Mach Number Calculator

What is Mach Number?

The Mach number (denoted as M or Ma) is a dimensionless quantity in fluid dynamics that represents the ratio of the speed of an object (or the speed of flow) to the speed of sound in the surrounding medium.

The Mach number (M) defined as:

\[ M = \frac{\text{speed of object}}{\text{speed of sound}} \]

\[ M = \frac{u}{c} \]

where:

\(M\) represents the local Mach number.
\(u\) is the local flow velocity relative to the boundaries.
\(c\) is the speed of sound in the medium (e.g., air).

The Ma number is used to classify the speed of an object relative to the speed of sound.

Note: As the temperature increases, the speed of sound also increases. The speed of sound in air at 20°C is approximately 343 m/s.

Related: Other Dimensionless Numbers

This calculator helps user to input the speed of an object and the speed of sound at the required temperature to determine the Mach number. Based on the calculated value of Ma number it classifies the flow as subsonic, sonic, supersonic, or hypersonic.

Mach_Number Calculator

Significance of the Mach Number

The Ma Number can be classified based on the speed of object relative to the speed of sound. For example the Ma number of 0.85 means the speed of the object is 85% of the speed of the sound.

For Subsonic Flow (Ma < 1) the object travels slower than the speed of sound. eg. Commercial passenger jets, such as the Boeing 737, typically cruise at Mach 0.8.

For Transonic (Ma ≈ 1) the object travel at speed close to the speed of sound, it usually ranges from Mach 0.8 to Mach 1.2. eg. High performance military aircraft and jet fighters.

For Supersonic (1 < Ma < 5) the object travels faster than speed of sound. eg. Concorde, a retired supersonic passenger airliner

For Hypersonic (Ma ≥ 5) the object travels much faster than the speed of sound. e.g the space shuttle during re-entry or hypersonic missiles.

Mach Number Applications

Ma number is used by engineers and scientists to predict the effects of high-speed travel through different mediums, which is used to ensure safety, efficiency, and performance of various vehicles and systems.

In Meteorology Ma Number is used to understand the weather patterns in atmosphere.
In Aerospace Engineering for the designing and testing of missiles and spacecraft to ensure efficient performance at various speeds and altitudes.
Important in the Acoustics study of sound propagation, for objects moving at high speeds, such as supersonic jets.
For the design and operation of space vehicles that re-enter the Earth’s atmosphere, so that vehicles can manage the thermal and pressure loads experienced at high Ma numbers.

Python Code for Mach Number Calculation

This Python code helps user to calculate the Mach number for a range of velocities (0 to 500 m/s) at different temperatures. It plots the Mach number against velocity for each temperature.

Note: This Python code solves the specified problem. Users can copy the code and run it in a suitable Python environment. By adjusting the input parameters, and observe how the output changes accordingly.

import numpy as np
import matplotlib.pyplot as plt

# Function to calculate the speed of sound in air at a given temperature
def speed_of_sound(temperature):
    # Speed of sound formula: a = 331.3 + 0.606 * T (T in Celsius)
    return 331.3 + 0.606 * temperature

# Function to calculate Mach number
def calculate_mach_number(velocity, speed_of_sound):
    return velocity / speed_of_sound

# Define range of velocities (in meters per second)
velocities = np.linspace(0, 2000, 100)  # From 0 to 500 m/s

# Define temperatures (in Celsius)
temperatures = [-20, 0, 20, 40, 100]  # Example temperatures

# Plot the results
plt.figure(figsize=(10, 6))

for temp in temperatures:
    sos = speed_of_sound(temp)  # Calculate speed of sound at this temperature
    mach_numbers = calculate_mach_number(velocities, sos)  # Calculate Mach numbers
    plt.plot(velocities, mach_numbers, label=f'Temperature = {temp}°C')

# Add horizontal lines for reference
plt.axhline(y=1, color='r', linestyle='--', label='Mach 1 (Speed of Sound)')
plt.axhline(y=0.8, color='g', linestyle='--', label='Mach 0.8 (Transonic Lower Bound)')
plt.axhline(y=1.2, color='b', linestyle='--', label='Mach 1.2 (Transonic Upper Bound)')

# Add titles and labels
plt.title('Mach Number vs. Velocity at Different Temperatures')
plt.xlabel('Velocity (m/s)')
plt.ylabel('Mach Number')
plt.legend()
plt.grid(True)

# Show plot
plt.show()

Output:

Resources

“Fluid Mechanics” by Frank M. White
“Introduction to Fluid Mechanics” by Robert W. Fox, Alan T. McDonald, and Philip J. Pritchard
“Principles of Heat and Mass Transfer” by Frank P. Incropera and David P. DeWitt
Python.org – The official Python website offers tutorials, documentation, and resources for learning Python.
Physics Tutorial: The Speed of Sound (physicsclassroom.com)

Disclaimer: The Solver provided here is for educational purposes. While efforts ensure accuracy, results may not always reflect real-world scenarios. Verify results with other sources and consult professionals for critical applications. Contact us for any suggestions or corrections.

Mach Number Calculator – Significance and Applications

Table of Contents

What is Mach Number?