J. Inst. Eng. India Ser. C DOI 10.1007/s40032-016-0295-0
CASE STUDY
Investigation and Parameter Optimization of a Hydraulic Ram Pump Using Taguchi Method Dhrupad Sarma1 • Monotosh Das1 • Bipul Brahma1 • Deepak Pandwar1 Sermirlong Rongphar1 • Mafidur Rahman1
•
Received: 6 August 2015 / Accepted: 18 May 2016 Ó The Institution of Engineers (India) 2016
Abstract The main objective of this research work is to investigate the effect of Waste Valve height and Pressure Chamber height on the output flow rate of a Hydraulic ram pump. Also the second objective of this work is to optimize them for a hydraulic ram pump delivering water up to a height of 3.81 m (12.5 feet ) from the ground with a drive head (inlet head) of 1.86 m (6.11 feet). Two one-factor-ata-time experiments have been conducted to decide the levels of the selected input parameters. After deciding the input parameters, an experiment has been designed using Taguchi’s L9 Orthogonal Array with three repetitions. Analysis of Variance (ANOVA) is carried out to verify the significance of effect of the factors on the output flow rate of the pump. Results show that the height of the Waste Valve and height of the Pressure Chamber have significant effect on the outlet flow of the pump. For a pump of drive pipe diameter (inlet pipe) 31.75 mm (1.25 in.) and delivery pipe diameter of 12.7 mm (0.5 in.) the optimum setting was found out to be at a height of 114.3 mm (4.5 in.) of the Waste Valve and 406.4 mm (16 in.) of the Pressure vessel providing a delivery flow rate of 93.14 l per hour. For the same pump estimated range of output flow rate is, 90.65–94.97 l/h.
Electronic supplementary material The online version of this article (doi:10.1007/s40032-016-0295-0) contains supplementary material, which is available to authorized users. & Dhrupad Sarma
[email protected] 1
Jorhat Engineering College, Garmur, Jorhat 785007, Assam, India
Keywords Hydraulic ram pump Taguchi method Orthogonal array One factor at a time method Analysis of variance Abbreviations An avg Average values of responses at the nth level of parameters A A1, A2, A3 Three levels of factor A ANOVA Analysis of variance Bnavg Average values of responses at the nth level of parameters B B1,B2,B3 Three levels of factor B C.I.CE Confidence Interval for a sample group (confirmation experiment) C.I. pop Confidence Interval for the population C.L. Confidence level D1 Diameter of the drive pipe D2 Diameter of the delivery pipe DOE Design of experiment f Degree of freedom (DOF) F Variance ratio Favg Overall mean of the response variable Fa (1, fe) The F-ratio at a confidence level of (1-a) against DOF 1 and error DOF (fe) G. I. Galvanized Iron L1 Length of the drive pipe L2 Length of the delivery pipe neff N/ (1? Total DOF associated in the estimate of the mean) N Total number of results N.R.V. Non Return Valve OA Orthogonal Array OFAT One-factor-at-a-time P Percent contribution
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J. Inst. Eng. India Ser. C
Qout r R R1, R2, R3 S S’ S/N V Ve Yn a l
Delivery flow rate Number of repetitions Sample size of confirmation experiment First, second and third repetition of the trial conditions Sum of squares Pure sum of square Signal to Noise Ratio Variance Error variance from ANOVA Value of the response variable at nth repetition Confidence level in percentage mean of the output variable
Introduction The Hydraulic Ram Pump is a pumping device that is capable of pumping water higher than its original source without using any external source of energy. Water enters the Hydraulic Ram Pump from a particular head at high flow rate and comes out with higher head but at a lesser flow rate. It functions on the principle of water hammer effect, a phenomenon that occurs when the flowing water is suddenly brought to rest by closing a valve or by any other device which results in a sudden increase in pressure in the pipe. As the water hammer effect is caused by the water itself, a part of the input water is lost due to spillage. So, a very less amount of the water is delivered at the outlet through the delivery pipe. The