WATER JET CONFERENCE - Waterjet Technology Association

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DIMENSIONLESS PIPE LENGTH ANALYSIS FOR <strong>JET</strong> MODULATION SYSTEMS J. L. Evers, D. L. Eddingfield and J. Y. Yuh College of Engineering and <strong>Technology</strong> Southern Illinois University at Carbondale Carbondale, Illinois 62901 ABSTRACT A dimensionless pipe length analysis has been developed to summarize the possible responses of a modulator system for any combination of pipe lengths. The parametric summary has as many variables as pipes in the modulator system. The transfer matrix method with pipe friction neglected is used for the response equations. The results are compared to the more exact method of characteristics. INTRODUCTION The pressure transient produced by the impact of the leading edge of a liquid jet or droplet with a solid surface has been estimated to be several times the stagnation pressure of the moving liquid [4, 5]. In order to increase the number of leading edge transients and thereby increase the fragmentation efficiency, conventional jets have been interrupted, pulsed or modulated to form a series of discrete water bunches each producing a water hammer pressure pulse [7, 8, 9]. Large interruption frequencies on the order of several thousand cycles per second are needed to maximize the number of liquid particle impacts while still producing a water package large enough to produce significant local fragmentation. Periodic jet flows with frequencies in this range have been produced by a periodic variation in the flow resistance [4], an oscillating volume in the flow circuit, or a self-excited oscillation [6]. With the proper frequency and wave shape, large water drops can be made to form near the impact surface producing repetitive water hammer pressure transients. One can speculate on the possibility of controlling the spacing between stress waves in such a way as to reinforce incident and reflected waves. In producing a modulated jet, the liquid compressibility and the elasticity of the piping system can cause the modulation response to be very different from the input signal. For example, it is not uncommon for the modulation response to be completely attenuated by the piping system at certain frequency intervals. A theoretical study of a periodic flow resistance modulator [3] predicted that a significant distortion of the wave shape, producing unwanted secondary droplets, is produced for all frequencies except those that place odd harmonics on both sides of the oscillator. Therefore, analytical methods that can predict modulator response can be very beneficial in assessing the relative merits of various oscillator and piping configurations. The transfer matrix method [2] and the method of characteristics [1] can both be used to predict modulator response. However, when the response wave shape is required, the method of characteristics must be used. This method retains all of the non-linear 3
frictional and piping component relationships and calculates the pressures and flow rates at selected points along the piping system for each time step from the start of the transient until a steady oscillatory condition is realized. Since a hundred or more oscillations are often required to reach the steady oscillatory state, considerable computer time is required to calculate a complete response spectrum for a single modulator configuration. During the design of a modulator system it is beneficial to obtain a system response spectrum showing the amplitude of the output oscillations over the entire range of driving frequencies. These relationships predict the frequencies for which the modulator operates most efficiently and regions where the oscillation is attenuated by the piping system. The transfer matrix method, which solves the governing equations directly for the steady state amplitudes of oscillation provides an economical means of obtaining the response diagrams. Even though approximations are made to linearize the viscous terms and the non-linear boundary conditions, this technique can be used to identify areas of interest for which more accurate calculation can be made with the method of characteristics. The possibility of developing a modulator that greatly amplifies the input signal by resonating the piping system is of interest in minimizing the power required to drive the oscillator. However, assessing the potential for a given modulator configuration to produce a large amplification of output would require a response spectrum for each combination of pipe length, pipe diameter, wave speed and boundary conditions. Even using the transfer matrix method, where only one closed form calculation is required to obtain a response at each driving frequency, the number of calculations required to obtain a clear picture of the modulation possibilities quickly becomes very time consuming if not prohibitive as the modulator complexity increases. In this study the transfer matrix method is used to predict the system response. However, the governing equations are developed in terms of dimensionless pipe lengths and parametric calculations are made in terms of these quantities. The resulting summary curves greatly reduce the number of calculations required to assess the modulation possibilities of a given system of components. Specific dimensions required to produce a particular condition predicted by the summary curves can be easily obtained. THE TRANSFER MATRIX METHCD Since the dimensionless pipe length analysis uses the transfer matrix method for the system response equations, a brief discussion of the method is included. Complete details of the method are presented by Chaudhry [2]. This technique develops linear equations relating pressures and flow rates at a point upstream of the particular modulator component to these quantities at the downstream end of the component. Then the relationship between flow rates and pressures at the upstream boundary of the entire system is obtained in terms of these quantities at the downstream boundary by an ordered multiplication of the equation matrices for each component in the modulator 4
Page 1 and 2: Proceedings of the Second U.S. WATE
Page 3 and 4: Visualization of the Central Core o
Page 5 and 6: A Status Report on the Conceptual D
Page 7 and 8: SESSION 7 - CIVIL & INDUSTRIAL Chai
Page 9: Cutting Hard Rock With Abrasive-Ent
Page 13 and 14: R = a1 ⋅ A1 A2 a2 I = 2H o Q o
Page 15 and 16: attenuation of the output. The tran
Page 17 and 18: Figure 1. Branch System Modulator F
Page 19 and 20: Figure 5. Modulation Response for B
Page 21 and 22: Figure 9. Modulation response for s
Page 23 and 24: can be used for any form of input.
