""" Interactive Pipe Flow Simulation
This module implements a real-time, interactive simulation of fluid flow through pipes with varying cross-sectional areas. It visualizes the effects of the continuity equation and Bernoulli's principle using particle animation and dynamic graphs.
Key Features:
- Interactive sliders for controlling flow parameters
- Real-time visualization of fluid particles
- Dynamic graphs showing velocity and pressure profiles
- Configurable pipe geometry with multiple sections
Usage: sim = InteractivePipeFlowSimulation(initial_velocity=2.0) sim.add_pipe_section(length=2, diameter=0.3) sim.add_pipe_section(length=1, diameter=0.15) fig, ani = sim.create_interactive_visualization() plt.show() """
class InteractivePipeFlowSimulation: """ Main simulation class for modeling and visualizing pipe flow.
Attributes:
initial_velocity (float): Starting velocity at inlet (m/s)
density (float): Fluid density (kg/m³)
sections (list): Storage for pipe section data
particles (dict): Particle system for visualization
p0 (float): Reference pressure (Pa)
"""
def __init__(self, initial_velocity=2.0, density=1000):
"""
Initialize the simulation with default parameters.
Args:
initial_velocity (float): Initial fluid velocity in m/s
density (float): Fluid density in kg/m³
"""
# [implementation details...]
def add_pipe_section(self, length, diameter, position=None):
"""
Add a new pipe section to the simulation.
Args:
length (float): Section length in meters
diameter (float): Inner diameter in meters
position (float, optional): Starting x-position. If None, connects to previous section.
"""
# [implementation details...]
def calculate_velocities(self):
"""
Calculate fluid velocities in all pipe sections using the continuity equation.
Updates the 'velocity' field for each section in the sections list.
"""
# [implementation details...]
def calculate_pressures(self):
"""
Calculate pressures in all pipe sections using Bernoulli's equation.
Updates the 'pressure' field for each section in the sections list.
Requires velocities to be calculated first.
"""
# [implementation details...]
def initialize_particles(self, n_particles=100):
"""
Create particles for flow visualization.
Args:
n_particles (int): Number of particles to create
"""
# [implementation details...]
def update_particles(self, dt=0.05):
"""
Update particle positions based on local fluid velocity.
Args:
dt (float): Time step for position updates
"""
# [implementation details...]
def create_interactive_visualization(self):
"""
Create an interactive matplotlib figure with animation and sliders.
Returns:
tuple: (matplotlib figure, animation object)
"""
# [implementation details...]
The simulation demonstrates these core fluid dynamic principles:
1.Continuity Equation: As fluid flows through changing pipe diameters,
the product of area and velocity remains constant.
This is visually demonstrated by faster-moving particles in narrow sections.
2.Bernoulli's Principle: The inverse relationship between velocity and pressure
is shown in the dynamic graphs, where pressure drops in sections with higher velocity.
3.Conservation of Mass: The simulation maintains constant mass flow rate throughout the pipe system,
regardless of geometry changes.
4.Flow Adaptation: The visualization shows how fluid adapts to changing
geometries while maintaining physical constraints.