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TitleTransients in Hydraulic Systems - Bentley Hammer
TagsFluid Dynamics Liquids Elasticity (Physics) Waves Partial Differential Equation
File Size1.6 MB
Total Pages52
Document Text Contents
Page 1




Thomas M. Walski

Donald V. Chase

Dragan A. Savic

Walter Grayman

Stephen Beckwith

Edmundo Koelle

Contributing Authors

Scott Cattran, Rick Hammond, Kevin Laptos, Steven G. Lowry,

Robert F. Mankowski, Stan Plante, John Przybyla, Barbara Schmitz

Peer Review Board

Lee Cesario (Denver Water), Robert M. Clark (U.S. EPA),

Jack Dangermond (ESRI), Allen L. Davis (CH2M Hill),

Paul DeBarry (Borton-Lawson), Frank DeFazio (Franklin G. DeFazio Corp.),

Kevin Finnan (Bristol Babcock), Wayne Hartell (Bentley Systems),

Brian Hoefer (ESRI), Bassam Kassab (Santa Clara Valley Water District),

James W. Male (University of Portland), William M. Richards

(WMR Engineering), Zheng Wu (Bentley Systems ),

and E. Benjamin Wylie (University of Michigan)

Click here to visit the Bentley Institute
Press Web page for more information

Page 2


Transients in Hydraulic Systems

A hydraulic transient is the flow and pressure condition that occurs in a hydraulic sys-
tem between an initial steady-state condition and a final steady-state condition. When
velocity changes rapidly because a flow control component changes status (for exam-
ple, a valve closing or pump turning off), the change moves through the system as a
pressure wave. If the magnitude of this pressure wave is great enough and adequate
transient control measures are not in place, a transient can cause system hydraulic
components to fail.

This chapter presents the basic concepts associated with transient flow, discusses var-
ious methods to control hydraulic transients, and introduces aspects of system design
that should be considered during transient analysis. Special attention is given to the
specification of system equipment and devices that are directly related to causing and
controlling hydraulic transients.

The primary objectives of transient analysis are to determine the values of transient
pressures that can result from flow control operations and to establish the design crite-
ria for system equipment and devices (such as control devices and pipe wall
thickness) so as to provide an acceptable level of protection against system failure due
to pipe collapse or bursting. Because of the complexity of the equations needed to
describe transients, numerical computer models are used to analyze transient flow
hydraulics. An effective numerical model allows the hydraulic engineer to analyze
potential transient events and to identify and evaluate alternative solutions for control-
ling hydraulic transients, thereby protecting the integrity of the hydraulic system.


System flow control operations are performed as part of the routine operation of a
water distribution system. Examples of system flow control operations include open-
ing and closing valves, starting and stopping pumps, and discharging water in
response to fire emergencies. These operations cause hydraulic transient phenomena,
especially if they are performed too quickly. Proper design and operation of all

Page 26

Section 13.3 Magnitude and Speed of Transients 597

Figure 13.11��
Celerity determination

Attenuation and Packing

In a system without friction or tanks to dampen transients, transients could conceiv-
ably persist indefinitely. However, viscous and friction effects and loss of momentum
in tanks typically cause transients to attenuate within seconds to minutes.

Joukowsky’s equation (Equation 13.9) enables the engineer to compute the increase
in head that occurs due to the rapid closure of a downstream valve in a frictionless
system having an initial flow of Q0. The increase in head Ho�' = aQ0/gA = aV0/g is

referred to as the potential head change or potential surge.

Because friction does exist in an actual system, the potential head change calculated
using the Joukowsky equation underestimates the actual head rise. This underestima-
tion is due to packing—an additional increase in head occurring at the valve as the
pressure wave travels upstream.

Consider a pipe with a liquid flowing at V0 that connects a reservoir to a valve, similar
to the system shown at the top of Figure 13.12. As the wave travels upstream from a
closed valve, packing occurs because the hydraulic gradient in the pipe still exists
after the wave front passes. For an instantaneous closure or pump trip, an abrupt wave
moves upstream. Once the wave passes a point, the velocity downstream of the front
ostensibly goes to zero. However, a pressure gradient still exists in that section of the
pipe, and it causes a small (but nonzero) flow to continue toward the closed valve.
This additional water packs against the closed valve, resulting in an additional pres-
sure increase above the potential surge, a(V


The small velocity behind the wave front means that the velocity difference across the
wave front is less than V0, with the effect that the pressure change is progressively less
than the potential surge as the wave travels upstream. This effect, which is concurrent
with line packing, is called attenuation or reduction.

Page 27

598 Transients in Hydraulic Systems Chapter 13

Both line packing and attenuation are present continuously in real hydraulic systems.
The effect of attenuation and packing can be observed by solving the elastic wave
equations with and without the friction term. The difference between the two solu-
tions indicates the effect of packing and attenuation.

Figure 13.12 illustrates the change in system head over successive time increments.
The system consists of a 20-km-long pipeline with a diameter of 500 mm that carries
water from a reservoir with a water level of 100 m to a distribution reservoir at sea
level (reference datum). The internal roughness of the pipeline is 0.25 mm ( f 0.0175
for turbulent flow), the celerity is 1,000 m/s (2L/a = 40 seconds), and the flow rate is
approximately 330 l/s.

A transient is caused by a rapid linear valve closure (20 seconds) of a 500-mm globe
valve located at the downstream end of the pipeline. Because the friction loss coeffi-
cient (fL/D = 700) is considerably larger than the loss coefficient (K = 10) of an open
globe valve, most of the available energy is being lost along the pipeline in this sys-
tem. Thus, the system may be categorized as a high-friction system. Additionally, we
know that the effective stroke during closure is primarily at the end of the closure
period, due to the relatively low value of K over much of the valve’s travel. Although
the valve closure time for the system being considered is 20 seconds, the effective clo-
sure time is much less. A rapid and significant rise in head at the valve is therefore
anticipated at a time of approximately 20 seconds. The series of graphs in Figure
13.12 shows the evolution of the wave front traveling along the pipeline with packing
occurring near the valve and attenuation occurring at the wave front.

Page 51

622 Transients in Hydraulic Systems Chapter 13


Read the chapter and complete the problems. Submit your work to Haestad Methods
and earn up to 11.0 CEUs. See Continuing Education Units on page xxix for more
information, or visit

13.1 A 12-inch ductile iron transmission main delivers water from an elevated tank with a water surface
elevation of 500 ft to a ground storage tank with a water surface elevation of 450 ft. A control valve
located at the inlet to the ground storage tank is throttled to maintain a flow rate of 1,000 gpm. The
transmission main has a wave celerity of 4,000 ft/s.

Page 52

Discussion Topics and Problems 623

a) How long will it take for a pressure wave to travel from one end of the system to the other?

b) What is the characteristic time for the system?

c) If the control valve is completely closed in 4 seconds, what will the potential head change be
immediately upstream of the control valve?

13.2 A horizontal pump delivers 10 million gallons/day from a water treatment plant clearwell with a
water surface elevation of 50 feet to an elevated storage tank with a water surface elevation of 375
feet. The water is conveyed through 20,000 feet of 30-in. steel transmission main. The transmission
main has a wave celerity of 3,500 fps.

a) What is the characteristic time for the system?

b) If an instantaneous emergency pump shutdown occurs due to a power loss, is water column sepa-
ration likely to occur at location A?

c) Would a pump bypass line be effective in preventing a vacuum condition at location A following
an emergency pump shutdown? If not, what could be done to prevent it?

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