pump is simple to operate with an economical maintenance requirement since it has very less moving parts. Some of its basic parts are drive pipe, delivery pipe, check valve and pressure chamber. It causes no pollution of any kind and has a commendable operational life even with continuous working, unlike other conventional pumps. A schematic diagram of the Hydraulic Ram Pump with its components is shown in Fig. 1. Some of the previous works on hydraulic ram pump are discussed below: Watt [1] designed analytically a hydraulic ram pump with source flow rate of 1 l per minute by taking length of the drive pipe as four times the supply head. Watt suggested the use of a stand pipe or feeder tank if the source is very far away from the ram pump. Krol [2] found out the performance curves for a ram pump whose drive head and drive pipe diameter were 4 metres and 50 mm respectively. Inversin [3] developed a Hydraulic Ram Pump that could deliver about 2.5 litres of water per minute for a delivery head of about 10 times the drive head with an efficiency of around 65–75 %. Mohammed [4] experimentally optimized a Hydraulic Ram Pump with a drive head of 2 m
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Fig. 1 Schematic diagram of Hydraulic Ram Pump
using combinations of the length to diameter ratio of the drive pipe, stroke length and weight of the impulse valve. The efficiency obtained was 57.3 %. From various literature study it has been found that details about two important parts of the Ram pump viz. the height of the Pressure Chamber and height of the Waste Valve and their effect on the performance of the Hydraulic Ram Pump were not fully studied. Therefore the basic objective of this research work is to investigate the effect of the height of the Waste Valve and the height of the Pressure Chamber on the output flow rate of ram pump. Also another objective of this study is to optimize these two parameters for a pump with the following assumed operational parameters: Drive head: 1.86 m Outlet head: 3.81 m Inlet flow: 720 l/h. Diameter of the drive pipe (D1): 31.75 mm. Length of the delivery pipe (L2): 9.75 m.
Methodology To investigate the effect of the two factors (height of the Waste Valve and height of the Pressure Chamber) on the output flow rate of ram pump a Design of Experiment (DOE) approach has been followed. At first two one factor at a time (OFAT) experiment have been conducted to mark the important levels of the aforesaid factors. Raw data ANOVA is carried out to check the significance of the factors selected. After deciding the important levels of the factors, a combined experiment has been designed using Taguchi’s Orthogonal Array (OA). The response variable selected for each experiment is the output flow rate of the pump at a height of 3.81 m from ground level. The details of the experiments are given below: Experiment I: OFAT with three repetitions. The trial conditions along with levels of the variable
J. Inst. Eng. India Ser. C Table 1 Trial conditions of Experiment I
Table 4 Trial conditions of Experiment III
Trial no.
Trial no.
Factor A (Height of the waste valve) Level
Value of Factor A, mm (in.)
Column assignment of factors A
B
A9B
A9B
1
A1
88.9 (3.5)
1
88.9
355.6
1
1
2
A2
114.3 (4.5)
2
88.9
406.4
2
2
3
A3
139.7 (5.5)
3
88.9
457.2
3
3
4
114.3
355.6
2
3
5
114.3
406.4
3
1
6
114.3
457.2
1
2
Table 2 Trial conditions of Experiment II
7 8
139.7 139.7
355.6 406.4
3 1
2 3
Trial no.
Factor B (Height of the pressure chamber)
9
139.7
457.2
2
1
Level
Value of Factor B, mm (in.)
1
B1
355.6 (14)
2
B2
406.4 (16)
Under the interaction column A 9 B, [1,1],[2,2],[3,3]..etc represent levels of interactions between Factor A and B. They do not represent levels of independent factors. These levels are according to Taguchi OA L9 standard design
3
B3
457.2 (18)
Constant factor Height of Pressure Chamber (355.6 mm)
Constant Factor Height of the Waste valve (114.3 mm)
Table 3 Variable factors of Experiment III Factor A (Height of the waste valve)
Factor B (Height of the pressure chamber)
Level
Level
Value of Factor B, mm (in.)
Value of Factor A, mm (in.)
