John R. Womersley

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John Ronald Womersley
Born (1907-06-20)June 20, 1907
Morley, West Yorkshire
Died March 7, 1958(1958-03-07) (aged 50)
Columbus Ohio
Nationality British
Fields Mathematics, Computer Science, Fluid Dynamics
Institutions Shirley Institute, National Physical Laboratory, Wright Air Development Center
Alma mater Imperial College of Science and Technology
Known for Womersley number

John Ronald Womersley (20 June 1907 – 7 March 1958) was a British mathematician and computer scientist who made important contributions to computer development, and hemodynamics.[1] Nowadays he is principally remembered for his contribution to blood flow, fluid dynamics and the eponymous Womersley number, a dimensionless parameter characterising unsteady flow.


Early life and education[edit]

Womersley was born on 20 June 1907 in Morley, near Leeds in the West Riding of Yorkshire.[2] He was the only child of George William and Ruth Womersely; his father managed a grocery store in Morley.[3] He was educated at Morley Grammar School from 1917 to 1925. In 1925 he was awarded an Open Scholarship to the University of Cambridge and the Royal Scholarship in Physics at Imperial College of Science and Technology, but he chose to read mathematics at Imperial College.[3] His courses included Pure and Applied Mathematics, Physics, Hydrodynamics and the Kinetic Theory of Gases.[3] He was awarded a BSc degree with first-class honours in mathematics in 1929 and became an associate of the Royal College of Science.[3] He remained at Imperial College for another two years and was awarded the Diploma of Imperial College (D.I.C.) in 1930.


Pilot ACE (Automatic Computing Engine)

In 1930 Womersely left Imperial College to take up a position as a junior research officer at the Shirley Institute (British Cotton Industry Research Institute), Manchester.[3] There he applied mathematical techniques to problems in textile manufacture, including research on cotton spinning, drafting fibrous materials, and, through L. H. C. Tippett,[4] the use of mathematical statistics in industrial production and quality control.[2][3] While at the Shirley Institute he also met Leslie Comrie and became interested in computational techniques.[3] As a result, he spent a month at HM Nautical Almanac Office, London learning Comrie's numerical approaches.[3] In 1936 he collaborated with Douglas Hartree who had built a Differential Analyser at the University of Manchester; together they devised a much cited method for the numerical integration of partial differential equations.[3] In 1937, with war looming, he joined the armaments research department at Woolwich as a scientific officer, and worked on using statistical techniques applied to ballistics and ammunition proofing. In 1942, after the outbreak of World War II, he was appointed assistant director of scientific research at the Ministry of Supply and asked to set up and head the Advisory Service on Statistical Methods (later known as SR17).[5] This organization was responsible for advice and research into ammunition supply, engineering factories and the investigations of a range of Government Inspectorates. It was particularly important in ensuring quality control and promoting sample inspection methods to British Industry during wartime. In 1944 he joined the British Association mathematical tables committee and in the same year he was appointed as the first superintendent of the Mathematics Division of the National Physical Laboratory (NPL).[6] In addition to being responsible for statistical quality control, NPL was tasked with building an electronic computer, for which Womersley coined the name Automatic Computing Engine (ACE), echoing Babbage's Analytical Engine. Womersely was therefore responsible for the set up and operation of the first national computing centre in UK. One of his first actions was to visit the USA for a fact-finding tour, where he learned about ENIAC (Electronic Numerical Integrator and Computer), Howard Aitken's Harvard machine, George Stibitz's machines and von Neumann's plans for the binary computer, EDVAC (Electronic Discrete Variable Automatic Computer). On his return, he recruited Alan Turing to work on the ACE section and backed him strongly.[3][7] Womersley also recruited Donald Davies in 1947.[8] However, progress on the ACE project was delayed and Turing developed a dislike of Womersley and disdain for his abilities[9] and left the project in 1948. Davies then took over from Turing and a small experimental model, pilot ACE was produced in 1950.[10] Whether Womersely led NPL successfully has been questioned,[11] although the consensus seems to be that he did a good job in difficult circumstances.[3][12][13] He himself left the project in 1950, before the prototype pilot ACE was completed, to join the British Tabulating Machine Company (BTM), a forerunner of International Computers Limited (ICL). There he recognised that the computers previously developed by academia or governments were too large and expensive to be commercially viable and he recruited Andrew Booth who had developed the All Purpose Electronic Computer at Birbeck University, as a consultant to develop a smaller inexpensive computer.[14] The computer copied from Booth's original design by Ray Bird was named the Hollerith Electronic Computer (HEC1), and was Britain's first mass-produced business computer.[15]

Womersley flow
Simulation showing the predicted flow velocity profile in tubes with different Womersley numbers

In 1954 Womersley left BTM and joined a research team, led by Donald McDonald at St Bartholomew's Hospital, who were studying blood flow in arteries. This change seems to have been a temporary arrangement to 'fill in time whilst awaiting completion of arrangements to come to WADC' (the Wright Air Development Center)[3] and may have been prompted by his eldest daughter, Barbara, who was studying medicine at St Bartholomew's.[16] Whatever the reason, this move led to a new and highly productive period in his research, as he applied mathematical and computational techniques to the analysis of blood flow and hemodynamics. Most notably in 1955 he published an article[17] which described a dimensionless parameter (α) which characterised the nature of unsteady flow;[18][19] subsequently this has been called the Womersley number.[18] In July 1955, as planned, he moved to WADC, Dayton, Ohio, USA to take a post as acting chief of the Analysis Section, System Dynamics Branch Aeronautical Research Laboratory. In 1956, he was promoted to Supervisory Mathematician and then Supervisory Aeronautical Research Engineer (Flight Systems), although he continued to publish on mathematical aspects of blood flow until his early death in 1958.[20] His 1957 monograph on 'An elastic tube theory of pulse transmission and oscillatory flow in mammalian arteries' is widely regarded as a major influence in the field.[16] In 1957 he returned to Britain for treatment of cancer. He underwent a number of operations in London and returned to Ohio in 1957, but never fully recovered and died at Ohio State University Hospital, Columbus, on 7 March 1958.

