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Experimental Evaluation of Effective Parameters on Characteristic Curves of 1
Hydraulic Ram-Pumps 2 3
Reza Fatahi-Alkouhi1, Babak Lashkar-Ara
*2 4
1. M.Sc Graduated, Civil Engineering Department, Jundi-Shapur University of Technology, Dezful, Iran 5
2. Corresponding Author and Assistant Professor, Department of Civil Engineering, Jundi-Shapur University of 6
Technology, Dezful, Iran. [email protected] 7
8
Abstract 9
The effects of non-dimensional parameters on the characteristic curves of a ram pump were evaluated 10
in this study using an experimental model. To do so, after providing dependent and independent 11
parameters using dimensional analysis, effect of each independent parameter was examined on the 12
dependent parameter. Experimental observations showed that relative pumping discharge (q/QT), 13
relative wasting discharge (Q/QT) and pump efficiency (η) were depended on length to diameter ratio 14
of drive pipe (L/D) and pressure head ratio (h/hm). Impulse valve parameter (nD/v0) was depended on 15
L/D, h/hm and Reynolds number of flow in drive pipe. Characteristic curves were presented for ram 16
pump used in this study to estimate dependent parameters as function pressure head ratio for various 17
ratios of length to diameter. In addition, characteristic equations of the used ram pump were 18
introduced using nonlinear regression. Evaluation of results showed that the characteristic curves and 19
equations can be designed a ram pump system with high accurate, and this design method can be 20
proposed for any kinds of ram pumps to use in engineering purpose. 21
Keywords: Ram pump, dimensional analysis, characteristic curves, non-linear regression, and impulse 22
valve. 23
24
1. Introduction 25
Water supply in remote sites is often chosen with pump driving energy as limiting factors. Some of 26
these factors such as access road and energy sources have been made to limitations in pump choices. 27
On sites that stream with a considerable gradient are available, water can be piped down a grade to 28
power a hydraulic ram pump that will lift water to the higher location in 24 hours a day. A Hydraulic 29
Ram Pump is a device which feasible solution for the geographic and economic condition without an 30
external energy source, such as electricity or fossil fuels. This system can pump water to the rural and 31
tribal areas, where the construction of water transfer systems cannot be justified economically. The 32
ram pump using water hammer energy and the management of its own energy receives from the water 33
supply head, will enable it to pump the water to a considerable height after a periodic operating cycle. 34
2
1.1. The working cycle of hydraulic ram pump 35
The cycle of ram pump is divided into the three phases: acceleration, pumping and recoil. At the start 36
of acceleration phase, the flow in the drive pipe is at rest. Impulse valve is open and the delivery valve 37
is closed. The flow accelerates under the action of the supply head until the dynamic force this flow 38
exerts on the impulse valve is sufficient to cause it to begin closing. Flow velocity in drive pipe 39
continues to increase and the impulse valve starts to close at a certain critical velocity. At the end of 40
acceleration phase the impulse valve is closed rapidly and water hammer phenomenon is occurred. 41
Pumping now takes place as shock waves induced by water hammer passing up and down the drive 42
pipe at the velocity of pressure wave and the delivery valve is opened in response to each pressure 43
pulse and flow is pumped toward the storage tank. Recoil, the reversal of flow in the drive pipe, occurs 44
at the end of the pumping phase after becoming closed the delivery valve. The suction resulting from 45
the recoil causes the impulse valve to open and the cycle is ready to begin again. Components of a ram 46
pump system are shown in figure 1. 47
Fig1. Layout of hydraulic ram pump system
48
1.2. Review of previous studies 49
The ram pump was invented by Whitehurst in 1797 to supply water to a brewery factory. After the 50
invention of the hydraulic ram pump, there were unsuccessful attempts to provide a rational theory to 51
explain the ram pump performance until the early of twentieth century [1]. The first rational 52
theoretical analysis of the ram pump behavior was presented by O’Brien and Gosline [2]. They 53
assumed four time zones in the ram pump cycle. In [2] pumping phase is occurring when the impulse 54
valve is closed, and the propagation of pressure waves occurs in the drive pipe after water hammer. 55
Krol [3] assumed seven phases in the ram pump cycle and gave a complex analysis for it. Rennie and 56
Bunt [4] investigated the operation of the hydraulic ram pump. They studied various impulse valves 57
and drive pipe diameters experimentally. Schiller and Kahangire [5] by using numerical methods 58
concluded that the exact theories for predicting the performance of ram pumps were complex. They 59
assumed four phases in ram pump cycle and ignored the effect of pressure waves during acceleration 60
due to their complexity. In their model, an increase or a decrease in speed during acceleration, and the 61
3
duration of impulse valve closure are linearly. The output of their model includes the delivered 62