A1
88.9 (3.5)
B1
355.6 (14)
A2
114.3 (4.5)
B2
406.4 (16)
A3
139.7 (5.5)
B3
457.2 (18)
factor Height of the waste valve (Factor A) are shown in Table 1. Experiment II: OFAT with three repetitions The trial conditions along with levels of the variable factor Height of the pressure chamber (Factor B) are shown in Table 2. Experiment III: L9 Taguchi OA with three repetitions. The variable factors with their levels are shown in Table 3, while the trial conditions are shown in Table 4. From Experiment I and Experiment II, three levels for each of the two factors are decided. To investigate the effect of the two factors when both of them are varied, the third experiment is designed. In this experiment interaction effect of these two factors are also studied. For this experiment L9 OA has been used since this is the smallest three level array having degree of freedom (DOF) greater than the DOF of the experiment. After referring to a three level triangular Table [5], Factor A is positioned in the first column, Factor B in the second column and their
interaction (A 9 B) is placed in the third and fourth column. Main effect curve and Interaction effect curve are drawn from the experimental data to find out the optimal setting of the factors. The experimental data obtained from this experiment is analyzed with Raw data ANOVA and S/N data ANOVA. The selected quality characteristic of the response variable is Higher the Better for S/N data analysis of ANOVA. An MS Excel template has been developed for the ease of analysis of the experimental data. From the two types of analysis of ANOVA, depending on their effect on mean or variance of the response, the factors segregation is done and predicted mean of the response variable at optimal factor setting is found out. Signal to Noise Ratio (S/N Ratio) Calculation Raw data obtained from experiments are converted to S/N ratio using the formula [5]: S=N ¼ 10log10 ðMSDÞ
ð1Þ
where the expression for the term Mean Squared Deviation (MSD) is different for different quality characteristics. 1. For smaller the better quality characteristics: MSD ¼ Y21 þ Y22 þ . . . þ Y2n =r; where Yn is the value of the response variable at nth repetition and r is the number of repetitions 2.
For nominal the best quality characteristics: n o MSD ¼ ðY1 Y0 Þ2 þðY2 Y0 Þ2 þ. . . þ ðYr Y0 Þ2 =r; where Y0 is the target value.
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J. Inst. Eng. India Ser. C
factor at level q, which is not included in the interaction term.
3. For higher the better quality characteristics: MSD ¼ 1=Y21 þ 1=Y22 þ . . . þ 1=Y2n =r A high value of S/N ratio implies that the effect of the factors under consideration is higher than the random effects of the noise factors. It reflects the desirability of that particular combination of factor levels. Prediction of Mean The mean (l) of the output variable (response) at the optimal condition is estimated depending on the following two situations [5]: 1.
When the optimal setting is one of the trial condition of the experiment, then the average value of the responses of that trial condition is considered as mean (l). This method is recommended, when interaction term contains significant factors.
l ¼ ðAm Bn Þavg
ð2Þ
Where, ðAm Bm Þavg ¼ Average values of responses of the trials when both Factor A and Factor B are in mth and nth level.
2.
When the optimal setting is not within the trial condition of the experiment, then the mean (l) is estimated as follows: a.
When there is no significant interaction: l ¼ Favg þ Amavg Favg þ Bnavg Favg
ð3Þ
Where, Favg ¼ Overall mean of the output variable (Response) Amavg ; Bnavg ¼ Average values of responses at the mth and nth level of parameters A and B respectively
A, B are the significant factors as indicated by ANOVA and m, n are their optimal level setting respectively. b. When there is interaction present and found significant by ANOVA, then from interaction effect plot the optimal levels are selected and average values of responses, with that factor setting is considered as mean (l). The average effect of other significant factors (if any), which are not included in the interaction term; can be added in the estimation of mean (l). l ¼ Ao Bp avg þ Cq Favg
ð4Þ
Where, Ao and Bp are the optimal setting of the factors as indicated by interaction plot; and C is a significant
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Confidence Interval (C.I.) To find out the range, within which for a given level of confidence the mean of the response variable is likely to fall; the confidence interval is calculated out. The Confidence Interval is added to mean and subtracted from the mean value to get the maximum and minimum limit of the range respectively. The two categories of Confidence Interval are proposed by Taguchi [5]: 1. 2.
Confidence Interval for the population (C.I. pop). Confidence Interval for a sample group (C.I.CE).
The C.I. pop is for the entire population and C.I. CE is for only a sample group made under the specified condition (confirmation experiments). The confidence intervals and range for population and sample group is calculated as follows [5]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fa ð1; f e ÞVe C:I: POP ¼ ð5Þ neff sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1 1 C:I:CE ¼ Fa ð1; f e ÞVe þ ð6Þ neff R where Fa (1, fe) is the F-ratio at a confidence level of (1-a) against DOF 1 and error DOF fe; Ve is the Error variance from ANOVA; neff is the N/ (1? Total DOF associated in the estimate of the mean); N is the Total number of results; and R is the Sample size of confirmation experiment. Range of Confidence Interval: RangePOP : l C:I: POP l l þ C:I: POP RangeCE : l C:I: CE l l þ C:I: CE Confirmation Experiment (CE) To verify the result, after finding out the optimum setting of the factors; a confirmation experiment has been conducted with three repetitions, keeping the factors at their optimum setting.
