iemisc: Calculating the Reynolds number Examples

In iemisc: Irucka Embry's Miscellaneous Functions

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Replicate the R code

Note: If you wish to replicate the R code below, then you will need to copy and paste the following commands in R first (to make sure you have all the packages and their dependencies):

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install.packages(c("install.load", "iemisc", "units", "round"))
# install the packages and their dependencies

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# load the required packages
install.load::load_package("iemisc",  "units", "round")
# load needed packages using the load_package function from the install.load package (it is assumed that you have already installed these packages)

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Problem 1 Statement

Problem 17.2 [Lindeburg Practice]

“Points A and B are separated by 3000 ft of new 6 in schedule-40 steel pipe. 750 gal/min of 60°F water flows from point A to point B. Point B is 60 ft above point A.”

What is the Reynolds number?

From Appendix 16.B Dimensions of Welded and Seamless Steel Pipe [Lindeburg Manual], the internal diameter for a 6 inch nominal diameter new schedule-40 steel pipe is 0.5054 ft with an internal area of 0.2006 ft^2^.

From Table 17.2 Values of Specific Roughness for Common Pipe Materials [Lindeburg Manual], the specific roughness, $\epsilon$, for a steel pipe is 0.0002 (2e^-04^) ft.

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Solution 1

# 60 degrees Fahrenheit water
# new 6 in schedule-40 steel pipe
# determine the Reynolds number


# given the water flow of 750 gal / min
# create a numeric vector with the units of gallons per minute for the volumetric flow rate
Vdot <- set_units(750, gallon/min)
Vdot


# create a numeric vector with the units of cubic feet per second for the volumetric flow rate
Vdot <- Vdot

units(Vdot) <- make_units(ft^3/s)
Vdot



# given temperature of 60 degrees Fahrenheit
# create a numeric vector with the units of degrees Fahrenheit
T_F <- set_units(60, degree_F)


# create a numeric vector to convert from degrees Fahrenheit to Kelvin
T_K <- T_F
T_K

# create a numeric vector with the units of Kelvin
units(T_K) <- make_units(K)
T_K

# saturated liquid density at 60 degrees Fahrenheit (SI units)
rho_SI <- density_water(drop_units(T_K), units = "Absolute")

rho_SI <- set_units(rho_SI, kg/m^3)
rho_SI


# saturated liquid density at 60 degrees Fahrenheit (US Customary units)
rho_Eng <- density_water(drop_units(T_F), units = "Eng", Eng_units = "lbm/ft^3")

rho_Eng <- set_units(rho_Eng, lb/ft^3) # lbm/ft^3
rho_Eng


# kinematic viscosity at 60 degrees Fahrenheit and density of rho (SI units)
nu_SI <- kin_visc_water(mu = dyn_visc_water(Temp = drop_units(T_K), units = "Absolute"), rho = density_water(Temp = drop_units(T_K), units = "Absolute"), rho_units = "kg/m^3", mu_units = "Pa*s or kg/m/s")

nu_SI <- set_units(nu_SI, m^2/s)
nu_SI



# kinematic viscosity at 60 degrees Fahrenheit and density of rho (US Customary units)
nu_Eng <- kin_visc_water(mu = dyn_visc_water(Temp = drop_units(T_F), units = "Eng", Eng_units = "lbf*s/ft^2"), rho = density_water(Temp = drop_units(T_F), units = "Eng", Eng_units = "lbm/ft^3"), rho_units = "lbm/ft^3", mu_units = "lbf*s/ft^2")

nu_Eng <- set_units(nu_Eng, ft^2/s)
nu_Eng


# absolute or dynamic viscosity at 60 degrees Fahrenheit and density of rho (SI units)
mu_SI <- dyn_visc_water(Temp = drop_units(T_K), units = "Absolute")

mu_SI <- set_units(mu_SI, Pa*s)
mu_SI


# absolute or dynamic viscosity at 60 degrees Fahrenheit and density of rho (US Customary units)
mu_Eng <- dyn_visc_water(Temp = drop_units(T_F), units = "Eng", Eng_units = "lbf*s/ft^2")

mu_Eng <- set_units(mu_Eng, lbf*s/ft^2)
mu_Eng


# create a numeric vector with the units of feet for the given specific roughness
epsilon <- set_units(2e-04, ft)
epsilon