quantity, pump efficiency and cycle time. They concluded that a general empirical formula couldn’t 63
compare the different designs. Basfeld and Muller [6] presented a simplified theory developing from 64
Newton's equations of motion and taking into account loss factors and boundary conditions. The 65
results from their theory were compared with the measurements of Plexiglas’ model of a hydraulic 66
ram pump. In particular, the time dependence of the flow velocity in the drive pipe, the water volume 67
delivered per work cycle and the efficiency were experimentally determined as the functions of 68
various parameters. Tacke [7] carried out some experiments on 12 commercial ram pumps and 69
explained their behavior using a modified version of [2] and the velocity diagram divided into three 70
time zones. Rennie and Bunt [8] presented a graphical approach in order to design ram pumps by 71
using analytical model and experimental validation. Young [9] presented two simple equations to 72
design the ram pump ( BqhH , AqhnL ). These equations contained some empirical factors which 73
depended upon ram size, delivery head, material, wall thickness of the drive pipe and the configuration 74
of the impulse valve. Young [10] studied Wilcox's ram pump and presented a simplified analysis 75
under ideal condition (recoil is zero) for ram pump action. Under this condition, equations (1) to (4) 76
offered to design the ram pump. These equations can be used for designing ram pumps in sizes of 19 77
to 102 mm. 78
2 20nLD qh (1)
2 4.6HD qh (2)
20.7TQ D (3)
110maxL HD (4)
Young [11] introduced optimum design range for non-dimensional parameters that determined 79
analytically under ideal condition by using experimental results of previous researchers. Najm et al. 80
[12] developed a numerical model for the analysis of water hammer pressure waves in the ram pump 81
and the impact of the waves on the ram pump components was examined. Maratos [13] investigated 82
the relationship between quantities delivered and drive pipe diameter and evaluated the change of 83
velocity in time cycle on the velocity-time diagram. Filipan and Virag [1] presented a mathematical 84
model using method of characteristic. In this model, the mathematical modeling of particular 85
4
components such as drive and delivery pipes, supply and storage tanks and set of ram pump explained 86
in detail. Then by using boundary conditions, 11 equations with 11 dependent variables solved by an 87
iterative procedure for each time step of the computational run. The outputs of model presented in the 88
form of pressure and velocity versus time graphs. Suarda and Wirawan [14] examined the effect of air 89
chamber on the ram pump performance. They showed that the efficiency of the ram pump without air 90
chamber was about 1 percent and the efficiency of the ram pump with air chamber was about 20 91
percent. Saito et al [15] evaluated the effects of the air volume in air chamber on the hydrodynamic 92
characteristics and operating conditions of ram pumps. Evaluations were showed that the peak 93
pressures in the valve and air chambers vary depending on the pump head and the peak pressure in the 94
valve chamber and the peak pressure in the air chamber tend to decrease as the air volume in the air 95
chamber increases. Nwosu and Madueme [16] constructed hydraulic ram pump which is used to 96
increase the head of the falling water. The rate of flow of water, from the tank and pumping water into 97
the tank are designed to operate in an optimum manner. A controlled actuator is used In order to 98
maintain the flow rates. The underground tank is made to store rain water and is capable of meeting 99
the water need of the micro hydropower plant for the off rain periods. Sheikh et al. [17] studied the 100
literature available and prepared a structured design methodology for hydraulic ram pump 101
(HYDRAM) which covers design parameters, design procedure along with the mathematical 102
relationship used for the design work. Yang et al. [18] by using experimental evaluation showed that 103
the adding a short cambered diffuser between the elbow and the impulse valve in the ram pump caused 104
to increase the ram pump efficiency to 53 percent. Inthachot et al. [19] added an off-the-shelf clap 105
check valve on the ram pump and increased the efficiency of pump increased over 30 percent. The 106
results of the field observations showed that this ram pump supplied the irrigation of lands for North 107
area of Thailand with efficiency of 44 percent in range of six week. Mbiu et al. [20] highlighted on 108
design development of a durable and locally made hydram using inexpensive and readily available 109
materials. A test rig was fabricated and used to analyze the different parameters of the hydram. 110
Optimizing these parameters ensures that the hydram performance is enhanced and as a result giving 111
the pump a longer life. Experimental and analytical modelling results were generalized in performance 112
5
charts and compared to commercially available types operating characteristics. These results will 113
enable the targeted users to be able to select appropriate sizes for their water pumping needs. 114
1.3. Objectives of study 115