Page 25 and 26: with a cylindrical shape to the jet
Page 27 and 28: m/s. The range of power found from
Page 29 and 30: Figure 3. Power vs nozzle diameter
Page 31 and 32: Figure 5. Frequency vs length of th
Page 34 and 35: NAME: Gerald Zink COMPANY: StoneAge
Page 36 and 37: modulatornozzle assembly. The ordin
Page 38 and 39: DISCUSSION OF FLUID MECHANICS The i
Page 40 and 41: This process serves to protect the
Page 42 and 43: For test purposes, these concrete b
Page 44 and 45: REFERENCES CITED 1. Barker, C. R.,
Page 46 and 47: FIGURE 4. INNER CORE OF PERCUSSIVE
Page 48 and 49: FIGURE 9. EXAMPLE OF HIGH-PRESSURE
Page 50 and 51: NAME: John E. Wolgamott COMPANY: St
Page 52 and 53: THE FOCUSED SHOCK TECHNlQUE FORPROD
Page 54 and 55: The reflected wave is thus also cyl
Page 56 and 57: neglected. The introduction of a co
Page 58 and 59: DISCUSSION NAME: George Savanick CO
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H’ mean shape factor Hj theoretic
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Required streamline curvature at th
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2 x 2 ≅ ( e − 2 p + w)/k2 (2-8)
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eliminating 2 n r 2 from equations
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approximation to the actual flow si
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skin friction coefficient but are c
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where: (H) = A1H 3 + A2H 2 + A3H +
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effect (< 0.5%) on coefficients of
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TABLE 5 Rei x 10 5 β 3 4 5 6 Po Po
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TABLE 6 D(mm) d o(mm) L t(mm) L f(m
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expanding rather than contracting a
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25. Weber, H.E., 1978, Boundary lay
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Figure 5. Wall velocity distributio
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Figure 9. Effect of nozzle design o
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Figure 12. CA+T Design Philosophy.