Experimental Setup To perform the trials, a Hydraulic Ram Pump has been designed using data obtained from already published literatures. To design the pump it is assumed that the pump will deliver water upto the height of a single storied building
J. Inst. Eng. India Ser. C
Fig. 2 Line diagram showing various dimensions of the prototype
(12.5 ft or 3.81 m) having a inlet pipe of dia 31.75 mm (1.25 in.) and inlet head (6.12 ft or 1.86 m) being roughly half of that outlet head. The following are the operational factors assumed for the proposed pump: Vertical Lift (Outlet head): 3.81 m (Height of a single storied building) Vertical Fall (Drive head): 1.86 m (Roughly half of the outlet head) Inlet flow: 720 l/h. (Experimentally decided at the outlet of the delivery tank). Diameter of drive pipe (D1): 31.75 mm Length of the delivery pipe (L2): 9.75 m (Decided as per convenience at the installation site) If L1 is the Length of the drive pipe, From Calvert Equation [6], Length of Drive Pipe L1 ¼ ¼ 150 to 1000 Diameter of Drive Pipe D1
Fig. 3 Ram pump body with header tank
ð7Þ
Taking L1 =D1 ¼ 200 ¼ [ L1 ¼ 200 0:03175 m ¼ 6:4 m Again from ‘‘Typical ram pump specification’’ published by Clemson University (USA) [7], for Inlet flow: 720 l/h, theDiameter of drive pipe (D1) and Diameter of delivery pipe (D2) is established as 31.75 and 12.7 mm respectively. The diameter of the swing check valve, waste valve and the pipe connecting the pressure chamber to the main body and main body pipe is kept same as the diameter of the inlet pipe(31.75 mm) for ease of fabrication. The pressure Chamber used here is a 2 l plastic bottle of length 335.2 mm. A detailed diagram showing the various dimensions of the setup is shown in Fig. 2.
During experimentation all the trials are carried out randomly to minimize errors. The measurement of height of Waste Valve is taken from center of the main pipe body to the center of the waste valve and height of Pressure Chamber is taken from center of the main pipe body to pipe end as shown in Fig. 2. The ram pump body with the header tank is shown in Fig. 3. Material Selection for Pipes The components of the system should not absorb the shocks of the water hammer effect for better performance of the Ram pump. Since G.I pipes are very rugged and tough, it has been selected for making the Ram pump body.
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J. Inst. Eng. India Ser. C Table 5 Experimental data of Experiment I Trial no.
Table 7 Experimental data of Experiment II
Factor A(Waste Valve Height, QOUT (l/hr) mm) R1 R2 R3 60
Average
60.89 61.1 60.66
Trial no.
Factor B (Pressure Chamber height, mm)
QOUT (l/hr) R1
R2
Average R3
1
88.9
1
355.6
77.5 74.46 76.2 76.05
2
114.3
78.6 77.2
77.9 77.90
2
406.4
90.7 90.8
3
139.7
73.5 74.7
73.5 73.90
3
457.2
82.5 80.57 81.2 81.42
91
90.83
Where R1, R2 and R3 are repetitions of the trial conditions
Output flow rate (l/hr)
Output flow rate (l/hr)
92 87 82
77.90
77
73.90
72 67 62 57
88.9 (A1)
87 82
114.3 (A2)
139.7 (A3)
81.42
77
76.05
72 67 62 57
60.66
90.83
92
355.6 (B1)
406.4 (B2)
457.2 (B3)
Height of the Pressure chamber (mm)
Height of the Waste valve (mm) Fig. 5 Main effect plot of height of the pressure chamber Fig. 4 Main effect plot of height of the waste valve