Reviewing in the previous studies about hydraulic ram pumps showed that simultaneous evaluations 116
of all effective parameters on the ram pump performance are not performed. Therefore, the aim of this 117
study is to evaluate the performance of ram pump using the selective effective parameters. To 118
accomplish the objective of this study, several experiments were performed. At first, all effective 119
dimensional parameters on ram pump performance have been identified. Then, numerous experiments 120
have been performed to evaluate the performance of ram pump based on each of the identified 121
effective parameters. The performance results were used to develop characteristic curves that could be 122
used for practical application of ram pump. 123
2. Materials and Methods 124
2.1. Experimental set up 125
Experimental results were used to evaluate effective parameters on ram pump characteristic curves. 126
Thus, by developing an experimental model consists a ram pump set (with 51 mm in diameter) and 127
auxiliary equipment such as pressure control board of delivery head and pressure control board of 128
supply head, the performance of ram pump system was evaluated in research laboratory of Hydraulic 129
and River Engineering of Jundi-Shapur University of Technology. Fig 2 shows a schematic of the 130
experimental model used in this study. 131
Fig 2. Schematic of experimental setup
132
In order to perform experiments using laboratory model, the flow was connected to the system. Then, 133
by opening the control valve of the supply control board, the supply head was adjusted. By adjusting 134
the control board of delivery head in the desired height, the tests were performed. By the automatic 135
opening and closing of impulse valve, and the occurrence of intermittent cycles, a part of input 136
discharge was pumped and the excess of it was removed from the system through impulse valve as 137
wastewater. Then, the quantities of pumping and wasting discharge and frequency of impulse valve 138
were recorded during of each test. The duration of each test was approved for twenty minutes. In each 139
6
scenario, the pump performance was evaluated for delivery heads of 2, 3 and 4 meters versus supply 140
heads of 1 and 1.5 meters. Similarly, the performance of the pump was investigated in delivery heads 141
of 3 and 4 meters versus supply heads of 2 and 2.5 meters. Table 1 shows the governing scenarios in 142
this study. 143
Table1. Condition of Length to diameter ratios of drive pipe in this study 144 145
2.2. Dimensional analysis 146
After recording laboratory values, the analysis of the results was carried out. Hence, applying a 147
dimensional analysis and the π-Buckingham theory, the effective parameters on the ram pump 148
performance were determined. According to Fig 1 and hydraulic flow in this category of pumps, the 149
dependent and independent parameters of the pumping system of the ram pump were listed as the 150
following: 151
The delivery head or pumping head ( h ), supply head of water source system ( H ), characteristics of 152
drive pipe including pipe modules of elasticity ( E ), pipe diameter ( D ) and length of pipe ( L ), 153
characteristics of fluid including density ( ), bulk modules ( K ) and dynamic viscosity of fluid ( ), 154
acceleration due to gravity ( g ), density of the constituent materials of the impulse valve ( m ), friction 155
coefficient of fluid and internal pipe wall ( f ), the total input discharge ( TQ ) and maximum pumping 156
head or delivery head ( mh ) indicating the independent parameters of the hydraulic ram pump systems. 157
On the other hand, the variables such as pumping discharge ( q ), wasting discharge ( Q ), frequency of 158
impulse valve ( n ), the velocity of pressure wave ( C ), the critical velocity required to closing impulse 159
valve ( 0v ) and pump efficiency ( ) indicating the dependent variables. It was assumed that the 160
modulus of elasticity and Bulk modulus only influence on the pressure wave velocity, and the density 161
of the constituent of impulse valve only influence on the critical velocity required to closing impulse 162
valve. On the other hand, the kinematics viscosity of the fluid (υ) was used instead of the values of 163
dynamic viscosity (μ) and fluid density (ρ) in order to reduce the independent variables. Thus, the 164
independent variables were limited to the eleven variables including ( 0,,,,,,,,,, vCgfLDHhhQ mT ), 165
and the dependent variables were limited to ( ,,, nQq ). Finally, the dimensional analysis was 166
7
conducted based on the dependent and independent variables of the hydraulic ram pump system, and 167
the relationship between independent these parameters was indicated as the following. 168
),,,,,( 0
0
01 f
D
L
h
h
C
v
v
gHDv
Q
q
mT (5)
),,,,,( 0
0
02 f
D
L
h
h
C
v
v
gHDv
Q
Q
mT (6)
),,,,,( 0
0
03
0
fD
L
h
h
C
v
v
gHDv
v
nD
m (7)
),,,,,( 0
0
04 f
D
L
h
h
C
v
v
gHDv
m (8)
Where, the relative parameter /0Dv indicates Reynolds number, the relative parameter 169
02 vgH indicates Froude number, and the relative parameter Cv /0 indicates the Mach number. On 170
the other hand, TQq / is relative pumping discharge, TQQ / is relative wasting discharge, 0/ vnD is 171
impulse valve parameter, is pump efficiency, mhh / is pressure head ratio, DL / is length to diameter 172
