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Related Concept Videos

Shock Waves01:16

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While deriving the Doppler formula for the observed frequency of a sound wave, it is assumed that the speed of sound in the medium is greater than the source's speed through it. When this condition is breached, a shock wave occurs.
When the source's speed approaches the speed of sound, constructive interference between successive wavefronts emitted by the source occurs immediately behind it. Initially, scientists believed that this constructive interference would result in such high...
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As with waves on a string, the speed of sound or a mechanical wave in a fluid depends on the fluid's elastic modulus and inertia. The two relevant physical quantities are the bulk modulus and the density of the material. Indeed, it turns out that the relationship between speed and the bulk modulus and density in fluids is the same as that between the speed and the Young's modulus and density in solids.
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Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation04:01

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Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws.
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Sound waves, which are longitudinal waves, can be modeled as the displacement amplitude varying as a function of the spatial and temporal coordinates. As a column of the medium is displaced, its successive columns are also displaced. As the successive displacements differ relatively, a pressure difference with the surrounding pressure is created. The gauge pressure varies across the medium.
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The speed of sound in a gaseous medium depends on various factors. Since gases constitute molecules that are free to move, they are highly compressible. Hence, sound waves travel slowly through gases. Thermodynamics helps us understand the relationship between pressure, volume, and temperature of gases, thus, the speed of sound in an ideal gas can be determined using the laws of thermodynamics. At the same time, Newton's laws of motion and the continuity equation of fluid dynamics also come...
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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
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Blast Quantification Using Hopkinson Pressure Bars
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Exact solutions for shock waves in dilute gases.

F J Uribe1, R M Velasco1

  • 1Department of Physics, Universidad Autónoma Metropolitana-Iztapalapa 09340, CDMX, México.

Physical Review. E
|October 3, 2019
PubMed
Summary

Researchers found exact solutions for gas shock waves using the soft-spheres model. This extends Becker's 1922 work by analyzing temperature-dependent viscosity and thermal conductivity.

Area of Science:

  • Fluid dynamics
  • Gas dynamics
  • Non-equilibrium thermodynamics

Background:

  • Becker (1922) provided an exact solution for gas shock waves using Navier-Stokes-Fourier equations with constant transport coefficients.
  • Subsequent research explored extensions for implicit exact solutions under specific conditions.

Purpose of the Study:

  • To investigate exact implicit solutions for shock waves in gases within the soft-spheres model.
  • To analyze the impact of temperature-dependent viscosity and thermal conductivity (η, κ ∝ T^σ) on shock wave behavior.

Main Methods:

  • Utilized the soft-spheres model where viscosity and thermal conductivity are power functions of temperature.
  • Derived and presented implicit exact solutions for specific viscosity indices (σ).

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Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions
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Main Results:

  • Obtained implicit exact solutions for shock waves under the soft-spheres model.
  • Solutions are provided for the Maxwell model (σ=1), hard spheres (σ=1/2), and cases where σ is a natural number.

Conclusions:

  • The study successfully extends Becker's findings to a more general case with temperature-dependent transport properties.
  • The derived solutions offer valuable insights into gas dynamics under non-ideal conditions.