\[ \begin{align}\begin{aligned}\newcommand\blank{~\underline{\hspace{1.2cm}}~}\\% Bold symbols (vectors) \newcommand\bs[1]{\mathbf{#1}}\\% Poor man's siunitx \newcommand\unit[1]{\mathrm{#1}} \newcommand\num[1]{#1} \newcommand\qty[2]{#1~\unit{#2}}\\\newcommand\per{/} \newcommand\squared{{}^2} % % Scale \newcommand\milli{\unit{m}} \newcommand\centi{\unit{c}} \newcommand\kilo{\unit{k}} \newcommand\mega{\unit{M}} % % Angle \newcommand\radian{\unit{rad}} \newcommand\degree{\unit{{}^\circ}} % % Time \newcommand\second{\unit{s}} % % Distance \newcommand\meter{\unit{m}} \newcommand\m{\meter} \newcommand\inch{\unit{in}} \newcommand\feet{\unit{ft}} \newcommand\mile{\unit{mi}} \newcommand\mi{\mile} % % Volume \newcommand\gallon{\unit{gal}} % % Mass \newcommand\gram{\unit{g}} \newcommand\g{\gram} % % Frequency \newcommand\hertz{\unit{Hz}} \newcommand\rpm{\unit{rpm}} % % Voltage \newcommand\volt{\unit{V}} \newcommand\V{\volt} \newcommand\millivolt{\milli\volt} \newcommand\mV{\milli\volt} \newcommand\kilovolt{\kilo\volt} \newcommand\kV{\kilo\volt} % % Current \newcommand\ampere{\unit{A}} \newcommand\A{\ampere} \newcommand\milliampereA{\milli\ampere} \newcommand\mA{\milli\ampere} \newcommand\kiloampereA{\kilo\ampere} \newcommand\kA{\kilo\ampere} % % Resistance \newcommand\ohm{\Omega} \newcommand\milliohm{\milli\ohm} \newcommand\kiloohm{\kilo\ohm} % correct SI spelling \newcommand\kilohm{\kilo\ohm} % "American" spelling used in siunitx \newcommand\megaohm{\mega\ohm} % correct SI spelling \newcommand\megohm{\mega\ohm} % "American" spelling used in siunitx % % Inductance \newcommand\henry{\unit{H}} \newcommand\H{\henry} \newcommand\millihenry{\milli\henry} \newcommand\mH{\milli\henry} % % Temperature \newcommand\celsius{\unit{^{\circ}C}} \newcommand\C{\unit{\celsius}} \newcommand\fahrenheit{\unit{^{\circ}F}} \newcommand\F{\unit{\fahrenheit}} \newcommand\kelvin{\unit{\K}} \newcommand\K{\unit{\kelvin}}\\% Power \newcommand\watt{\unit{W}} \newcommand\W{\watt} \newcommand\milliwatt{\milli\watt} \newcommand\mW{\milli\watt} \newcommand\kilowatt{\kilo\watt} \newcommand\kW{\kilo\watt} % % Torque \newcommand\ozin{\unit{oz}\text{-}\unit{in}} \newcommand\newtonmeter{\unit{N\text{-}m}}\end{aligned}\end{align} \]

Apr 16, 2025 | 267 words | 3 min read

2.2.5. Fluid Mechanics

The Reynolds number is a key parameter used to determine whether fluid flow will be laminar or turbulent. For fluid flow through a pipe, the Reynolds number is given by (2.1):

(2.1)\[R_e={Vd \over v}\]

where \(R_e\) is the Reynolds number (a dimensionless value), \(V\) is the velocity \((\frac{\meter}{\second})\) or \((\frac{\feet}{\second})\) of the fluid, \(d\) is the diameter of the pipe \((\meter)\) or \((\feet)\), and \(v\) is the kinematic viscosity of the fluid \(({\meter \over \second^2})\) or \(({\feet \over \second^2})\). The kinematic viscosity, v, is a measure of the fluid’s resistance to flow and stress.

Except when at extremely high pressures, a liquid fluid’s kinematic viscosity is dependent on temperature and is independent of pressure. The following chart lists the kinematic viscosity of water at three different temperatures:

Table 2.10 Viscosity Data

Temperature\((\C)\)	Kinematic Viscosity (\({\meter^2 \over s}\))
\(5\)	\(1.52\times 10^{-6}\)
\(20\)	\(1.00\times 10^{-6}\)
\(50\)	\(5.54\times 10^{-7}\)

Using this information, write a Python program that asks the user for the velocity of the water flowing through a pipe (\((V)\)), for the pipe’s diameter \((d)\), and to select a temperature \((T)\) from \(5\C\), \(20\C\), and \(50\C\). Your program should then calculate the Reynolds number based on the input values.

Hint

The string for printing \(^\circ\) is “\u00b0”, which is the Unicode value for this symbol.

Sample Output

Use the values in Table 2.11 below to test your program.

Table 2.11 Test Cases

Case	\(T \ (\C)\)	\(V \ ({\meter \over \second})\)	\(d \ (\meter)\)
1	5	3.5	1.5
2	20	0.001	0.15
3	50	0.9	0.02

Ensure your program’s output matches the provided samples exactly. This includes all characters, white space, and punctuation. In the samples, user input is highlighted like this for clarity, but your program should not highlight user input in this way.

Case 1 Sample Output

$ python3 fluid_mechanics_login.py Enter the temperature in °C as 5, 20, or 50: 5 Enter the velocity of water in the pipe (m/s): 3.5 Enter the pipe's diameter (m): 1.5 At 5.0°C, the Reynolds number for flow at 3.5 m/s in a 1.5 m diameter pipe is 3.45e+06.

Case 2 Sample Output

$ python3 fluid_mechanics_login.py Enter the temperature in °C as 5, 20, or 50: 20 Enter the velocity of water in the pipe (m/s): 0.001 Enter the pipe's diameter (m): 0.15 At 20.0°C, the Reynolds number for flow at 0.001 m/s in a 0.15 m diameter pipe is 1.50e+02.

Case 3 Sample Output

$ python3 fluid_mechanics_login.py Enter the temperature in °C as 5, 20, or 50: 50 Enter the velocity of water in the pipe (m/s): 0.9 Enter the pipe's diameter (m): 0.02 At 50.0°C, the Reynolds number for flow at 0.9 m/s in a 0.02 m diameter pipe is 3.25e+04.

Deliverables

Save your finished program as fluid_mechanics_login.py, replacing login with your Purdue login. Then submit it along with all the deliverables listed in Table 2.12 below.

Table 2.12 Deliverables

Deliverable	Description
fluid_mechanics_login.py	Your finished program.
Screenshot(s)	PNG(s) capturing all 3 test cases.