ratio of drive pipe and f is friction coefficient. 173
2.3. Methodology 174
To present characteristic curves of ram pump, hydraulic features of pumping system such as maximum 175
delivery head and loss values of impulse valve were determined. Losses in the impulse valve can be 176
divided into two parts: (1) loss due to the drag coefficient which was determined using the rule of drag 177
force [3], and (2) loss due to the friction coefficient of impulse valve, measured by water manometer 178
using the slop difference of energy line between the sides of the impulse valve at different lengths of 179
stroke valve. Therefore, attempts were made to provide the empirical equations and graphs to 180
determine the loss coefficients of impulse valve. To measure maximum delivery head of ram pump, 181
after closing control valve that installed on the delivery pipe, and under various laboratory conditions, 182
maximum delivery head with regardless of the loss values in delivery pipe was measured by using 183
pressure gauge. According to the relationship between dependent and independent parameters in 184
equations (5) to (8), and performing experimental evaluation, the effect of independent parameters on 185
the ram pump performance was taken into account. By evaluating the ram pump performance versus 186
the effective parameters on its performance, characteristic curves of ram pump were presented. 187
8
Characteristic equations governing on the research were presented to estimate the relative pumping 188
discharge, relative wasting discharge, parameter of impulse valve and pump efficiency. The SPSS 189
software was used in order to detect the nonlinear relationship between the dependent and independent 190
parameters of the dimensional analysis. After the dimensional analysis and the determination of the 191
general form of characteristic equations in this study, it was necessary to change the process of the 192
independent parameters and their effect on the dependent parameters evaluated. To do this, it was 193
necessary to do a statistical analysis. The error functions used in the present study to evaluate the 194
results of the proposed equations include the mean percentage error (MPE), root mean square error 195
(RMSE), correlation coefficient (R2), standard error estimates (SEE) and modeling efficiency (EF). 196
The gradient of regression line (m) between results and experimental observations was calculated for 197
evaluating the performance of the equations in a way that the intercept elevations of them become 198
zero. It is worth noting if the value m is close to one, the predicted results are close to the experimental 199
observations. 200
3. Results 201
After recording the experimental observations and evaluating ram pump performance versus Reynolds 202
number, Froude number, Mach number, pressure head ratio, length to diameter ratio of drive pipe and 203
friction coefficient of fluid and pipe, effective parameters were selected. To do so, independent 204
parameters were changed under identical laboratory condition then; the changes of dependent 205
parameters were measured. Experimental observations showed that the changes in Reynolds number 206
had not an effect on the quantities of relative pumping and wasting discharge and pump efficiency. On 207
the other hand, the changes in the Reynolds number had an effect on the impulse valve parameter. On 208
the other hand, the changes in parameters of Froude number, Mach number and friction coefficient 209
had not effects on the ram pump performance and can be neglected. Out of other independent 210
parameters of dimensional analysis, the pressure head ratio and length to diameter ratio of drive pipe 211
are notable. The experimental evaluation of these parameters indicated that the changes ratios of 212
length to diameter of drive pipe and pressure head had significant effects on the ram pump 213
performance. Thus, the effects of these parameters cannot be ignored. Table 2 shows the ranges of 214
experimental observations of dependent and effective independent parameters. 215
9
Table2. The ranges of experimental data used in the present study 216 217
As mentioned in section of material and methods, the loss of impulse valve divided into two parts 218
including the loss caused by friction coefficient and the loss of the drag coefficient. Results of loss 219
values measured for an impulse valve with disc diameter of 35 mm and weight of 135 gr were 220
provided in table 3. 221
Table3. Experimental values of impulse valve loss in the various valve strokes 222 223
In order to facilitate the exploitation of the results presented in table 3, two empirical equations based 224
on the experimental observations were presented in the form of relations (9) and (10) to determine 225
friction coefficient and drag coefficient. Note that these relations are corresponding to the 226
specifications of impulse valve used in this study’s ram pump. 227
(9) 08.099.0,0453.0 2
0381.2
0
RMSERD
SK
vd
(10) 83.099.0,7312.0 2
4141.1
0
RMSERD
Sc
v
Out of the other features of the ram pump used in this study, it is necessary to point out to the 228
maximum delivery head. In general, every pump can pump water to a certain height depending on the 229