# create a numeric vector with the units of feet for the given internal pipe diameter
Di <- set_units(0.5054, ft)
Di



# relative roughness (dimensionless) of the steel pipe
rel_roughness <- epsilon / Di
rel_roughness


# internal area of the steel pipe
Ai <- Di ^ 2 * pi / 4
Ai


# average velocity of the flowing water
V <- Vdot / Ai
V


# Reynolds number using the kinematic viscosity
Re_nu <- Re2(D = drop_units(Di), V = drop_units(V), nu = drop_units(nu_Eng))
Re_nu


# Reynolds number using the absolute or dynamic viscosity
Re_mu <- Re1(D = drop_units(Di), V = drop_units(V), rho = drop_units(rho_Eng), mu = drop_units(mu_Eng), units = "Eng")
Re_mu


# display Re_nu with scientific notation
format(Re_nu, scientific = TRUE)

# display Re_mu with scientific notation
format(Re_mu, scientific = TRUE)

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Michael Lindeburg calculated the Reynolds number as r round_r3((8.33*0.5054)/(1.217e-05), d = 2) [rounded to 3.46e^05^].

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Problem 2 Statement

“This month’s problem asked what flow rate of water would be needed to have fully developed turbulent flow in a circular tube.” [Fosse]

What is the Reynolds number given the mass flow rate?

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Solution 2

# given temperature of 22 degrees Celsius
# create a numeric vector with the units of degrees Celsius
T_C <- set_units(22, degree_C)
T_C


# create a numeric vector to convert from degrees Celsius to Kelvin
T_K <- T_C
T_K

# create a numeric vector with the units of Kelvin
units(T_K) <- make_units(K)
T_K


# saturated liquid density at 22 degrees Celsius (SI units)
rho_SI <- density_water(drop_units(T_K), units = "Absolute")

rho_SI <- set_units(rho_SI, kg/m^3)
rho_SI


# kinematic viscosity at 60 degrees Fahrenheit and density of rho (SI units)
nu_SI <- kin_visc_water(mu = dyn_visc_water(Temp = drop_units(T_K), units = "Absolute"), rho = density_water(Temp = drop_units(T_K), units = "Absolute"), rho_units = "kg/m^3", mu_units = "Pa*s or kg/m/s")

nu_SI <- set_units(nu_SI, m^2/s)
nu_SI


# absolute or dynamic viscosity at 60 degrees Fahrenheit and density of rho (SI units)
mu_SI <- dyn_visc_water(Temp = drop_units(T_K), units = "Absolute")

mu_SI <- set_units(mu_SI, Pa*s)
mu_SI



# create a numeric vector with the units of inches for the given internal pipe diameter
Di <- set_units(4, inch)
Di

# create a numeric vector with the units of meters for the given internal pipe diameter
Di <- Di
Di

units(Di) <- make_units(m)
Di


# given the mass flow rate of 0.765 kg/s (rounded in HTML)
# create a numeric vector with the units of kilograms per second for the mass flow rate
G <- set_units(0.76486004, kg/s)
G


# display the Reynolds number
re3 <- Re3(D = drop_units(Di), G = drop_units(G), mu = drop_units(mu_SI), units = "SI")
re3

# display the Reynolds number from Re3 with scientific notation
format(re3, scientific = TRUE)

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Kendall Fosse provided 1e^04^ for the Reynolds number.

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Works Cited

Kendall Fosse, “What rate is needed for turbulent flow? [Challenge Solved]”, ChEnected, https://www.aiche.org/chenected/2010/10/what-rate-needed-turbulent-flow-challenge-solved.

Michael R. Lindeburg, PE, Civil Engineering Reference Manual for the PE Exam, Twelfth Edition, Belmont, California: Professional Publications, Inc., 2011, page 17-4, 17-7, and A-22.

Michael R. Lindeburg, PE, Practice Problems for the Civil Engineering PE Exam: A Companion to the “Civil Engineering Reference Manual”, Twelfth Edition, Belmont, California: Professional Publications, Inc., 2011, pages 17-1 and 17-7.

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.

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

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Copyright and License

All R code written by Irucka Embry is distributed under the GPL-3 (or later) license, see the GNU General Public License {GPL} page.

All written content originally created by Irucka Embry is copyrighted under the Creative Commons Attribution-ShareAlike 4.0 International License. All other written content retains the copyright of the original author(s).

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