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Publication detail
ŠTIGLER, J.
Original Title
Analytical Formula for the Mean Velocity Profile in a Pipe Derived on the Basis of a Spatial Polynomial Vorticity Distribution
Type
journal article in Web of Science
Language
English
Original Abstract
The derivation of the mean velocity profile for a given vorticity distribution over the pipe cross-section is presented in this paper1. The velocity profile and the vorticity distribution are axisymmetric, which means that the radius is the only variable. The importance of the vortex field for the flow analysis is discussed in the paper. The polynomial function with four free parameters is chosen for the vorticity distribution. Free parameters of this function are determined using boundary conditions. There are also two free exponents in the polynomial. These exponents are determined based on the comparison of this analytical formula with experimental data. Experimental data are taken from the Princeton superpipe data which consist of 26 velocity profiles for a wide range of Reynolds numbers (Re). This analytical formula for the mean velocity profile is more precise than the previous one and it is possible to use it for the wide range of Reynolds number <31,577; 35,259,000>. This formula is easy to use, to integrate, or to derivate. The empirical formulas for the profile parameters as a function of Re are also included in this paper. All information for the mean velocity profile prediction in the mentioned Re range are in the paper. It means that it is necessary to know the average velocity v((av)), the pipe radius R, and Re to be able to predict the turbulent mean velocity profile in a pipe.
Keywords
fluid flow in pipe; turbulent mean velocity profile; vorticity
Authors
Released
14. 5. 2021
Publisher
MDPI
Location
BASEL
ISBN
2073-4441
Periodical
Water
Year of study
13
Number
10
State
Swiss Confederation
Pages from
1
Pages to
27
Pages count
URL
https://www.mdpi.com/2073-4441/13/10/1372
Full text in the Digital Library
http://hdl.handle.net/11012/201645
BibTex
@article{BUT172540, author="Jaroslav {Štigler}", title="Analytical Formula for the Mean Velocity Profile in a Pipe Derived on the Basis of a Spatial Polynomial Vorticity Distribution", journal="Water", year="2021", volume="13", number="10", pages="1--27", doi="10.3390/w13101372", issn="2073-4441", url="https://www.mdpi.com/2073-4441/13/10/1372" }