specifications of the ram pump system. The observations showed that the parameters such as supply 230
head (H) or effect of it on flow velocity in steady state ( 0.5
2v gH ), length to diameter ratio (L/D) 231
and the critical velocity to close impulse valve (v0) have a significant effect on the maximum delivery 232
head. By evaluating the ratio of hm/H versus independent parameters of v/v0 and L/D, a diagram was 233
provided in Fig 3 to determine the maximum delivery head. 234
Fig 3. Determination head ratio of hm/H versus velocity ratio of v/v0 for different ratios of L/D
235
Using the statistical functions, an equation was presented to determine the maximum delivery head for 236
the ram pump designed in this study. The mapping between the independent parameters L/D and v0/v 237
and dependent parameter hm/H was presented as the relation (11): 238
10
0.6440.7292
0
0.247 , 0.97 , 0.53mh L vR RMSE
H D v
(11)
Where v0 is the required velocity to close the impulse valve, and v is flow velocity in a steady state. To 239
determine the critical velocity required for closing the impulse valve, equation (12) was provided 240
based on law of drag force [3]. 241
(12) vd AK
Wgv
0
Where, W is weight of impulse valve, ρ is fluid density and Av is disc area of impulse valve. 242
The aim of this study is presented the characteristic curves of ram pump used in present study. To do 243
so, attempts were made to provide the necessary conditions for estimating the quantities of pumping 244
discharge, wasting discharges, impulse valve parameter and pump efficiency under different 245
conditions. Thus, all experimental observations of the dependent parameters were evaluated in versus 246
the pressure head ratio for different ratios of length to diameter of drive pipe. Figs 4 to 7 show the ram 247
pump characteristic curves to determine the relative pumping discharge, relative wasting discharge, 248
impulse valve parameter and pump efficiency. 249
Fig 4. Characteristic curve to determine the values of q/QT versus h/hm for different ratios of L/D
Fig 5. Characteristic curve to determine the values of q/QT versus h/hm for different ratios of L/D
250
Fig 6. Characteristic curve to determine the values of nD/v0 versus h/hm for different ratios of L/D
251
Fig 7. Characteristic curve to determine the values of η versus h/hm for different ratios of L/D
252
In order to facilitate the use of results in Figs (4) to (7), characteristic equations were presented. 253
According to evaluate the effects of independent parameters on the ram pump performance, it was 254
found that relative pumping discharge, relative wasting discharge and pump efficiency were depended 255
11
on changes of length to diameter ratio of drive pipe and pressure head ratio. On the other hand, 256
impulse valve parameter was depended on Reynolds number and ratios of pressure head and length to 257
diameter of drive pipe. The mappings of proposed equations between the dependent and independent 258
parameters were provided as the following: 259
(13)
2051.4
3971.0
0498.0
1525.0
m
T
h
h
D
L
Q
q
(14)
2561.01039.0
56.0
mT h
h
D
L
Q
Q
(15)
0.330.6791.087
0
0.000096 Rem
nD L h
v D h
(16)
2507.10479.0
4763.02688.0
mh
h
D
L
4. Discussion 260
As mentioned in subsection of methodology, the error functions were used to evaluate the results of 261
study. Statistical analysis is performed on equations (13) to (16) and the brief results of error functions 262
based on the prediction parameters q/QT, Q/QT, nD/v0 and η are provided in table 4. 263
Table4. The brief results of error functions based on the proposed equations 264 265
Statistical analysis of error functions due to the prediction of experimental values by produced 266
equations showed that the equation (13) predicted the relative pumping values by root mean square 267
error of 0.0338. Also, the evaluation of the gradient of regression line between the calculated results 268
and experimental observations showed that this equation predicted relative pumping discharge 2.26 269
percent less than the experimental observation. On the other hand, the proposed equations had root 270
mean square error of 0.0405 and 0.0105 to estimate the relative wasting discharge and impulse valve 271
parameters, respectively. The evaluation of the gradient of regression line between calculated results 272
and experimental observations showed that the equation (14) predicted the relative wasting discharge 273
0.24 percent less than the experimental observations. Similarly, the equation (15) predicted the 274
impulse valve parameter 0.76 percent less than the experimental observations. Equation (16) had a 275
12
RMSE of 0.0357 to predict the ram pump efficiency. Therefore, this equation predicted it 1.55 percent 276
less than the experimental observations. The other error functions in table 4 showed that the proposed 277
equations, called characteristic equations, can be used to design the ram pump in height accuracy. Figs 278
8 to 11 show the gradient of regression line based on the predicted values by the proposed equations 279
versus experimental observations, and the correlation coefficient of these equations. 280
Fig8. The predicted values of q/QT by equation (13) versus experimental observations.
281
Fig9. The predicted values of Q/QT by equation (14) versus experimental observations.
