acceptable then the valve is considered satisfactory. On the other hand
if closure is protracted in relation to the rate of deceleration, a sub-
stantial reversed velocity V
o
can develop with a correspondingly large
inertial head rise when the valve shuts. Free-acting valve response
can be improved to give a smaller V
o
. Modelling of the pipeline
system can be carried out without detailed consideration of the specific
free-acting valve up until the moment of closure so that the methods
described in Chapter 20 can be employed without modification.
The second option to improve closure conditions is to delay the
valve closure and allow the reversed flow to develop. By controlling
the time of closure the reversed flow can gradually be ‘throttled’ up
until the moment of closure. Thus as the reversed flow is progres-
sively eliminated, the deceleration gradient dV=dt can be made as
low as necessary to avoid unacceptable transient effects on closure.
Response of this ‘damped’ valve has to be modelled as an integral
part of the pipeline network, including the characteristics of the
damping mechanism.
Using the common swing-check valve as an example both of the
above types of valve modification are considered. Alterations shown
in Fig. 21.2b—e retain the free-acting nature of the valve while Fig.
21.2f and 21.2g illustrate valve damping mechanisms.
21.2.1 Free-acting modifications
An external lever and weight can be added with the lever at an angle to
the valve door (Fig. 21.2b). This enhances the closure moment and
produces an important closing moment even when the door is close
to its seat. The angle between the valve door and the lever can be
used to alter closure performance or indeed to make it easier for the
valve to open if required, although this is liable to have a detrimental
affect on closure performance. The size of weight and the length of
lever arm also influences performance. The greater the additional
closing moment provided by the lever and weight the shorter the
closure time but with the penalty of increased flow velocity to get the
valve fully opened.
Two forms of external spring can be introduced. A linear spring
connected to the lever (Fig. 21.2d) or a torsional spring on the
projecting hinge shaft (Fig. 21.2e). When the valve is open the spring
is in tension and so additional closure moment is achieved without
significantly increasing the moment of inertia of moving parts. Spring
stiffness will improve performance, with a stiffer spring improving
414
Pressure transients in water engineering