References

[1]

 Fluid transients in closed conduits, First Annual Report, Fluid Power Research Center, Oklahoma State University, Stillwater, Oklahoma. 1965.

 

[2]

 Womersley, J. R., Oscillatory flow in arteries: the constrained elastic tube as a model of arterial flow and pulse transmission, Phys. Med. Biol., 1958, 2, 178-187.

 

[3]

 McDonald, D. A., The relation of pulsatile pressure to flow in arteries, J. Physiol., Lond., 1955, 127. 533-552.

 

[4]

 Rayleigh, J. W. S. 3rd Baron, Theory of sound, Vol. II, Second Edition, 1896. First American Edition, 1945. 18-26, (Dover, New York).

 

[5]

 Symposium on water hammer, 1933, Second Printing, 1949, (ASME, New York).

 

[6]

 Jaeger, C., Fluid transients in hydro-electric engineering practice, 1977, (Blackie, Glasgow).

 

[7]

 Bergeron, L., Water hammer in hydraulics and wave surges in electricity, 1961, (Wiley, New York).

 

[8]

 Wylie, E. B., Resonance in pressurized piping systems, Trans. ASME, J. Basic Engng, 1965, 87, 960-966.

 

[9]

 Streeter, V. L., Unsteady flow calculations by numerical methods, Trans. ASME J. Basic Engng, 1972, 94, 457-466.

 

[10]

 Weng, C. K., Transmission of power by pulsating flow (P-F) concept in hydraulic systems, Trans. ASME, J. Basic Engng, 1966, 88, 316-322.

 

[11]

 Parmakian, J., Water hammer analysis, 1963, (Dover, New York).

 

[12]

 Constantinesco, G., Theory of wave transmission - a treatise on transmission of power by vibrations, 1922, (Walter Haddon, London).

 

[13]

 Wood, F. M., The application of heaviside's operational calculus to the solution of problems in water hammer, Trans. ASME, 1937, 59, HYD-59-15, 707-713.

 

[14]

 Schuder, C. B. and Binder, R. C., The response of pneumatic transmission lines to step inputs, Trans. ASME, J. Basic Engng, 1959, 81, 578-584.

 

[15]

 Oldenburger, R. and Goodson, R. E., Simplification of hydraulic line dynamics by use of infinite products, Trans. ASME, J. Basic Engrig, 1964, 86, 1-10.

 

[16]

 Walker, M. L. Kirkpatrick, L T. and Rouleau, W. T., Viscous dispersion in water hammer, Trans. ASME, J. Basic Engng, 1960, 82,759-764.

 

[17]

 Grace, S. F., Oscillatory motion of a viscous liquid in a long straight tube, Phil. Mag., 1928, 7th Series, 5(31), 933- 939.

 

[18]

 Richardson, E. G. Proc. Phys. Soc., Lond.. 1928, 40, 206-220.

 

[19]

 Richardson, E. G. and Tyler, E., The transverse velocity gradient near the mouths of pipes in which an alternating or continuous flow of air is established, Proc. Phys. Soc., Lond., 1929-30, 42, Pt. 1(231), 1-15.

 

[20]

 Sexl, T., Über den von E. G. Richardson entdeckten 'Annulareffekt', Z. Phys., 1930, 61, 349-362.

 

[21]

 Lambossy, P., Oscillations forcees d'un Liquide incompressible er visqueux dans un tube rigide et horizontal. Calcul de la force de frottement, Helv. Phys. Acta, 1952, 25, 371-386.

 

[22]

 Uchida. S., The pulsating viscous flow superimposed on the steady laminar motion of incompressible fluid in a circular pipe, Z.A.M.P., 1956, 7(5), 403-421.

 

[23]

 Womersley, J. R., Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known, J. Physiol. Lond., 1955, 127, 553-563.

 

[24]

 Wornersley, J. R., Oscillatory flow in arteries II: the reflection of the pulse wave at junctions and rigid inserts in the arterial system, Phys. Med. Biol., 1958, 2. 313-323.

 

[25]

 Womersley, J. R. Oscillatory flow in arteries III: flow and pulse-velocity formulae for a liquid whose viscosity varies with frequency. Phys. Med. Biol., 1958, 2, 374-382.

 

[26]

 Cotton, K. L. and Gabe, I. T., Fluid inductance and its measurement in rigid tubes, Phys. Med. Biol., 1961, 6, 87-104.

 

[27]

 Linford, R. G. and Ryan, N. W., Pulsatile flow in rigid tubes, J. Appl. Physiol., 1965, 20(5), 1078-1082.

 

[28]

 Karreman, G., Some contributions to the mathematical biology of blood circulation, reflections of pressure waves in the arterial system, Bull. Math. Biophys., 1952, 14, 327-350 (see Appendix pp 341-350).

 

[29]

 Morgan, G. W. and Kiely, J. P., Wave propagation in a viscous liquid contained in a flexible tube, J. Acoust. Soc. Am., 1954, 26(3), 323-328.

 

[30]

 Morgan, G. W. and Ferrante, W. R. Wave propagation in elastic tubes filled with streaming liquid. J. Acoust. Soc. Am., 1955, 27,(4), 715-725.

 

[31]

 Atabek, H. B. and Chang, C. C., Oscillating flow near the entry of a circular tube, Z.A.M.P., 1961, 12, 3, 185-201.

 

[32]

 Florio, P. J. and Mueller, W. K., Development of a periodic flow in a rigid tube, Trans. ASME, J. Basic Engrig, 1968, 90, 395-399.

