Re1: Calculating the Reynolds Number 1

In iemisc: Irucka Embry's Miscellaneous Functions

Calculating the Reynolds Number 1

Description

Various Methods of Calculating the Reynolds number

Usage

Re1(D, V, rho, mu, gc = NULL, units = c("SI", "Eng", "slug"))

Arguments

D	numeric vector that contains the hydraulic diameters '(four times the area in flow divided by the wetted surface) is a characteristic length' (m or ft) Reference: Lindeburg Manual
V	numeric vector that contains the average fluid velocity (m/s or ft/s) Reference: Lindeburg Manual
rho	numeric vector that contains the fluid density (kg/m^3 or lbm/ft^3) Reference: Lindeburg Manual
mu	numeric vector that contains the absolute or dynamic viscosity of the fluid (Pa-s or lbf-sec/ft^2) Reference: Lindeburg Manual
gc	numeric vector that contains the gravitational constant (32.2 lbm-ft/lbf-sec^2) Reference: Lindeburg Manual
units	character vector that contains the system of units options are SI for International System of Units, Eng for English units (United States Customary System in the United States and Imperial Units in the United Kingdom), and slug for the English unit slug which is a consistent unit of mass

Details

The Reynolds number, named after Osborne Reynolds, is a dimensionless number that is used to determine the type of fluid flow (laminar, transition, or turbulent). References: Lindeburg Manual and Subramanian

Re1 - uses the absolute or dynamic viscosity (\mu) Re2 and Re4 - use kinematic viscosity (\nu) Re3 - uses the 'mass flow rate per unit area' (G) Reference: Lindeburg Manual

The Reynolds number equation can be expressed in the following ways (Reference: Lindeburg Manual):

Re = \frac{inertial_forces}{viscous_forces}

Re = \frac{DV\\rho}{\\mu}

Re

the Reynolds number (dimensionless)

D

the hydraulic diameters (m)

V

average velocity of the fluid (m/s)

\rho

density of the fluid at a certain temperature (kg/m^3)

\mu

absolute or dynamic viscosity of the fluid at a certain temperature (Pa-s)

Re = \frac{DV\\rho}{\\mug_c}

Re

the Reynolds number (dimensionless)

D

the hydraulic diameters (ft)

V

average velocity of the fluid (ft/sec)

\rho

density of the fluid at a certain temperature (lbm/ft^3)

\mu

absolute or dynamic viscosity of the fluid at a certain temperature (lbf-sec/ft^2)

g_c

gravitational constant (32.2 lbm-ft/lbf-sec^2) used for dimensional analysis so that the Reynolds number will be dimensionless with US Customary units

Re = \frac{DG}{\\mu}

Re

the Reynolds number (dimensionless)

D

the hydraulic diameters (m)

G

'mass flow rate per unit area' (kg/m^2-s)

\mu

absolute or dynamic viscosity of the fluid at a certain temperature (Pa-s)

Re = \frac{DG}{g_c\\mu}

Re

the Reynolds number (dimensionless)

D

the hydraulic diameters (ft)

G

'mass flow rate per unit area' (lbm/ft^2-sec)

\mu

absolute or dynamic viscosity of the fluid at a certain temperature (lbf-sec/ft^2)

g_c

gravitational constant (32.2 lbm-ft/lbf-sec^2) used for dimensional analysis so that the Reynolds number will be dimensionless with US Customary units

where

G = {\\rhoV}

G

'mass flow rate per unit area' (kg/m^2-s)

\rho

density of the fluid at a certain temperature (kg/m^3)

V

average velocity of the fluid (m/s)

Re = \frac{DV}{\\nu}

Re

the Reynolds number (dimensionless)

D

the hydraulic diameters (m)

V

average velocity of the fluid (m/s)

\nu

kinematic viscosity of the fluid at a certain temperature (m^2/s)

Re = \frac{DV}{\\nug_c}

Re

the Reynolds number (dimensionless)

D

the hydraulic diameters (ft)

V

average velocity of the fluid (ft/sec)

\nu

absolute or dynamic viscosity of the fluid at a certain temperature (lbf-sec/ft^2)

g_c

gravitational constant (32.2 lbm-ft/lbf-sec^2) used for dimensional analysis so that the Reynolds number will be dimensionless with US Customary units

where

\\nu = \frac{\\mu}{\\rho}

\nu

kinematic viscosity of the fluid at a certain temperature (m^2/s)

