Discussion: “Distortion of Short Pulses in Tapered Tube Pulse Transformers. Part II–Viscous Liquid’” (Rouleau, W. T., and Young, F. J., 1965, ASME J. Basic Eng., 87, pp. 471–476)

Abstract

/ q» .4 .8 1.2 1.6 2.0 t x 103 sgc 2.4 2.8-8 Fig. 4 input and output pulses of volume flux in water-filled line of Example 2 as determined from equation (49) 10-3 boundary layer. In Example 2, for which the viscous distortion is very pronounced, we would expect a relatively thick boundary layer, considering the much greater length and higher viscosity.

Progress in Analytical Modeling of Water Hammer

“…This impedance, which can be subdivided for arbitrarily short sections of a line, is independent of the compressibility of the medium. The above was confirmed by Holmboe in his doctoral dissertation [14]: "… nothing apparently was lost by the assumption of incompressible flow to evaluate the impedance". In the same work Holmboe, derived an analytical solution of the pressure history for the first cycle of the water hammer event discussed and presented later in the paper [15].…”

“…Holmboe [14] obtained the final set of partial differential equations of the hyperbolic type that describe unsteady fluid pipe flow in a simple pipe system (Fig. 2) in a form widely recognized today:…”

“…The review of analytical models for frequency-dependent cases shows that there is no analytical solution for velocity and wall shear stress determined for large frequencies (represented with acceptable compliance for a relatively large unsteady time range). We have decided to fill this gap by developing novel solutions using the method discussed by Holmboe [14] and later by Muto and Takahashi [26]. By computing the derivative with respect to x from Eq.…”