and maximum discharge of 0.866 m3/s·m.
0.035n c
bm
y
C0.1 10
h
−

= ×


(3)
Figures 4 and 5 show the variation of Cbm with step numbers “n”.
It is observed that there is increase in Cbm with step height for n = 0 and this effect decreases with increase in
value of “n”. Pfister [3] studied mean bottom air concentration with step height, h = 0.093 m. The Authors se-
lected the step heights 0.0775 m, 0.062 m and 0.0465 m for studying the effect of step height on Cbm. Figures 4
and 5 indicate that the mean bottom air concentration increases with step height in the upstream reach of stepped
spillway, which is prone to cavitation. The trend of Cbm variation with step height is same for the minimum and
maximum discharge.
Figure 3. Comparison of uniform bottom air concentration
(Cbu).
Figure 4. Variation of Cbm with step number for q = 0.109
m3/s·m.

A. I. Dhatrak, S. P. Tatewar
56
4. Measurement of Pressure Fluctuations on Stepped Spillway
In case of stepped spillways the flow is highly turbulent and there is an every possibility of development of neg-
ative pressure on some of the steps which lead to cavitations. Therefore, it is necessary to measure pressure on
each step of the stepped spillway. In this model study, the peizometric tubes are fixed on step numbers 5, 7, 9,
14, 19, 24, 29 and 32 and pressure was measured on the centre of horizontal face of steps.
Measurement of Pressure Fluctuations
Figure 6 shows the variation of measured pressure between the parameter p/h and Z/H on stepped spillway
model for different values of yc/h, where p is the pressure head, h is the step height, Z is the vertical height from
crest up to step of pressure measurement, and H is the height of spillway.
Similar pressure profiles had been presented by Matos, J., Sanchez, M., Quintela, A., and Dolz, J., [5] in
skimming flow for a downstream slope of 1V: 0.75H stepped chute. The Figure 7 shows the comparison of
Figure 5. Variation of Cbm with step number for q = 0.866
m3/s·m.
Figure 6. Mean pressure profiles on stepped spillway model.
Figure 7. Comparison of observed mean pressure profile with
calculated values by Jorge Matos method.

A. I. Dhatrak, S. P. Tatewar
57
pressure profiles observed in present study and study conducted by Jorge Matoes. In both the cases, pressure
profiles (p/h) exhibit a wavy pattern down the stepped chute. Further, the pressure on each step increases with
increase in yc/h value. The differences in the value of Z/H for these two profiles are due to different locations of
measurement of pressure and different values of yc/h.
5. Conclusion
It is observed that air concentration increases with discharge as well as with number of step. Air concentration
increases along the length of spillway. It is also observed that the bottom mean air concentration increases with
step height in the upstream reach of stepped spillway, which is prone to cavitation. The pressure profiles exhibit
a wavy pattern down the stepped chute. Further, the pressure on each step increases with increase in yc/h value.
References
[1] Buwa, V.V. and Ranade, V.V. (2005) Characterization of Gas-Liquid Flows in Rectangular Bubble Columns Using
Conductivity Probes. Chemical Engineering Communications, 192, 1129-1150.
http://dx.doi.org/10.1080/009864490522704
[2] Boes, R.M. and Hager, W.H. (2003) Two-Phase Flow Characteristics of Stepped Spillways. Journal of Hydraulic En-
gineering, ASCE, 129, 661-670. http://dx.doi.org/10.1061/(ASCE)0733-9429(2003)129:9(661)
[3] Pfister, M., Hager, W.H. and Minor, H.E. (2006) Bottom Aeration of Stepped Spillways. Journal of Hydraulic Engi-
neering, ASCE , 132, 850-853. http://dx.doi.org/10.1061/(ASCE)0733-9429(2006)132:8(850)
[4] Boes, R.M. (2000) Zweiphasenstrőmung and Energieumsetzung auf Grosskaskaden (Two Phase Flow and Energy Dis-
sipation on Cascades). Ph.D. Thesis, VAW, ETH Zurich. (In German)
[5] Matos, J., Sanchez, M., Quintela, A. and Dolz, J. (1999) Characteristic Depth and Pressure Profiles in Skimming Flow
over Stepped Spillways. Proceeding of the 28th IAHR World Congress, Graz, Session B14, 6 p.