\mu

absolute or dynamic viscosity of the fluid at a certain temperature (Pa-s)

\rho

density of the fluid at a certain temperature (kg/m^3)

where

\\nu = \frac{\\mug_c}{\\rho}

\nu

kinematic viscosity of the fluid at a certain temperature (ft^2/sec)

\mu

absolute or dynamic viscosity of the fluid at a certain temperature (lbf-sec/ft^2)

g_c

gravitational constant (32.2 lbm-ft/lbf-sec^2) used for dimensional analysis so that the kinematic viscosity units will work in US Customary units

\rho

density of the fluid at a certain temperature (lbm/ft^3)

Value

the Reynolds number as a list for Re1

Note

Please Note: The conventional wisdom that a Reynolds number less than 2100 is laminar flow, between 2100 and 4000 is transitional or critical flow, and greater than 4000 is turbulent flow is not accurate. 'Reynolds himself observed that turbulence was triggered by inlet disturbances to the pipe and the laminar state could be maintained to Re \u2248 12,000 if he took great care in minimizing external disturbances to the flow. By careful design of pipe entrances Ekman (1910) has maintained laminar pipe flow up to a Reynolds number of 40,000 and Pfenniger (1961) up to 100,000 by minimising ambient disturbances.' References: Lindeburg Manual and Trinh

'Numerous experiments have shown that the flow in a pipe changes from laminar to turbulent in the range of R between the critical value of 2,000 and a value that may be as high as 50,000.* In these experiments the diameters of the pipe was taken as the characteristic length in defining the Reynolds number. When the hydraulic radius is taken as the characteristic length, the corresponding range is from 500 to 12,500,* since the diameters of a pipe is four times its hydraulic radius. * = It should be noted that there is actually no definite upper limit.' Reference: Chow

Note: Units must be consistent

Author(s)

Irucka Embry

References

1. Ven Te Chow, Ph.D., Open-Channel Hydraulics, McGraw-Hill Classic Textbook Reissue, New York City, New York: McGraw-Hill Book Company, 1988, pages 7-8.

2. Michael R. Lindeburg, PE, Civil Engineering Reference Manual for the PE Exam, Twelfth Edition, Belmont, California: Professional Publications, Inc., 2011, pages 17-1, 17-5, 17-8 - 17-9.

3. The NIST Reference on Constants, Units, and Uncertainty, Fundamental Constants Data Center of the NIST Physical Measurement Laboratory, "standard acceleration of gravity g_n", https://physics.nist.gov/cgi-bin/cuu/Value?gn.

4. R. Shankar Subramanian, "Pipe Flow Calculations", page 9, Clarkson University Department of Chemical and Biomolecular Engineering, https://web2.clarkson.edu/projects/subramanian/ch330/notes/Pipe%20Flow%20Calculations.pdf.

5. R. Shankar Subramanian, "Reynolds Number", page 1, Clarkson University Department of Chemical and Biomolecular Engineering, https://web2.clarkson.edu/projects/subramanian/ch330/notes/Reynolds%20Number.pdf.

6. Khanh Tuoc Trinh, "On the Critical Reynolds Number for Transition From Laminar to Turbulent Flow", page 2, https://arxiv.org/abs/1007.0810.

7. Wikimedia Foundation, Inc. Wikipedia, 15 May 2019, "Conversion of units", https://en.wikipedia.org/wiki/Conversion_of_units.

See Also

f1, f2, f3, f4, f5, f6, f7, and f8 for the Darcy friction factor (f) for pipes

Re2, Re3, Re4

Examples

# from Lindeburg Reference page 17-8
# D = 0.3355 ft
# V = 7.56 ft/sec

# from the Chow reference, water at 68 F (20 C) has the following properties

library(iemisc)

# mu (dynamic viscosity) = 2.09 * 10 ^ -5 slug/ft-sec
# rho (density) = 1.937 slug/ft^3
# v (kinematic viscosity) = mu / rho = 1.08 * 10 ^ -5

Re1(D = 0.3355, V = 7.56, rho = 1.937, mu = 2.09 * 10 ^ -5, units = "slug")

iemisc documentation built on Sept. 25, 2023, 5:09 p.m.