Hydrodynamic Entrance Lengths for Ducts of Arbitrary Cross Section

1967 ◽  
Vol 89 (4) ◽  
pp. 847-850 ◽  
Author(s):  
S. T. McComas
Keyword(s):  
Velocity Profile ◽  
Detailed Analysis ◽  
Cross Section ◽  
Analytical Method ◽  
Arbitrary Cross Section ◽  
Numerical Results ◽  
Entrance Length ◽  
Flow Development

A general analytical method is presented for determination of the hydrodynamic entrance length of ducts of arbitrary cross section. Only knowledge of the fully developed velocity profile is required in order to determine this length in comparison to other approaches which require a detailed analysis of the flow development. This method is applied to circular, elliptical, annular, rectangular, and triangular ducts with numerical results presented.

Pressure Drop Due to the Entrance Region in Ducts of Arbitrary Cross Section

1964 ◽  
Vol 86 (3) ◽  
pp. 620-626 ◽  
Author(s):  
T. S. Lundgren ◽  
E. M. Sparrow ◽  
J. B. Starr
Keyword(s):  
Pressure Drop ◽  
Velocity Profile ◽  
Cross Section ◽  
Cross Sections ◽  
Circular Tube ◽  
Essential Feature ◽  
Arbitrary Cross Section ◽  
Entrance Region ◽  
Flow Development ◽  
Prior Analysis

A general analytical method has been devised for determining the pressure drop due to flow development in the entrance region of ducts of arbitrary cross section. The essential feature of the analysis is that the pressure drop can be determined without actually solving for the entrance-region velocity development. Instead, the calculation only requires a knowledge of the fully developed velocity profile. Application of the method is made to a variety of cross sections including the circular tube, elliptical ducts, rectangular ducts, isosceles triangular ducts, and annular ducts. Numerical results are presented and comparisons are made with available experiments and with prior analysis.

Graphical-Numerical Solution of Problems of Saint-Venant Torsion and Bending

1953 ◽  
Vol 20 (3) ◽  
pp. 321-326
Author(s):  
B. A. Boley
Keyword(s):  
Cross Section ◽  
Stress Function ◽  
Arbitrary Cross Section ◽  
Successive Approximations ◽  
Shear Stresses ◽  
Shearing Stress ◽  
First Approximation ◽  
Difference Form ◽  
Bending Of Beams

Abstract A simple successive-approximations procedure for the solution of the problems of Saint-Venant torsion and bending of beams of arbitrary cross section is presented. The shear stresses in a cross section of the beam are first calculated from the formulas valid for thin-walled sections, on the basis of an assumed set of lines of shearing stress. From these a first approximation to the stress function of either the torsion or the bending problem is found. The second approximation to the stress function is then obtained from the governing equation of the problem, expressed in finite-difference form; this in turn allows the determination of an improved set of lines of shearing stress, and hence of the shearing stress itself. The procedure can be repeated until the results of two successive steps are sufficiently close. Applications are presented for a beam cross section for which the exact solutions are known, and it is shown that no further difficulties arise in applications to more complicated shapes.

scholarly journals The regularities of resistance and flow in pipes and wide channels

2018 ◽  
Vol 193 ◽  
pp. 02034
Author(s):  
Ilya Bryansky ◽  
Yuliya Bryanskaya ◽  
Аleksandra Оstyakova
Keyword(s):  
Comparative Analysis ◽  
Velocity Profile ◽  
Hydraulic Resistance ◽  
Cross Section ◽  
Resistance Coefficient ◽  
Hydraulic Structures ◽  
Hydraulic Characteristics ◽  
Hydraulic Resistance Coefficient ◽  
Logarithmic Velocity Profile

The data of hydraulic characteristics of flow are required to be more accurate to increase reliability and accident-free work of water conducting systems and hydraulic structures. One of the problems in hydraulic calculations is the determination of friction loss that is associated with the distribution of velocities over the cross section of the flow. The article presents a comparative analysis of the regularities of velocity distribution based on the logarithmic velocity profile and hydraulic resistance in pipes and open channels. It is revealed that the Karman parameter is associated with the second turbulence constant and depend on the hydraulic resistance coefficient. The research showed that the behavior of the second turbulence constant in the velocity profile is determined mainly by the Karman parameter. The attached illustrations picture the dependence of logarithmic velocity profile parameters based on different values of the hydraulic resistance coefficient. The results of the calculations were compared to the experimental-based Nikuradze formulas for smooth and rough pipes.

Sign in / Sign up

Export Citation Format

Share Document