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Figure 16. Effect of inlet b 1 cond
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Figure 20. Relaminarization at nozz
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Figure 24. Pressure decay data. 88
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VISUALIZATION OF THE CENTRAL CORE O
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DISCUSSION Although employing the i
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5. Lambert, J. H., 1760, Photometri
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Figure 6. Spectral sensitivity curv
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NAME: W.C. Cooley COMPANY: Terraspa
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INTRODUCTION Pulsed liquid jets sho
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y=X ∨ P A dy = p p A p 2 (L c y=0
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Using equation (15), the value of X
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Thus about the first 10% of the dri
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Many design cases, including those
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surface spall occurred, resulting i
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Figure 3. Chamber pressure at pisto
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Figure 7. Effect of nozzle area rat
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Figure 11. Extrusion device schemat
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Figure 15. Typical chamber pressure
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DISCUSSION NAME: W. C. Cooley COMPA
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material which are, in turn, affect
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the water jet. This method was not
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where h is the depth of penetration
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obtained during this phase of the i
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observed that the smallest depth of
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Figure 2. Idealized Relationships b
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Figure 6. Penetration as a Function
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DEVELOPMENT OF VARIABLE DELIVERY TR
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THE STRUCTURE AND FUNCTION OF THE P
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The injection pressure can be contr
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ACKNOWLEDGEMENTS The authors gratef
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Figure 4. Theoretical required powe
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Figure 9. Variation of efficiency w
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THE "SKIPJACK" SEWER CLEANING NOZZL
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HYDRO-BLASTING SAFETY C.W. Adaway,
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Remember, your Hydro-Blasting work
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horizontal, sometimes vertical, and
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Figure 2. Safety Gear Figure 3. Tub
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DEVELOPMENTS IN CLEANING COKE OVEN
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causing chain breakages and the scr
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was encountered, then the rotation
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(C) Capital Expenditure: Material i
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Figure 9. Swivel coupling Figure 10
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OPTIMIZING JET CUTTING POWER FOR TU
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PRESSURE DROP (psi) ELEMENT Cv @10
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power output. Undersized nozzles re
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Subscripts n - Nozzle p - Pump t -
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Figure 1. Cutting effect as a funct
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CONSIDERATIONS IN THE COMPARISON OF
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pressure can be lowered to perhaps
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Figure 2: Fan jet issuing from a no
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DISCUSSION NAME: John Griffiths COM
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where Q = Flow rate - gpm D = Jet O
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Again, not limited to Newtonian flu
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REFERENCES 1. Brown, R.W. and Loper
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Table 2. Jet Cleaning Speeds and ot
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ANSWER: The utilization of the stat
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complexity and short component life
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Figure 4, for ap values ranging fro
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Decontamination Methods for rapidly
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a. “PULSER” b.”ORGAN-PIPE”
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Figure 5 - Removal rate for various
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DISCUSSION NAME: David A. Summers C
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DRILLING BORE HOLES IN COAL MINES U
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pile could not be judged as represe
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DISCUSSION NAME: David Summers COMP
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HYDRAULIC MINING EXPERIMENTS IN AN
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The monitor was fed pressurized wat
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The IH rig was considered to be sup
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REFERENCES 1. Okhrimenki, V. A., A.
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Figure 2. Jet cutting sandstone at
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Figure 5. Schematic plan view of In
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Figure 7. Suction Box. 226
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USE OF HIGH PRESSURE WATER JETS FOR
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flame torch to cut this block, redu
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the order of 360 rpm. Under these c
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Figure 3. Slot cut by jet at 11 o s
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JET-MINER SURFACE AND IN-SEAM TRIAL
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The hydraulic drive of the haulage
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The surface trials had have the obj
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Figure 2. Experimental version. Fig
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Figure. 7 Jet-Miner prototype Figur
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SOME PATTERNS OF TECHNOLOGY TRANSFE
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Development of High Pressure_Techno
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configurations, the design of an op
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and public sectors. After a haitus
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Souder, W.E. and Evans, R.J., "The
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Figure 5. Technological achievement
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Table 3. Perceived disadvantages of
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already been, or is being applied w
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Using the requirements profile and
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ant hose combination, a guiding sys
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HYDRAULIC MINING TESTS Site selecti
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SAFETY All operations were carried
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TABLE V. Categories of Jet Mining D
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Figure 2. Generalized geologic prof
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SECONDARY FRAGMENTATION WITH WATER
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do possess a maximum point (Fig. 8)
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Figure 4. Rossin-Rammler plot. Figu
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Figure 8. Non-dimensional plot for
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HYDRAULIC COAL MINING SYSTEM Typica
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Figure 4. (From ref. 1) DISCUSSION
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INTRODUCTION Developing an unique t
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The coefficients "b " in Eq. (1) ca
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By the end of 1982, a total of more
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Figure 4. Cutting ability of swing-
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Figure 10. An operating performance
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for an abrasive, the abrasive parti
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the particles, while at slower spee
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to break away the remaining segment
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Table 1. Concrete saw technology. T
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NAME: Tom Brunsing COMPANY: Foster-
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FEASIBILITY STUDY OF CUTTING SOME M
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hydraulic power required to cut thr
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pressure was varied from 103 to 310
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2.1 Heading and gutting fresh cod f
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Figure 5. The cuts surface of a blo
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Figure 17. Cuts made across the cla
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JET NOTCHING USED IN THE CONSTRUCTI
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Bottom notch diameter was determine
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σ H = in-situ stress in the horizo
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Figure 3. Final block displacement.
