Calculation of the Pressure Gradient in the Region near the Entrance of the Circular Pipe by the Variational Method

The variational method is used to calculate the pressure gradient in the region near the entrance of a circular pipe in the case of laminar flow. The functional of the velocity distribution is chosen, whose stationary value gives the pressure gradient along the axis of the pipe, and the condition th...

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Bibliographic Details
Published inNippon Kikai Gakkai Rombunshū Vol. 21; no. 105; pp. 321 - 324
Main Authors UEMATU, Tokio, HATTA, Keiji, NAKAMURA, Sadao
Format Journal Article
LanguageEnglish
Japanese
Published The Japan Society of Mechanical Engineers 1955
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Summary:The variational method is used to calculate the pressure gradient in the region near the entrance of a circular pipe in the case of laminar flow. The functional of the velocity distribution is chosen, whose stationary value gives the pressure gradient along the axis of the pipe, and the condition that the functional takes the stationary value coincides with the equation of motion. The velocity distribution is assumed to be the form of generalized parabolic arc. The result is that the correction of Hagenbach is 2.25 (ρu^-2/2), where ρ is the density of fluid and u^- is the mean velocity in the pipe. The velocity distribution also coincides fairly well with Nikuradse's experimental result.
ISSN:0029-0270
2185-9485
DOI:10.1299/kikai1938.21.321