Results and Discussions During all the three experimentations except height of the waste valve and height of the pressure chamber, all other design/operational parameters like delivery pipe length, pipe diameter etc. are kept at their designed level. The results obtained from the experiments are discussed below. The results of Experiment I are given in Table 5. TheMain Effect Plot of height of the waste valve (Factor A) is shown in Fig. 4. Raw data ANOVA of Experiment I is shown in Table 6. The ANOVA result shows that the factor. Height of the waste valve have significant effect (at 95 % Confidence Level) on pump output flow rate. From the main effect plot it can be seen that as the height of the waste valve increases from A1 to A2 output flow increases; but after A2 when the height is increased to A3, the flow rate decreases. Therefore further experimentation after A3 point is not needed. Thus for the Experiment III, level A1, A2 and A3 are selected for
Factor A. Main effect plot also shows, A2 is the optimum setting for Factor A. Therefore in experiment II, height of the waste valve is kept at its optimum value (A2) as predicted by Experiment I. The results obtained from Experiment II are given in Table 7. The Main Effect Plot of height of the pressure chamber (Factor B) is shown in Fig. 5. The Raw data ANOVA result (Table 8) shows that at 95 % Confidence Level the factor, Height of the pressure chamber have significant effect on pump output flow rate. From the main effect plot it can be seen that as the Height of the pressure chamber increases from B1 to B2 output flow increases; but after B2 when the height is increased to B3, the flow rate decreases. Therefore no further experimentation after B3 point is done. Thus for the Experiment III level B1, B2 and B3 are selected for Factor B. The experimental results of Experiment III are given in Table 9. Figures 6 and 7 shows Main Effect plot of Factor A (Height of waste valve) and Factor B (Height of Pressure
Table 6 Raw data ANOVA of Experiment I Source
f
S
V
F
S’
P
F(0.05) critical
Comment
Factor A
2
488.312
244.156
558.695
487.438
99.288
5.143
Significant
error Total
6 8
2.622 490.934
0.437 244.593
123
1
3.496
0.712 100
J. Inst. Eng. India Ser. C Table 8 Raw data ANOVA of Experiment II Source
f
S
V
F
S’
P
F(0.05) critical
Comment
Factor B
2
335.833
167.917
151.801
333.621
97.416
5.143
Significant
error
6
6.637
1.106
Total
8
342.470
169.023
1
8.849
2.584 100
Table 9 Experimental data of Experiment III Trial no.
Column assignment of L9 OA A (Waste Valve Height, mm)
QOUT (l/hr)
B (Pressure Chamber Height, mm)
A9B
A9B
R1
R2
R3
Average (l/hr)
S/N ratio (dB)
1
88.9
355.6
1
1
63.92
60.28
61.45
61.88
35.824
2
88.9
406.4
2
2
80
75
73.47
76.16
37.617
3 4
88.9 114.3
457.2 355.6
3 2
3 3
74.23 75.79
77.42 79.12
75.79 80.89
75.81 78.60
37.591 37.899
5
114.3
406.4
3
1
94.8
91.34
92.29
92.81
39.349
6
114.3
457.2
1
2
87.8
80.89
82.76
83.82
38.451
7
139.7
355.6
3
2
72
76.71
74.76
74.49
37.433
8
139.7
406.4
1
3
83.72
84.71
87.38
85.27
38.612
9
139.7
457.2
2
1
79.12
80
77.42
78.85
37.933
94
89
85.08
84 79.54
79 74 69 64
71.28
Output flow rate (l/hr)
Output flow rate (l/hr)
94
89 84.75 84 79
69 64
88.9 (A1)
114.3 (A2)
139.7 (A3)
71.66 355.6 (B1)
457.2 (B3)
Fig. 7 Main effect plot of height of pressure Chamber of Experiment III
Output flow rate (l/hr)
95
Chamber) respectively and Fig. 8 shows Interaction Effect Plot of the two factors. Raw data ANOVA and S/N data ANOVA results are shown in Tables 10 and 11 respectively. From ANOVA tables, it is clear that Factor A (Height of waste valve) and Factor B (Height of Pressure Chamber)have significant effect, both on mean and variation of the response variable whereas, a mild interaction is present between the two factors with 4.358 % contribution on mean but the interaction has insignificant effect on the variation of the response.
