We describe the physics of the “Windkessel effect” and its role in smoothing the output of water produced by piston-driven pumps found in early fire engines and modern residential well houses. We also construct a simple, analytical model of its operation and apply this model to the Windkessel in Richard Newsham's 1725 fire engine. We find that Newsham's Windkessel reduces the variations in the pump output stream from a high of 80% to a low of 16%.
REFERENCES
1.
Society of Antiquaries of London
, “
Fighting Fire with John Lofting's Patented ‘Sucking Worm Engine
,’ ” Harley Collection
Vol. 5 (1714-1727). See <https://www.sal.org.uk/collections/explore-our-collections/collections-highlights/john-lofting-fire-engine/>.2.
Great Britain, Patent Office
, Titles of Patents Chronologically Arranged, 1617–1852. Page 52, Number 263 (1690)
(
Internet Archive, Digitized by the University of Illinois
,
Champagne-Urbana
, 1854
).3.
Jan
Van der Heyden
, Fire Engines with Water Hoses and the Methods of Fighting Fires Now Used in Amsterdam
(
Science History Publications
,
Canton, MA
, 2009
) (Translated from the Dutch into English by Lette Stibbe Multhauf).4.
Peter M.
Molloy
, who wrote a Forward to Lette Stibbe Multhauf's 2009 translation of van der Heyden's book, writes that “An air chamber allows water to be pumped in a continuous stream. This provides more water and makes aiming a stream much easier. The air chamber was known to the ancient Greeks, but apparently no European engine builders incorporated this feature until the van der Heydens.”5.
Great Britain, Patent Office
, Titles of Patents Chronologically Arranged, 1617–1852, Page 87, Number 479 (1721) and Page 90, Number 494 (1725)
(
Internet Archive, Digitized by the University of Illinois
,
Champagne-Urbana
, 1854
).6.
Richard
Bissel Prosser
, “
Richard Newsham
,” Dictionary of National Biography 1885–1900
(
Smith, Elder, and Co
.,
London
, 1894
), Vol.
40
.7.
Kim H.
Parker
, “
A brief history of arterial wave mechanics
,” Med. Biol. Eng. Comput.
47
(2
), 111
–118
(2009
).8.
Otto
Frank
, “
The basic shape of the arterial pulse. First treatise: mathematical analysis 1899
,” J. Mol. Cell. Cardiol.
22
(3
), 255
–277
(1990
).9.
It is easy to confuse an “expansion tank” with a “pressure tank.” Only the latter is a true Windkessel. The former refers to a tank connected to hot water systems that allows the volume of water it contains to expand when heated. “Pressure tanks” are attached to pump systems that draw water from the ground for residential purposes. Unfortunately, the devices seem not to have a uniform nomenclature. See the link <https://yourh2home.com/expansion-tank-vs-pressure-tank-which-one-do-you-need/>.
10.
Erich
Kamke
, Differentialgleichungen, Lösungsmethoden Und Lösungen
(
Akademische Verlagsgesellschaft, Geest & Prtig
,
Leibzig
, 1951
), pp. 26
, 302, 303, 326, 327, and 545.11.
In particular, the ratio of the height
of the step consisting of the lower half period of the continuous and smooth profile
to the height
consisting of its higher half-period that conserves the net injection rate during one period
is given by
.
13.
See the website of the Hall of Flame in Phoenix, Arizona USA, <https://hallofflame.org>. See also the YouTube video at <https://youtu.be/KvBHxfyRnu8?si=ge_n1VKLEkeLgQrD>
14.
See the Colonial Williamsburg, <https://emuseum.history.org>
15.
Fabien
Anselmet
,
Fabien
Ternat
,
Muriel
Amielh
,
Olivier
Boiron
,
Patrick
Boyer
,
Laurence
Pietri
et al, “
Axial development of the mean flow in the entrance region of turbulent pipe and duct flows
,” C. R. Mec.
337
(8
), 573
–584
(2009
).© 2024 Author(s). Published under an exclusive license by American Association of Physics Teachers.
2024
Author(s)
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.