e). c = (K / ρ)1/2 (2) where. Calculation of the pipe support factor varies based on how the pipe is supported. Summary. The tables below have been compiled as an easy point of reference when trying to ascertain the sound speed in water, liquids and materials. Speed of sound can be calculated by the formula: Speed of sound = Frequency of sound wave * Wavelength. Speed of Sound Formula The speed of sound can be computed as, speed of sound = the square root of (the coefficient ratio of specific heats × the pressure of the gas / the density of the medium). The velocity of sound in some common liquids are indicated in the table below. For an ideal, perfectly rigid pipe, the general speed of sound can be calculated using the Newton-Laplace equation as shown above. The following section includes a list of correlations to determine the pipe support factor for several cases. Communication time is an important parameter in transient analysis as any event that occurs within a time frame shorter than the communication time is equivalent to an instantaneous event. It is the square root of the product of the coefficient of adiabatic expansion and pressure of the gas divided by the density of the medium. Speed of Sound in Gases, Fluids and Solids. Speed of Sound for Fluids For the general case the speed of sound in liquids and gases can be calculated using the Newton-Laplace equation: \displaystyle a = \sqrt {\frac {K} {\rho}} a = ρK The bulk modulus of a range of fluids may be found in this article. For example, if a valve closes at the end of a long pipeline the time it takes to observe an increase in pressure at the start of the pipeline may be calculated by dividing the pipe length by the speed of sound. For the general case the speed of sound in liquids and gases can be calculated using the Newton-Laplace equation: The bulk modulus of a range of fluids may be found in this article. The speed of sound is a function of a fluid’s density Speed of sound in air at standard conditions is 343 m/s. \displaystyle a = \sqrt{\frac{1}{\rho\left(\frac{1}{K}+\frac{D\psi}{Ee}\right)}}. \displaystyle \psi = \frac{2e}{D}(1+\nu)+\frac{D}{D+e}, \displaystyle \psi = \frac{2e}{D}(1+\nu)+\frac{D}{D+e}(1-\frac{\nu}{2}), \displaystyle \psi = \frac{2e}{D}(1+\nu)+\frac{D}{D+e}(1-\nu^{2}), \displaystyle \psi = \frac{2e}{D}(1+\nu). The formula for speed of sound is given with respect to gases. D/e \gt 10 . 1) Based on temperature 25oC 1 m/s = 3.6 km/h = 196.85 ft/min = 3.28 ft/s = 2.237 mph K = Bulk Modulus of Elasticity (Pa, psi) ρ = density (kg/m3, lb/ft3) This equation is valid for liquids, solids and gases. sudden valve closure) to a source (pressure transmitter) is known as the communication time. An approximate sound speed in air (in meters per second) can be calculated using the following formula: where (theta) is the temperature in degrees Celsius (°C). The acoustic velocity can alternatively be expressed with Hook's Law as. The speed of sound (also known as wave celerity or phase speed) is the speed at which a pressure wave travels in a given medium. The pipe support factor is a function of the Possion’s ratio of the pipe material ( Communication time can be calculated from the speed of sound using the following equation. In a fluid at rest, the wave speed of a fluid is equivalent to the speed of sound in the same medium, whether liquid or gas. \nu ), the pipe diameter ( K. Determination of the speed of sound allows the prediction of how long it will take a wave (such as a sudden pressure change) to propagate through a system and is therefore a necessary parameter in transient analysis. Speed of Sound in Fluids and Fluid in Pipes, Thin-walled pipe free to expand throughout, Thin-walled pipe anchored at upstream end only, Thick-walled pipe free to expand throughout, Thick-walled pipe anchored at upstream end only. For the calculation of the pipe support factor a pipe is considered thin walled if The speed of sound is calculated from the Newton-Laplace equation: (1) Where c = speed of sound, K = bulk modulus or stiffness coefficient, ρ = density. For a pipe with elastic walls the speed of sound in the fluid is impacted by the elasticity of the pipe wall and the pipe supports. v = f × λ. The speed of sounds is important in piping systems for the calculation of choked flow for gases and pressure transient analysis of liquid filled systems. \rhoand bulk modulus, When the pipe material has a large bulk modulus, as is the case for steel piping, or frequent expansion joints have been installed along the line, the pipe support factor can typically be taken as unity without significant error. The time it takes for a pressure wave to travel from its origin (i.e. This article provides the formulae for the calculation of speed of sound in fluids and fluid filled circular pipes. D) and the pipe wall thickness (
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