Chemical Engineering July 2021 - 38

400
350
300
250
200
150
100
50
Head rise network = 191 m (627 ft)
Straight pipe
- Networked pipe
1,000
simple Equation (3) should be considered.
Ref. 9 provides some guidance
to chemical engineers on how
to approach this.
The
Joukowsky
500
equation
is
a
Head rise Equation (1) = 130 m
0 10 20 30 40 50
Time, s
FIGURE 5. Simulation results at the valve from Example 4, using the straight and networked pipe systems
in Figure 4 (from Ref. 1)
for Example 3, assuming instantaneous
valve closure:
a = 1,291 m/s (4,236
ft/s),
the
wavespeed of the fluid
∆V = -2.04 m/s (-6.68 ft/s)
Using Equation (3), the Joukowsky
pressure rise (∆PJ) can be
determined to be 2,367 kPa (343
psi). This was shown in Equation 7.
If an engineer took Equation 3 as
the worst-case pressure rise, that
person would add this to the initial
valve pressure of 6,638 kPa (963
psia) to obtain maximum pressure
of 9,005 kPa (1,306 psia). It is true
that this would be the pressure rise
immediately after the valve closed.
However, this is not the maximum
pressure, because the pressure will
continue to rise after valve closure
as the frictional recovery of pressure
occurs.
A truly conservative maximum
pressure rise can be obtained by
adding the two together, as shown in
Equation (8):
∆Pmax = ∆PJ + ∆Pfr = 5,729 kPa
(or 831 psi)
(8)
The maximum possible pressure
is then obtained by adding the
Equation (8) pressure rise to the initial
valve pressure (Pvalve). This result
is 12,367 kPa (1,794 psia), as
shown in Figure 3, where the results
from a full transient simulation are
also shown. The method in Ref. 7
by Liou is shown also. Here, it is
clear that the maximum pressure
of 11,967 kPa (1,736 psia) is much
higher than what is predicted by
Equation (3).
The line pack pressure rise can be
38
seen in Figure 3 from 0 to about 75
s, and totals 2,962 kPa (430 psi).
With a keen eye for line pack now
at our disposal, look back to the experimental
results in Figure 1. After
the initial Joukowsky pressure rise
of 104 m (340 ft), it is evident that
the pressure continues to increase
for another 0.1 s or so. This increase
is about 5 m (16 ft), which happens
to be roughly the frictional pressure
loss. Hence, one can see line pack
in the Figure 1 experimental results,
as well as the simulation results,
when one looks closely.
Example 4: Reflected pressure
waves. Ref. 1 discusses numerous
ways that a reflected wave can
cause a pressure rise greater than
what would be given by Equation (3).
Consider the systems in Figure 4,
which shows a straight pipe system
and a similar networked system. This
example appears in Ref. 1 and was
first published in Ref. 8.
In each system in Figure 4, the
valve at the end is closed instantly.
Figure 5 shows the results. It is clear
that the pressure rise in the networked
piping is higher than what
would be predicted by Equation (1)
at 20 s.
Numerous other situations
can
cause reflected waves that exceed
the values obtained using Equation
(3). These situations include a pipe
diameter change, a branch going to
a dead-ended pipe and the presence
of a gas accumulator [1].
Concluding remarks
Waterhammer can be a complicated
issue to address. When possible,
a more detailed analysis than the
powerful tool for engineers when
used with a proper understanding
of its limitations. Engineers should
not assume that it always provides
a worst-case, conservative pressure
rise. The examples presented
here clearly show cases where the
pressure rise can be much larger
than what the Joukowsky equation
predicts. Keep this in mind the next
time someone tells you they have
calculated " the maximum theoretical
waterhammer pressure. " Just smile
and reply, " are you sure you can
trust that? "
n
Edited by Scott Jenkins
References
1. Walters, T. W. and Leishear, R. A., 2019, " When the Joukowsky
Equation Does Not Predict Maximum Water Hammer Pressures, "
ASME Journal of Pressure Vessel Technology, Vol. 141
/ 060801-1, December 2019.
2. Joukowsky, N., Über den hydraulischen Stoss in Wasserleitungsröhren.
(On the hydraulic hammer in water supply
pipes), Me´moires de l'Acade´mie Impe´riale des Sciences de
St.-Petersbourg, Series 8, Vol. 9, No. 5 (in German, English
translation, partly, by Simin, 1904). 1900.
3. Tijsseling, A. S., and Anderson, A., Johannes von Kries and the
History of Water Hammer, ASCE Journal of Hydraulic Engineering,
Vol. 133, Issue 1, pp. 1-8, 2007.
4. Bergant, A., Simpson, A. R. and Tijsseling, A. S., Water hammer
with Column Separation: A Historical Review, Journal of Fluids
and Structures, 22, pp. 135-171, 2006.
5. Martin, C. S., " Experimental Investigation of Column Separation
With Rapid Closure of Downstream Valve " , 4th International Conference
of Pressure Surges, BHRA, pp. 77-88, Bath, UK, 1983.
6. Applied Flow Technology, AFT Impulse 8, Colorado Springs,
Colo., USA., 2020.
7. Liou, C. P., Understanding Line Packing in Frictional Water Hammer, "
ASME J Fluid Eng, Vol. 138(8), New York, 2016.
8. Karney, B. W., McInnis, D., Transient Analysis of Water Distribution
Systems, Journal AWWA, Vol. 82 (7), pp. 62-70, 1990.
9. Prentice, W., 2021, Understand and Mitigate Waterhammer in
Fluid Processes, Chem. Eng., March 2021, pp. 28-32.
Author
Trey Walters is the founder and
president of Applied Flow Technology
(AFT; 2955 Professional Place,
Suite 301, Colorado Springs, CO
80904; Email:
treywalters@aft.
com; Phone: 1-719-686-1000).
Walters founded AFT in 1993. He
holds a B.S.M.E. (1985) and
M.S.M.E. (1986), both from the
University of California, Santa Barbara
and is a registered professional engineer. Walters is
the original developer of AFT Fathom, AFT Arrow and
AFT Impulse and has taught hundreds of training
classes on AFT's software products in twelve countries
across every populated continent. He worked previously
for General Dynamics in cryogenic rocket design and
Babcock & Wilcox in steam/water equipment design.
Walters is a fellow of the American Society of Mechanical
Engineers.
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