Sound travels through fluids at different speeds, depending on the medium's properties. The speed of sound in air is about 343 m/s, while in water it's much faster at 1,480 m/s. Temperature, compressibility, and molecular weight all affect sound speed.
Mach number, the ratio of flow velocity to local sound speed, helps categorize flow regimes. It's crucial in aerodynamics, determining whether a flow is subsonic, transonic, supersonic, or hypersonic. This impacts vehicle design and performance in high-speed applications.
Speed of Sound and Mach Number
Speed of sound in fluids
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Top images from around the web for Speed of sound in fluids
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Phase Changes – Fundamentals of Heat, Light & Sound View original
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8.2: Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law | General College ... View original
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Speed at which small pressure disturbances travel through a fluid medium
For ideal gases, calculated using the equation: c=γRT
γ: ratio of specific heats (heat capacity ratio) represents the fluid's compressibility (air at standard conditions: 1.4)
R: gas-specific constant depends on the gas composition (air: 287 J/kg·K)
T: absolute temperature of the gas affects molecular motion and energy (room temperature: 293 K)
Depends on fluid compressibility more compressible fluids have lower sound speeds (water: 1,480 m/s, air: 343 m/s)
Increases with temperature due to higher molecular motion and energy transfer (air at 20℃: 343 m/s, air at 100℃: 386 m/s)
Decreases with molecular weight heavier molecules have slower sound propagation (helium: 1,007 m/s, carbon dioxide: 259 m/s)
Calculation of Mach number
Dimensionless ratio of flow velocity to local speed of sound represents compressibility effects
Defined as: M=cV
V: flow velocity in the medium (aircraft speed, wind tunnel velocity)
c: local speed of sound depends on fluid properties and temperature
Calculation steps:
Determine flow velocity (V) from given information or flow equations (pitot tube measurement, numerical simulation)
Calculate local speed of sound (c) based on fluid properties and temperature (ideal gas equation, experimental data)
Divide flow velocity by local speed of sound to obtain Mach number (subsonic: < 0.8, supersonic: > 1.2)
Flow regimes vs Mach number
Subsonic flow: M<0.8
Flow velocity below local sound speed minimal compressibility effects
Density variations small often treated as incompressible (low-speed wind tunnels, propeller aircraft)
Transonic flow: 0.8≤M≤1.2
Flow velocity near sound speed significant compressibility effects
Shock waves may form leading to abrupt changes in flow properties (transonic aircraft, high-speed wind tunnels)