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Figure 8. Comparison of Slurry Pump
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THE FURTHER DEVELOPMENT OF AN UNDER
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use taps or hydrants. To achieve th
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supply line. It was determined that
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The rotating head requires major mo
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Figure 4. System field test set-up
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Figure 10. Bentonite drilled clay s
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MECHANICAL TOOLS Cutting Tool Energ
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Ψ = cos −1 ⎧ ⎪ ⎪ ⎨ ⎪
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mode also contributes to chip flush
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NAME: Simon Johnson COMPANY: Newcas
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ROLLER TOOLS COMBINED WITH HIGH-PRE
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Various designs and applications ar
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Figure 1. Full-face tunneling machi
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Figure 11. roadway profile cutting
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Figure 19. High-pressure water jet
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DESIGN AND OPERATION OF TWO LARGE-S
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The hydraulic system for the thrust
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Results of Trial Tests As part of m
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cutting rates, degree of bit wear,
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Overall approximate Weight: Basic M
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Figure 5. 3 ft. diameter laboratory
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nozzle diameter and cutting speed w
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2. Cutting Speed The influence of c
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energy it effects an increase in me
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Tip angle (degrees) 87 Off-set angl
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Figure 5. Figure 6. Figure 7 Figure
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Figure 17. Figure 18. Figure 19. Fi
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SCHEMES OF COAL MASSIF BREAKAGE BY
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out thoroughly an efficient scheme
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Research analysis has proved that t
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DEPENDENCE OF POWER INDICES OF COMB
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The experiments have shown how the
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K Ay = coefficient correcting for f
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Figure 1. Schemes of combined break
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Figure 5. Dependence of specific en
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Figure 12. Percentage of grade R -6
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Figure 1. Particle size analysis. T
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NAME: Dr. Henkel COMPANY: Bergbau-F
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presented. This study, of course, i
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identifying a general trend for the
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Effect of Abrasive Hardness, Shape
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In some situations, especially in c
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Figure 1. Abrasive waterjet nozzles
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Figure 8. Effect of standoff distan
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Figure 13. Abrasive waterjet cuts i
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CUTTING WITH ABRASIVE WATERJETS M.
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3.3 Abrasive Feed Systems For abras
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Because of the large number of infl
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due to wear. Although actual operat
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from this new technology. Table 2 l
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Table 1. materials cut by abrasive
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Figure 1. Abrasive waterjet nozzles
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a) kerfs in mild steel b) S.S. 15.5
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a) circle cutting in glass b) lamin
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DISCUSSION NAME: Andrew F. Conn COM
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CUTTING HARD ROCK WITH ABRASIVE-ENT
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slurry nozzle. Testing at water pre
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DISCUSSION OF TEST RESULTS Jet Conf
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materials. The flexibility in nozzl
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pressure can be wiped out if diffic
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9. Maurer, W.C., and Heilheckler, J
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Figure 5. Effect of abrasive feed r
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Figure 9. Accumulated depth of mult
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Figure 13. Close-up view of quartzi
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ABRASIVE INJECTION USAGE IN THE UNI
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sudden changes in the feed rate eff
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or the abrasive must be manually to
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clog; there not being sufficient ar
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CODE OF PRACTICE FOR THE USE OF ABR
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Figure 5. Water abrasive cleaning h
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Figure 15. 360 0 abrasive pipe clea
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ECONOMIC CONSIDERATIONS IN WATER JE
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Other criteria to be considered in
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3 MANUAL METHODS OF JET CLEANING &
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contractor with old, unsafe, equipm
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Figure 1. Showing the increased cos
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Figure 8. Automatic tube bundle cle
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ackground to the subsequent coopera
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The molecules of SUPER-WATER posses
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shaken just before use. SUPERWATER
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26. Bednarz, L.P., "Effects of Poly
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