282
Fig10. The predicted values of nD/v0 by equation (15) versus experimental observations
283
Fig11. The predicted values of η by equation (16) versus experimental observations
284
In order to design a pumping system using the results in this study, at first length of drive pipe is 285
determined according to the topographical conditions of water supply and installation position of 286
pump device. In addition, diameter of it is selected by taking into account the discharge capacity of 287
supply source and economic conditions. As well, pressure head ratio is estimated after calculating 288
maximum delivery head (eq. 11) and measuring delivery head. In practice, total input discharge (QT) is 289
depended on capacity of water supply source and it is determined using hydrometric methods or other 290
empirical method. Finally, pumping discharge, wasting discharge, frequency of impulse valve and 291
pump efficiency can be determined using Figs (4) to (7) or equations (13) to (16), respectively. 292
Experimental results showed that, by increasing length of drive pipe, pumping discharge was 293
increased, and wasting discharge and frequency of impulse valve were decreased. On the other hand, 294
increasing length to diameter ratio of drive pipe caused to increase pump efficiency and according Fig 295
13
7, after L/D=500, pump efficiency was decreased. Reducing pump efficiency means that it is better to 296
increase the size of the ram pump. 297
A practical example was presented to explain how to use the proposed method for designing a ram 298
pump system. In this example, source capacity (QT) of pumping system was 27 l/m, supply head and 299
delivery head were 2.5 and 15 m, respectively. In order to evaluate performance of ram pump used in 300
this study, at first a pumping system includes Wilcox ram pump was designed using Young's method 301
(equations (1) to (4)) that was presented to design Wilcox ram pump. The brief results of system 302
designed were showed in table 5. 303
Table5. Steps of design a pumping system using Wilcox's ram and Young's method 304
305
In similar condition, ram pump used in present study was designed using proposed method. To 306
evaluate ram pump used in study, attempt was made to consider some features of ram pump system 307
designed in table 5 such as length and diameter of drive pipe. Therefore, independent variables and 308
features of a ram pump used in study were selected and brief of results were showed in table 6. With 309
having sufficient variables and information about pump set and location of it, pumping system of ram 310
pump used in study was designed and steps of design process were presented in table 7. 311
312
Table6. Selection of ram pump features and independent variables to design a pumping system 313
314
Table7. Steps of design a pumping system using ram pump used in present study and proposed method 315
316
According to the results in tables 5 to 7, under identical geometric and hydrometric condition the ram 317
pump used in study can be pumped about 3196.8 litres during 24 hours to height of 15 m. However, 318
Wilcox ram pump can be pumped about 2030.4 litres during 24 hours to same height. In addition, 319
comparison performance of ram pump used in study and Wilcox ram pump for various delivery head 320
were showed in table 8. Delivery heads were selected between 6 to 20 m with step of 2 m. 321
Table8. Performance comparison between ram pump used in this study and Wilcox's ram pump 322
323
It is worth noting that parameter of efficiency in table 8 was determined using Rankine's efficiency or 324
ηR ( ( ) /q h H QH ) that used to compare the performance of ram pumps in identical situation. Brief 325
14
results in table 8 show that ram pump designed in present study can be operated with high efficiency 326
and it can pump more discharge in compared to Wilcox' ram in low delivery heads. 327
5. Conclusions 328
The results showed that relative pumping discharge (q/QT), relative wasting discharge (Q/QT) and ram 329
pump efficiency (η) are independent from the Reynolds number (Re), Froude number (Fr), Mach 330
number (Ma) and friction coefficient of fluid (f). Consequently, dependent parameters are function of 331
pressure head ratio (h/hm) and length to diameter ratio of the drive pipe (L/D). However, impulse valve 332
parameter or frequency is function of Reynolds number, pressure head ratio and length to diameter 333
ratio of drive pipe. The characteristic curves and the related governing characteristic equations 334
