#!/usr/bin/env python
# coding: utf-8

# # Buckingham $\pi$:  Dimensional Analysis
# **Mokbel Karam, and Prof. Tony Saad (<a href='www.tsaad.net'>www.tsaad.net</a>) <br/>Department of Chemical Engineering <br/>University of Utah**
# <hr/>

# In[1]:


from IPython.display import Image
from IPython.core.display import HTML 


# In this Jupyter notebook we will execute the code presented in the paper.

# # Example 1: Pressure Inside a Bubble
# ---

# Using mass, length and time as fundamental physical dimensions:

# In[2]:


from buckinghampy import BuckinghamPi

Pressure_In_Bubble = BuckinghamPi()
Pressure_In_Bubble.add_variable(name='{\\Delta}p',units='M*L^(-1)*T^(-2)')  # pressure 
Pressure_In_Bubble.add_variable(name='R',units='L')                         # diameter
Pressure_In_Bubble.add_variable(name='\\sigma',units='M*T^(-2)')            # surface tension
try:
    Pressure_In_Bubble.generate_pi_terms()
    Pressure_In_Bubble.print_all()
except Exception as e:
    print(e)


# ---

# Using force and length as fundamental physical dimensions:

# In[3]:


from buckinghampy import BuckinghamPi

Pressure_In_Bubble = BuckinghamPi()
Pressure_In_Bubble.add_variable(name='{\\Delta}p',units='F*L^(-2)')       # pressure 
Pressure_In_Bubble.add_variable(name='R',units='L')                       # diameter
Pressure_In_Bubble.add_variable(name='\\sigma',units='F*L^(-1)')          # surface tension

Pressure_In_Bubble.generate_pi_terms()
Pressure_In_Bubble.print_all()


# # Example 2: Pressure Drop in a Pipe
# ---

# In[4]:


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()


# # Example 3: Economic Growth
# ---

# In[5]:


from buckinghampy import BuckinghamPi

Economic_Growth = BuckinghamPi()
Economic_Growth.add_variable(name='P',units='K',explicit=True)           # capital
Economic_Growth.add_variable(name='L',units='Q/T')                       # labor per period of time
Economic_Growth.add_variable(name='{\\omega_{L}}',units='K/Q')           # wages per labor
Economic_Growth.add_variable(name='Y',units='K/T')                       # profit per period of time
Economic_Growth.add_variable(name='r',units='1/T')                       # rental rate period of time
Economic_Growth.add_variable(name='{\\delta}',units='1/T')               # depreciation rate

Economic_Growth.generate_pi_terms()
Economic_Growth.print_all()