Notebook

Buckingham $\pi$ : Dimensional Analysis¶

Mokbel Karam, and Prof. Tony Saad (www.tsaad.net)
Department of Chemical Engineering
University of Utah

This notebook represents the graphical user interface of `buckinghamPy`

In [1]:

#HIDDEN
# please run this cell to get access the GUI app
from buckinghampy import BuckinghamPiGui
GUI=BuckinghamPiGui()

HBox(children=(BoundedIntText(value=5, continuous_update=True, description='Number of Variables:', style=Descr…

VBox(children=(Box(children=(Textarea(value='', description='Name:', layout=Layout(height='32px', width='auto'…

Output()

Example 1: Pressure Drop in Pipe¶

In [2]:

from buckinghampy import BuckinghamPi

Pressure_Drop = BuckinghamPi()
Pressure_Drop.add_variable(name='{\\Delta}p',units='M*L^(-1)*T^(-2)')     # pressure drop
Pressure_Drop.add_variable(name='R',units='L')                            # length of the pipe
Pressure_Drop.add_variable(name='d',units='L')                            # diameter of the pipe
Pressure_Drop.add_variable(name='\\mu',units='M*L^(-1)*T^(-1)')           # viscosity
Pressure_Drop.add_variable(name='Q',units='L^(3)*T^(-1)')                 # volumetic flow rate

Pressure_Drop.generate_pi_terms()
Pressure_Drop.print_all()

$\text{Set }1: \quad\pi_1 = \frac{R}{d}\quad\pi_2 = \frac{Q \mu}{d^{3} {\Delta}p}\quad$

$\text{Set }2: \quad\pi_1 = \frac{R \sqrt[3]{{\Delta}p}}{\sqrt[3]{Q} \sqrt[3]{\mu}}\quad\pi_2 = \frac{d \sqrt[3]{{\Delta}p}}{\sqrt[3]{Q} \sqrt[3]{\mu}}\quad$

$\text{Set }3: \quad\pi_1 = \frac{d}{R}\quad\pi_2 = \frac{Q \mu}{R^{3} {\Delta}p}\quad$

In [ ]:

Buckingham π\pi: Dimensional Analysis¶

Example 1: Pressure Drop in Pipe¶

Buckingham $\pi$ : Dimensional Analysis¶