presented in this study could be used for design and performance evaluation of a ram pump system. 335
1.5. Acknowledgments 336
The authors would like to thank the Jundi-Shapur University of Technology for the supports that made 337
the experimental programmer possible, and special thanks to Mr. Ali Bandari who's made the 338
experimental model in the Hydraulic and River Engineering Laboratory. 339
1.6. References 340
[1]. Filipan, V., and Virag, Z. "Mathematical modeling of a hydraulic ram pump system", Strojniški vestnik 341
Journal of Mechanical Engineering., 49, pp. 137-149 (2003). 342
[2]. O'Brien, M. P., and Gosline, J. E. "The Hydraulic Ram, by Morrough P. O'Brien and James E. Gosline", pp. 343
20-117, University of California Press (1933). 344
[3]. Krol, J. "The automatic hydraulic ram", Proceedings of the Institution of Mechanical Engineers, 165, pp. 53-345
73 (1951). 346
[4]. Rennie, L., and Bunet, E. "The automatic hydraulic ram". South African Mechanical Engineer, 31, pp. 258-347
273 (1981). 348
[5]. Schiller, E., and Kahangire, P. "Analysis and computerized model of the automatic hydraulic ram pump", 349
Canadian Journal of Civil Engineering, 11, pp. 743-750 (1984). 350
[6]. Basfeld, M., and Müller, E.-A. "The hydraulic ram", Forschung im Ingenieurwesen, A. 50, pp. 141-147 351
(1984). 352
[7]. Tacke, J. "Hydraulic rams; a comparative investigation" TU Delft, Report 88-1 (1988). 353
[8]. Rennie, L., and Bunt, E. "The automatic hydraulic ram—experimental results", Proceedings of the 354
Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 204, pp. 23-31 (1990). 355
[9]. Young, B. "Design of hydraulic ram pump systems", Proceedings of the Institution of Mechanical 356
Engineers, Part A: Journal of Power and Energy, 209, pp. 313-322 (1995). 357
[10]. Young, B. "Simplified analysis and design of the hydraulic ram pump", Proceedings of the Institution of 358
Mechanical Engineers, Part A: Journal of Power and Energy, 210, pp. 295-303 (1996). 359
15
[11]. Young, B. "Design of homologous ram pumps", Journal of Fluids Engineering, 119, pp. 360-365 (1997). 360
[12]. Najm, H., Azoury, P., and Piasecki, M. "Hydraulic ram analysis: a new look at an old problem", 361
Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 213, pp. 127-362
141 (1999). 363
[13]. Maratos, D. "Technical feasibility of wave power for seawater desalination using the hydro-ram 364
(Hydram)", Desalination 153, pp. 287-293 (2002). 365
[14]. Suarda, M., and Wirawan, I. "Kajian eksperimental pengaruh tabung udara pada head tekanan pompa 366
hidram", Jurnal Energi Dan Manufaktur 3, pp. 70-82 (2008). 367
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381
Figure Captions 382
Fig1. Layout of hydraulic ram pump system 383
Fig2. Schematic of experimental setup 384
Fig3. Determination head ratio of hm/H versus velocity ratio of v/v0 for different ratios of L/D 385
Fig4. Characteristic curve to determine the values of q/QT versus h/hm for different ratios of L/D 386
Fig5. Characteristic curve to determine the values of q/QT versus h/hm for different ratios of L/D 387
Fig6. Characteristic curve to determine the values of nD/v0 versus h/hm for different ratios of L/D 388
Fig7. Characteristic curve to determine the values of η versus h/hm for different ratios of L/D 389
Fig8. The predicted values of q/QT by equation (13) versus experimental observations 390
Fig9. The predicted values of Q/QT by equation (14) versus experimental observations 391
Fig10. The predicted values of nD/v0 by equation (15) versus experimental observations 392
Fig11. The predicted values of η by equation (16) versus experimental observations. 393
394
Table Captions 395
Table1. Condition of Length to diameter ratios of drive pipe in this study 396
Table2. The ranges of experimental data used in the present study 397
Table3. Experimental values of impulse valve loss in the various valve strokes 398
Table4. The brief results of error functions based on the proposed equations 399
Table5. Steps of design a pumping system using Wilcox's ram and Young's method 400
Table6. Selection of ram pump features and independent variables to design a pumping system 401
16
Table7. Steps of design a pumping system using ram pump used in present study and proposed method 402
Table8. Performance comparison between ram pump used in this study and Wilcox's ram pump 403
404
Figures 405
Fig1.
406
407 Fig 2. 408
17
0
2
4
6
8
10
12
3 4 5 6 7 8
L/D = 600
500
400
300
200
100
ovv
Hh
m
409
Fig 3. 410
411
0
0.1
0.2
0.3
0.4
0.5
0 0.2 0.4 0.6 0.8 1
100
D
L200300
400500600
TQ
q
mhh 412
