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Gas sonic velocity calculation

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1. Introduction
2. Sonic Velocity Calculation
3. Gas Sonic velocity calculation Excel

4. Critical pressure ratio

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1. Introduction

Calculating the sonic velocity is necessary for different design activities. It is also handy to be able to determine under which pressure drop a gas flow will reach sonic conditions.

What is the sonic velocity ?

The sonic velocity is the maximum velocity that can be reached by a gas in a pipe, or exiting from the system through an orifice or a nozzle for example. Knowing the sonic velocity is very important as the velocity of the gas will be "capped" by the sonic velocity, it cannot go quicker, which will induce some limitations for pressure safety valves for example. The sonic velocity of the gas is also called critical velocity.

2. Sonic Velocity Calculation

How to calculate a gas sonic velocity ?

The sonic velocity of a gas can be calculated thanks to the following equation :

With :
V_s = Sonic velocity (ft/s)
K = C_p/C_v around 1.4 for most diatomic gases
g = 32.2 ft/s²
R = 1544/M
T = Absolute temperature (°R)

The formula can also be expressed in SI units :


With :
V_s = Sonic velocity (m/s)
K = C_p/C_v around 1.4 for most diatomic gases
R = 8314 (J/kg mol/K) / M (kg/mol) (J/kg/K⁾
M = molecular weight of the gas (kg/mol)
T = Absolute temperature (°K)

Example of gas sonic velocity calculation for air at 20c :

In SI units :

K = 1.4 for air
M = 29 kg/kg mol for air
R = 8314 / 29 = 286.7 J/kg/K
T = 293.15 K

Vs = (1.4*286.7*293.15)^0.5 = 343 m/s

In Imperial units :

K = 1.4 for air
M = 29 kg/kg mol for air
R = 1544 / 29
T = 527.67 R
g = 32.2 ft/s

Vs = (1.4*32.2*1544/29*527.67)^0.5 = 1125 ft/s (=342.9 m/s)

For this particular example, it is interesting to note that the sonic velocity of air is just the speed of sound in air.

3. Gas sonic velocity calculator Excel

The gas sonic velocity can be calculated thanks to a free Gas sonic velocity calculator Excel

Warning : this calculator is provided to illustrate the concepts mentioned in this webpage, it is not intended for detail design. It is not a commercial product, no guarantee is given on the results. Please consult a reputable designer for all detail design you may need.

4. Critical pressure ratio

How to calculate the critical pressure ratio for a nozzle or orifice ?

Critical pressure ratio = P₂/P₁ = the ratio of pressure upstream and downstream an orifice or nozzle
K = C_p/C_v around 1.4 for most diatomic gases

If the critical pressure ratio is exceeded, then the gas sonic velocity will be reached, and the flow will be sonic. As a 1st approximation, we can consider that the critical pressure ratio is reached when P₁ = 2*P₂.

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