406.4 (B2)
Height of the Pressure chamber (mm)
Height of the Waste valve (mm)
Fig. 6 Main effect plot of height of the Waste Valve of Experiment III
79.49
74
92.81
90 85 80 75 70
85.27
83.82 76.16
78.85
78.60
74.49
75.81
65 60
61.88 88.9 (A1)
114.3 (A2)
139.7 (A3)
Height of the Waste valve (mm) 355.6 (B1)
406.4 (B2)
457.2 (B3)
Fig. 8 Interaction effect plot
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J. Inst. Eng. India Ser. C Table 10 Raw data ANOVA of Experiment III Source
f
S
V
F
S’
P
F(0.05) critical
Comment Significant
Factor A
2
866.902
433.451
76.131
855.515
46.151
3.555
Factor B
2
780.798
390.399
68.569
769.411
41.506
3.555
Significant
A9B
4
103.559
25.890
4.547
80.785
4.358
2.928
Significant
148.031
7.986
error
18
102.483
5.694
Total
26
1853.742
855.433
1
100
Table 11 Pooled S/N data ANOVA of Experiment III Source
f
S
V
F
S’
P
F(0.05) critical
Comment
Factor A
2
3.713
1.857
13.675
3.442
45.302
6.944
Significant
Factor B
2
3.341
1.671
12.304
3.070
40.402
6.944
Significant
A9B
[4]
[0.543]
Pooled
–
–
–
error Total
4 8
0.543 7.597
0.136 3.663
From Main Effect plot (Figs. 6 and 7) of Factor A and B, the optimum factor combination is A2, B2. A 9 B interaction plot also shows that A2, B2 combination gives the maximum output flow rate. Hence, the optimal factor combination is A2, B2 i.e. Height of Waste Valve = 114.3 mm and Height of Pressure Chamber = 406.4 mm. As the optimal setting of the two factor, is one of the trial condition of the Experiment III, the mean (l) is estimated by averaging the response values of that trial condition. From experiment data (Table 9), The average value of the response (output flow rate) of Trial number 5 is 92.81 l/ h. Thus, the mean output flow rate, at optimal setting (A2, B2) is, Qout ðlÞ ¼ 92:81 l=hr: At 95 % Confidence Level (C.L.), Confidence Interval for the population, C:I: pop ¼ 2:157 Confidence Interval for a sample group (confirmation experiment), C:I: CE ¼ 3:610 Range with 95 % C.L., Range POP:90.65 \ Qout (POP) \ 94.97 Range CE:89.20 \ Qout (CE) \ 96.42 Confirmation Experiment To ascertain the results obtained, a confirmation experiment for the optimum factor combinations of Height of the
123
14.296 100.000
Table 12 Confirmation experiment results Factor A(Height of waste valve, mm)
Factor B(Height of Pressure Chamber, mm)
Qout(l/hr)
114.3
406.4
91.13 94.7 93.59 93.14
R1
R2
R3
Average output flow rate (l/hr)
where R1,R2 and R3 are the repetitions
Waste Valve (114.3 mm) and Height of Pressure Chamber (406.4 mm) is conducted with three repetitions. The results are given in Table 12.
Conclusion In the investigation, the effect of Height of Waste Valve and Height of Pressure Chamber is found significant on both mean and variation of the response variable (delivery flow rate). A mild interaction is present between the two factors with 4.358 % contribution on mean but the interaction has insignificant effect on the variance of the response. Taguchi’s parameter design procedure is used to obtain optimum factor combination for maximization of delivery flow rate. For the designed prototype of Hydraulic Ram pump, 114.3 mm Height of the Waste Valve and 406.4 mm Height of the Pressure Chamber is found to be optimum with an estimated output flow rate 92.81 ± 2.157 l/h. A confirmation experiment is conducted to verify the result predicted from Taguchi Optimization. The average delivery flow rate of the optimized prototype is found to be 93.14 l/h which is well within the range (89.20 \ Qout (CE) \ 96.42) estimated for the confirmation experiment.
J. Inst. Eng. India Ser. C Acknowledgments We are thankful to the faculty members of Department of Mechanical Engineering, Jorhat Engineering College for providing necessary suggestions for this work.
References 1. S. B. Watt, Manual on the Hydraulic for Pumping Water, Reprinted edition, (Intermediate technology publication, London, 1981), pp. 1-27 2. J. Krol, The automatic hydraulic ram, vol. 164 (PROC. I. MECH. E., 1951), p. 103
3. A. Inversin, Hydraulic ram, Second printing (Volunters in Technical Assistance Inc., Virginia, 1987), pp. 5–10 4. S.N. Mohammed, Design and construction of a hydraulic ram pump. Leonardo El. J. Pract. Technol. 11, 59–70 (2007) 5. P.J. Ross, Taguchi Techniques for Quality Engineering, 1st edn. (McGraw-Hill Book Company, New York, 1988), pp. 118–124 6. Hydraulic Rams For Off-Stream Livestock Watering, (Cooperative Extension Service, The University of Georgia, 1988), http://www.caes. uga.edu/departments/bae/extension/pubs/documents/rampump3.pdf. Accessed 21 Mar 2015 7. Homemade Hydraulic Ram Pump, (Clemson University Cooperative Extension, 2014), http://www.clemson.edu/irrig/equip/ram. html. Accessed 7 Mar 2015
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