Lab 01: Python Fundamentals

Lab 01: Python Fundamentals#

Topics Covered:

  • Setting up and verifying your Anaconda environment

  • Basic Python math operations for engineering calculations

1. Demonstration#

1.1 Environment Setup and Verification#

Before we begin calculations, let’s verify that your environment is properly configured.

# Verify Python version and environment
import sys

# Check that key packages are installed
import pandas as pd
import numpy as np
import matplotlib

1.2 Basic Python Math Operations#

Python can perform mathematical calculations using basic arithmetic operators. Let’s explore how to use them for engineering calculations.

Example 1.2.1: Scientific Notation#

For very large or very small numbers, Python uses scientific notation with the e symbol.

# Scientific notation: 1.5e6 means 1.5 × 10⁶
avogadro = 6.022e23  # Avogadro's number
electron_mass = 9.109e-31  # kg
gas_constant = 8.314  # J/(mol·K)

Example 1.2.2: Power Calculations#

  • Syntax: base ** exponent

  • Built-in operator for exponentiation.

  • Works with integers, floats, and complex numbers.

  • Returns the same type as the input when possible.

2 ** 3        # 8 (int)
2.0 ** 3      # 8.0 (float)
2 ** 0.5      # 1.4142135623730951 (float)
(1+2j) ** 2   # (-3+4j) (complex)
2 ** -1       # 0.5

import math
# Compare ** operator vs math.pow()
print("Comparing ** and math.pow():")
print(f"2**3 = {2**3}")
print(f"pow(2, 3) = {pow(2, 3)}")
print(f"math.pow(2, 3) = {math.pow(2, 3)}")

Comparing ** and math.pow():
2**3 = 8
pow(2, 3) = 8
math.pow(2, 3) = 8.0

# Cube root example using fractional exponents
print("\nCube Root Example:")
volume_sphere = 113.1  # m³
# For a sphere: V = (4/3)πr³, so r = (3V/4π)^(1/3)

pi = 3.14159

Cube Root Example:

1.3. Chemical Engineering Applications#

Example 1.3.1: Ideal Gas Law#

Calculate pressure using the ideal gas law:

\[ PV = nRT \]

where:

  • n = 50.0 mol

  • R = 8.314 J·mol⁻¹·K⁻¹

  • T = 373.15 K (100 °C)

  • V = 0.5 m³

# # Calculate pressure of gas in a reactor

Example 1.3.2: Reynolds Number Calculation#

Determine whether the flow is laminar or turbulent using the Reynolds number:

\[ \mathrm{Re} = \frac{\rho v D}{\mu} \]

where:

  • ρ = 1000 kg/m³ (density of water)

  • v = 2.5 m/s (velocity)

  • D = 0.1 m (pipe diameter)

  • μ = 0.001 Pa·s (dynamic viscosity)

Determination criteria:

  • Re < 2300 → Laminar flow

  • 2300 ≤ Re ≤ 4000 → Transitional flow

  • Re > 4000 → Turbulent flow

# # Reynolds number for water flowing in a pipe

Example 1.3.3: Mass Balance - Dilution Calculation#

Calculate the final concentration (\(C_2\)) using the dilution equation:

\[ C_1 V_1 = C_2 V_2 \]

where:

  • C₁ = 12.0 mol/L (initial concentration)

  • V₁ = 0.250 L (initial volume)

  • V₂ = 1.000 L (final volume after dilution)

# # Dilute a concentrated solution

Practice Problems#

Now it’s your turn! Solve the following problems in the cells below. Make sure to:

  • Show your work with comments

  • Use appropriate variable names

  • Format your output professionally

  • Include units in your output

Problem 1: Pipe Flow Calculation#

Water flows through a circular pipe with a diameter of 0.15 m at a velocity of 3.2 m/s.

Calculate:

  1. The cross-sectional area of the pipe (A = π × (D/2)², use π = 3.14159)

  2. The volumetric flow rate (Q = A × v) in m³/s

  3. Convert the flow rate to L/min (1 m³ = 1000 L, 1 min = 60 s)

Format your output to show all results with appropriate decimal places and units.

# Your solution here

Problem 2: Pressure Drop in a Pipe#

Calculate the pressure drop in a horizontal pipe using the Darcy-Weisbach equation:

ΔP = f × (L/D) × (ρv²/2)

Where:

  • f = 0.025 (friction factor, dimensionless)

  • L = 100 m (pipe length)

  • D = 0.2 m (pipe diameter)

  • ρ = 1000 kg/m³ (fluid density)

  • v = 3.0 m/s (fluid velocity)

Calculate:

  1. The pressure drop ΔP in Pa

  2. Convert to kPa and to psi (1 psi = 6894.76 Pa)

Format your results with appropriate units.

# Your solution here

Problem 3: Friction Factor Calculation#

For turbulent flow in smooth pipes, the Blasius correlation is used to estimate the friction factor:

\[ f = \frac{0.316}{\mathrm{Re}^{0.25}} \]

where Re is the Reynolds number.

Given:

  • Reynolds number (Re) = 25,000

Tasks:

  1. Calculate the friction factor

  2. Verify that both methods give the same answer

Format your output to clearly show:

  • The Reynolds number

  • The friction factor calculated with math.pow(), pow(), and **

  • A statement confirming they are equal

# Your solution here
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