 

[33]

 Sarpkaya, T., Experimental determination of the critical Reynolds number for pulsating Poiscuille flow, Trans. ASME J. Basic Engng, 1966, 88, 589-598.

 

[34]

 Crandall, I. B., Theory of vibrating systems and sound, 1926, Appendix A. 229-241 (Van Nostrand, New York).

 

[35]

 Rohmann, C. P. and Grogan, E. C., On the dynamics of pneumatic transmission lines, Trans. ASME, 1957, 79, 853-874.

 

[36]

 Foster, K. and Parker, G. A., Transmission of power by sinusoidal wave motion through hydraulic oil in a uniform pipe, Proc. Instn. Mech. Engrs, 1964-65, 179, Pt. 1 (19), 599-614.

 

[37]

 Zwikker, C. and Kosten. C., Sound absorbing materials, 1949, (Elsevier, Amsterdam).

 

[38]

 Goldschmied, F. R., On the frequency response of viscous compressible fluids as a function of the Stokes number, Trans. ASME, J. Basic Engng., 1970, 92, 333-347.

 

[39]

 Iberall, A. S., Attenuation of oscillatory pressures in instrument lines, J. Res. Natn. Bur. Stand., USA, 1950. 45, 85-108.

 

[40]

 Nichols, N. B., The linear properties of pneumatic transmission lines, Trans. Instr. Soc. Am., 1962, 1, 5-14.

 

[41]

 Brown, F. T., The transient response of fluid lines, Trans. ASME, J. Basic Engrig., 1962, 84, 547-553.

 

[42]

 D'Souza, A. F. and Oldenburger. R., Dynamic response of fluid lines, Trans. ASME, J. Basic Engng., 1964, 86, 589-598.

 

[43]

 Cohen. H. and Tu, Y., Viscosity and boundary effects in the dynamic behaviour of hydraulic systems, Trans. ASME, J. Basic Engng., 1962, 84, 593-601.

 

[44]

 Gerlach. C. R., The dynamics of viscous fluid transmission lines with particular emphasis on higher mode propagation, PhD thesis, 1966, Oklahoma State University, USA.

 

[45]

 Geriach, C. R. and Parker, J. D., Wave propagation in viscous fluid lines including higher mode effects, Trans. ASME, J. Basic Engng., 1967, 89, 782-788,

 

[46]

 Urata, E., Unsteady flow of viscous liquid in long circular tube, Bull. J.S.M.E., 1971, 14(68), 147-155.

 

[47]

 Ohmi, M., Usui, R., Fukawa, M. and Hirasaki, S., Pressure and velocity distributions in pulsating laminar pipe flow, Bull. J.S.M.E., 1976, 19(129), 298-306.

 

[48]

 Inaba, T. et al., Pulsating laminar flow in a cylindrical pipe with through flow, Bull. J.S.M.E., 1977, 20(142), 442- 1449.

 

[49]

 Scarton, H. A., Waves and stability in viscous and inviscid compressible liquids contained in rigid and elastic tubes by the method of eigenvalues, PhD thesis, 1970, Carnegie-Mellon University, Pittsburgh, USA.

 

[50]

 Clarion, C. and Pelissier, R., A theoretical and experimental study of the velocity distribution and transition to turbulence in free oscillatory flow, J. Fluid Mech., 1975, 70(1), 59-79.

 

[51]

 Clamen, M. and Minton. P., An experimental investigation of flow in an oscillating pipe, J. Fluid Mech., 1977, 81(3), 421-431.

 

[52]

 Hershey, D. and lm, C. S., Critical Reynolds number for sinusoidal flow of water in rigid tubes, A.I.Ch.E.J1, 1968, 14(5), 807-809.

 

[53]

 Scarton, H. A. and Rouleau, W. T., Axisymmetric waves in compressible Newtonian liquids contained in rigid tubes: steady-periodic mode shapes and dispersion by the method of eigenvalleys, J. Fluid Mech., 1973, 8(3), 595-621.

 

[54]

 Sergeev, S. I., Fluid oscillations in pipes at moderate Reynolds numbers, Fluid Dynamics, 1966, 1(1), 121-122.

 

[55]

 Karam, J. T. and Franke, M. E., The frequency response of pneumatic lines, Trans. ASME, J. Basic Engng, 1967, 89, 371-378.

 

[56]

 Regetz, J. D., An experimental determination of the dynamic response of a long hydraulic line, NASA Technical Note, D-576, 1960.

 

[57]

 D'Souza, A. F., Dynamic response of fluid flow through straight and curved lines, PhD thesis, 1963, Purdue University, Lafayette, USA.

 

[58]

 Karim, S. M. and Rosenhead, L., The second coefficient of viscosity of liquids and gases, Rev. Mod. Phys., 1952, 24(2), 108-116.

 

[59]

 Herzfel, K. F., Bulk viscosity and shear viscosity in fluids according to the theory of irreversible processes, J. Chem. Phys., 1958, 28(4), 595-600.

 

[60]

 Libermann, L N., The second viscosity of liquids, Phys. Rev., 1949, 75(9), 1415-1422.

 

[61]

 Gerlach, C. R., Dynamic models for hydraulic conduits, Fluid Power Research Conference, Oklahoma State University, Stillwater, 1967, paper 5, Oklahoma.

 

[62]

 Goodson, R. E. and Leonard, R. G., A survey of modelling techniques for fluid line transients, Trans. ASME, J. Basic Engng, 1972, 94, 474-482.