Calculation of the Pressure Gradient along a Pipe of Uniform Cross-section

It is difficult to solve the differential equation determining the velocity distribution in a pipe of uniform cross-section, which has complicated boundaries. One of the methods of solution in such cases is to use the variational principle. When the quantity of flow is given, the functional which gi...

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Bibliographic Details
Published inNippon Kikai Gakkai Rombunshū Vol. 22; no. 117; pp. 301 - 306
Main Authors UEMATU, Tokio, HATTA, Keiji, OGAWA, Toru
Format Journal Article
LanguageEnglish
Japanese
Published The Japan Society of Mechanical Engineers 1956
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Summary:It is difficult to solve the differential equation determining the velocity distribution in a pipe of uniform cross-section, which has complicated boundaries. One of the methods of solution in such cases is to use the variational principle. When the quantity of flow is given, the functional which gives an approximate value of the pressure gradient along the axis greater than the true value is already known. The authors have got the functional which gives an approximate value smaller than the true value. Using these two values, it is .possib1e to determine the region in which the true value exists. As examples, the pipe of rectangular cross-section and the pipes of circular cross-section with one or two inside cores of circular cross-section are treated.
ISSN:0029-0270
2185-9485
DOI:10.1299/kikai1938.22.301