Fig4. 413
18
0.6
0.7
0.8
0.9
1
1.1
0 0.2 0.4 0.6 0.8 1
TQ
Q
mhh
600
D
L50
0
400
300
200
100
414
Fig5. 415
0
0.06
0.12
0.18
0.24
0.3
0 0.2 0.4 0.6 0.8 1
100DL
600
200
300
400
500
mhh
ov
nD
416 Fig6. 417
418
19
0
0.15
0.3
0.45
0.6
0.75
0 0.2 0.4 0.6 0.8 1
η
mhh
100
D
L
200
300
600
500
400
419 Fig7. 420
421 422
y = 0.9774x
0
0.1
0.2
0.3
0.4
0.5
0 0.1 0.2 0.3 0.4 0.5
Observed q/QT
Pre
dic
ted q
/QT
Observed vs Proposed Eq.(13)
Best Fit
25% Deviation Line
423
Fig8. 424
425
20
y = 0.9976x
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1 1.2Observed Q/QT
Pre
dic
ted Q
/QT
Observed vs Proposed Eq.(14)
Best Fit
15% Deviation Line
426
Fig9. 427
428
y = 0.9924x
0
0.05
0.1
0.15
0.2
0.25
0 0.05 0.1 0.15 0.2 0.25
Observed nD/v0
Pre
dic
ted
nD
/v0
Observed vs Proposed Eq.(15)
Best Fit
15% Deviation Line
429
Fig10. 430
431
21
y = 0.9873x
0
0.1
0.2
0.3
0.4
0.5
0 0.1 0.2 0.3 0.4 0.5
Observed efficiency
Pre
dic
ted
eff
icie
ncy
Observed vs Proposed Eq.(16)
Best Fit
20% Deviation Line
432
Fig11. 433
434
435
Tables 436
Table1. 437
Number of Scenarios Length of Drive pipe
L (m)
Diameter of Drive pipe
D (m)
Length to Diameter ratio
L/D
S1 5.10 0.05 100
S2 10.20 0.05 200
S3 15.30 0.05 300
S4 10.20 0.02 400
S5 12.75 0.02 500
S6 15.30 0.02 600
438
439
Table2. 440
No. Dimensionless Parameter Maximum Minimum Average Standard Deviation
1 q/QT 0.34 0.008 0.16 0.09
2 Q/QT
0.99 0.65 0.83 0.09
3 nD/v0 0.27 0.01 0.09 0.07
4 L/D 600 100 364.91 166.35
5 h/hm 0.86 0.2 0.48 0.18
7 v0D/υ 29568 12724 20877 7547
441
442
Table3. 443
Valve Strokes Velocity of valve closure Ratio of S0/Dv Drag Coefficient Friction Coefficient
22
S0 (mm) v0 (m/sec) (Dimensionless) Kd c
1.5 0.24 0.04 25.01 58.85
3.2 0.47 0.09 6.17 19.93
4.7 0.75 0.13 2.48 12.05
6.4 1.01 0.18 1.36 8.67
8 1.24 0.22 0.90 6.71
9.5 1.44 0.27 0.66 5.42
11.1 1.64 0.31 0.52 4.49
12.7 1.83 0.36 0.41 3.80
444
Table4. 445
Parameter Equation RMSE MPE SEE EF m
TQq
(13) 0.03 1.83 0.03 0.91 0.97
TQQ
(14) 0.04 0.22 0.03 0.88 0.99
0vnD
(15) 0.01 1.29 0.01 0.98 0.99
η (16) 0.03 1.83 0.03 0.88 0.98
446
Table5. 447
Dimension Parameter value Equation number Parameter design Step
m 0.02 Eq. (3) D 1
m 7.01 Eq. (4) L 2
Litre/min 1.41 Eq. (2) q 3
Litre/min 25.59 Q=QT-q Q 4
min-1 1.55 Eq. (1) n 5
beat/min 93 - Number of cycle per min 6
448
449
450
Table6. 451
No. Independent variables Symbol Value Dimension
1 Total input discharge QT 27 Liter/min
2 Length stroke of impulse valve S0 0.01 m
3 Disc diameter of impulse valve Dv 0.03 m
4 Supply head H 2.5 m
5 Delivery head h 15 m
6 Length of drive pipe L 7.01 m
7 Diameter of drive pipe D 0.02 m
8 Dead weight of impulse valve W 0.13 Kg
9 Acceleration due to gravity g 9.81 m/s2
10 Flow density ρ 981 Kg/m3
452
Table7. 453
Step number Determine dependent variables Equation number Parameter value Dimension
1 Drag Coefficient (Kd) Eq. (9) 0.35 No dimension
2 Friction coefficient (c) Eq. (10) 3.06 No dimension
3 Flow velocity in steady state (v) - 4 m/s
4 Critical velocity (v0) Eq. (12) 1.98 m/s
5 Maximum delivery head (hm) Eq. (11) 25.95 m
6 Rate of pumping discharge (q) Eq. (13) 2.22 Liter/min
7 Rate of wasting discharge (Q) Eq. (14) 24.14 Liter/min
8 Frequency of impulse valve (n) Eq. (15) 1.50 Beat/min
9 Number of cycle per minute - 90 Beat
10 Pump efficiency (η) Eq. (16) 22.47 %
454
Table8. 455
23
No Wilcox's Ram Pump Ram Pump used in Present Study
h/H q/QT Q/QT nD/v0 efficiency q/QT Q/QT nD/v0 efficiency
1 2.4 0.130 0.869 0.019 25.81 0.309 0.707 0.014 75.03
2 3.2 0.098 0.901 0.019 15.83 0.271 0.761 0.016 51.84
3 4 0.078 0.921 0.019 11.36 0.213 0.805 0.017 35.24
4 4.8 0.065 0.934 0.019 8.84 0.151 0.844 0.017 22.65
5 5.6 0.056 0.943 0.019 7.23 0.101 0.878 0.019 14.06
6 6.4 0.049 0.95 0.019 6.11 0.066 0.908 0.019 8.69
7 7.2 0.043 0.956 0.019 5.29 0.044 0.936 0.02 5.47
8 8 0.039 0.960 0.019 4.67 0.029 0.962 0.021 3.53
456
Biographies 457
458
Babk Lashkar-Ara is an Assistant Professor of Civil Engineering at Jundi Shapur University of 459
Technology. He received his PhD from the Shahid Chamran University, Ahwaz, Iran. His research 460
interests include sediment transport, river engineering and hydraulic structures. 461
462
Reza Fatahi-Alkouhi received the Diploma degree in civil engineering from Shahrekord's 463
conservatory of Fani 1, the Bachelor degree in civil engineering from the Daneshpajoohan institute 464
and higher education and the Master degree in civil and river engineering from Jundi-Shapur 465
University of Technology. Currently, he is Ph.D. student in civil and water resource management from 466
University of Isfahan. 467
