【正文】 a gap in the theory. Actually, a great deal of time and trouble can be saved if a paper and pencil analysis and design of the system is made before it is simulated on a puter for final refinements. If this is done carefully, with generous sprinklings of sound engineering judgments, then machine putation will not be necessary in most cases. In plicated cases in which judgments are most difficult, if not impossible, to make, machine putation is required。 however, this requirement is exceptional. The development of digital puter programs in recent years to solve plex sets of nonlinear differential equations strengthens the argument for preliminary analysis, for now exact solutions are possible for parison. In fact, preliminary analyses to determine approximate results are useful, and sometimes absolutely necessary, to obtain maximum benefits from machine putations. Availability of these programs allows more emphasis to be placed on the physics and mathematical formulation of problems and less on the solution dynamic analysis is necessarily restricted to linearized differential equations because only they may be solved without great difficulty. However, as far as dynamic performance is concerned, linearized analysis is an adequate tool considering the basic assumptions usually made to obtain initial equations, the preponderance of experimental correlation, and the fact that general performance indices have been developed only for linear systems. Furthermore, the algebraic or singlevalued nonlinearities which occur in hydraulic equations are not usually the source of discrepancies between predicted and actual results. Discrepancies can be traced to two basic phenomena: multivalued nonlincarities such as backlash (which is notorious for causing limit cycle oscillations) and the types of quantity involved in hydraulic analysis. Two basic types of physical quantity can be distinguished in hydraulic control analysis: hard and soft. A hard quantity is one that can be determined with fair precision and whose value remains relatively constant. In short, a hard quantity is easily identified, puted, and controlled. In contrast, a soft quantity is one whose value can, at best, be pinned down to a possible range of values. A soft quantity is unreliable, nebulous, and a function of variables not easily known or controlled. As an example, consider a simple springmass arrangement. The mass and spring constants are hard quantities and result in a hard, undamped natural frequency. However, the damping ratio, although it certainly has a value that can be measured, is difficult to pute and is soft quantity. The most important asset of a servo system is stability, and therefore Stability should be based on hard quantities. Indeed, the design of a system car be judged by the number of hard quantities on which its performance depends. If a certain performance index depends on soft quantities, correspondingly nebulous physical performance can be expected. For example, the stability of single stage relief valves depends on, among other things, the pressure sensitivity of the valve. This is a soft quantity because it depends on vaive geometry at null, valve wear, and so on, and these valves are well known for their ability to oscillate. In contrast, the stability of an unpensated electrohydraulic servo depends on hard quantities such as valve flow gain and piston area, and their stability is virtually assured. Therefore, an intent of this book is to instill a sense of judging the quality of quantities in addition to how quantities relate to performance. This sort of engineering judgment is absolutely necessary for the rational design of hydraulic controls. The designer should always ask whether the required performance depends on soft quantities. It is certainly safe to conclude that better systems can be built if more emphasis is placed on the quality of quantities and how this can be exploited to form a design rather than on a precise mathematical solution of a given set of equations which, supposedly, represents the system. PRESSUER TYRANSIST THEORYBefore embarking on the analysis of pressure transient phenomena and the derivation of the appropriate wave equations,it will be usefull to describe the general mechanism of pressure propagation by reference to the events fllowing the instantaneous closure of a value postioned at the medlength point of a frictionless pipeline carrying fluid between two two pipeline sections upstream and downstream of the value are identical in all pressure waves will be propagated in both pipes by valve operation and it will be assumed that rate of value closure precludes the use of rigid column theory.As the valve is closed,so the fluide approaching its upstream face is retarded with a consequent pression of the flude and an expansion od the pipe increase in pressure at the valve results in a pressure wave being propagated upstream which conveys the retardation of flow to the column of fluid approaching the valve along the upstream pressure wave travels through the fluid at the appropriate sonic velocity,which will be shown to depend on the properties of the fluid and the pipe material.Similarly,on the downstream side of the valve the retardation of flow results in a reduction in pressure at the valve,with the result that a negative pressure waves is propagated along the downstream pipe which,in turn,retards the fluid will be assumed that this pressure drop in the downstream pipe is insufficient to reduce the fluid pressure to either its vapour pressure or its dissolved gas release pressure,which maybe considerable different.Thus,closure of the valve results in propagation of pressure waves along both pipes and,although these waves are of different sign relative to the steady pressure in the pipe prior to valve operation,the effect is to retard the flow in both pipe pipe itself is affected by the wave propagation as the upstream pipe swells as the pressure rise wav