Personal life[edit]

Womersley married Jean Isobel Jordan in Hammersmith, London in 1931. The couple had three daughters, Barbara, Ruth and Marion. Womersley's wife, Jean lived in Dayton until 1996, and as of 2014, they were survived by two daughters and six grandchildren living in the US and Canada.

Selected publications[edit]

  • Womersley, JR (1937). "The application of differential geometry to the study of the deformation of cloth under stress". Shirley Institute Memoirs. 16 (1). 
  • Hartree, D. R.; Womersley, J. R. (1937). "A method for the numerical or mechanical solution of certain types of partial differential equations". Proc. Royal Soc. A161: 353–366. 
  • Womersley, JR (1946). "Scientific computing in Great Britain". Math. Tables and Aids to Computation. 2: 110–117. doi:10.2307/2002621. 
  • Womersley, JR (1955). "Oscillatory motion of a viscous liquid in a thin-walled elastic tube. I. The linear approximation for long waves". Phil. Mag. 46: 199–221. doi:10.1080/14786440208520564. 
  • Womersley, JR (1955). "Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known". J. Physiol. 127: 553–563. doi:10.1113/jphysiol.1955.sp005276. 
  • Womersley, JR (1957). An Elastic Tube Theory of Pulse Transmission and Oscillatory Flow in Mammalian Arteries, Wright Air Development Center Technical Report 56-614, (sometimes referred to as WADC TR56-614 and sometimes cited as 1958)
  • A complete bibliography may be found at[21]


  1. ^ Smithies, F. (1959). "John Ronald Womersley (Obituary)". J London Math Soc. 370: s1–34. 
  2. ^ a b "John Womersley". Retrieved 2017-05-06. 
  3. ^ a b c d e f g h i j k l Carpenter, B. E.; Doran, R. W. (2014-04-01). "John Womersley: Applied Mathematician and Pioneer of Modern Computing". IEEE Annals of the History of Computing. 36 (2): 60–70. ISSN 1058-6180. doi:10.1109/MAHC.2014.25. 
  4. ^ Smithies, F. (1959-07-01). "John Ronald Womersley". Journal of the London Mathematical Society. s1-34 (3): 370–372. ISSN 1469-7750. doi:10.1112/jlms/s1-34.3.370. 
  5. ^ E., Fienberg, Stephen (1985-01-01). Celebration of Statistics : the ISI Centenary Volume. Springer New York. ISBN 9781461385608. OCLC 958529610. 
  6. ^ Darwin, Sir Charles (1958). "John R. Womersley Obituary Tribute". Nature. 181 (461): 1240. 
  7. ^
  8. ^ "Donald Davies". Retrieved 2017-05-06. 
  9. ^ Andrew., Hodges,. Alan Turing : the enigma. Princeton University Press. ISBN 9780691155647. OCLC 898328463. 
  10. ^ "Computer Resurrection Issue 44". Retrieved 2017-05-07. 
  11. ^ "A Personal History of HM Nautical Almanac Office by D.H. Sadler". Retrieved 2017-05-06. 
  12. ^ ), Copeland, B. Jack, (1950- (2012-01-01). Alan Turing's electronic brain : the struggle to build the ACE, the world's faster computer. Oxford University Press. ISBN 9780199609154. OCLC 812620790. 
  13. ^ Mary., Croarken, (1990-01-01). Early scientific computing in brain. Clarendon Press. ISBN 9780198537489. OCLC 802656819. 
  14. ^ "Computer Resurrection Issue 22". Retrieved 2017-05-06. 
  15. ^ "Ray Bird - the HEC1 computer". The British Library. Retrieved 2017-05-07. 
  16. ^ a b F., O'Rourke, Michael; Charalambos., Vlachopoulos, (2011-01-01). McDonald's blood flow in arteries : theoretical, experimental and clinical principles. Hodder Arnold. ISBN 9780340985014. OCLC 779679482. 
  17. ^ Womersley, J. R. (1955-03-28). "Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known". The Journal of Physiology. 127 (3): 553–563. ISSN 0022-3751. PMC 1365740Freely accessible. PMID 14368548. 
  18. ^ a b Wood, N. B. (1999-07-21). "Aspects of fluid dynamics applied to the larger arteries". Journal of Theoretical Biology. 199 (2): 137–161. ISSN 0022-5193. PMID 10395811. doi:10.1006/jtbi.1999.0953. 
  19. ^ Loudon, Catherine; Tordesillas, Antoinette. "The Use of the Dimensionless Womersley Number to Characterize the Unsteady Nature of Internal Flow". Journal of Theoretical Biology. 191 (1): 63–78. doi:10.1006/jtbi.1997.0564. 
  20. ^ Carpenter, B.E.; Doran, R.W.; Womersley, John (2014). "Applied Mathematician and Pioneer of Modern Computing". IEEE Annals of the History of Computing. 36 (2): 60–70. doi:10.1109/MAHC.2014.25. 
  21. ^

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