In this post I want to share how to calculate sonic velocity. Before we jump into the equation, let’s review about sonic velocity briefly.

**Sonic velocity** or **critical velocity** is the maximum velocity that can be attained by a compressible fluid. We usually use this parameter in sizing pipe, control valve, and flare.

Sonic velocity is a function the following parameters:

- Ratio of specific heats in the gas (k or C
_{p}/C_{v}) - Temperature
- Molecular weight of the gas

The molecular weight is expressed in absolute temperature, therefore we will use temperature unit of ^{o}R or ^{o}K.

**Then how to calculate?**

If we use imperial units, then use the following equation to calculate sonic velocity:

**V _{s }(sonic velocity) = 223 (k T/M)^{0.5}**

Where:

V_{s} = sonic velocity (ft/s)

k = ratio of specific heats in the gas (C_{p}/C_{v})

T = absolute temperature (^{o}R)

M = molecular weight of gas

If we use metric units, then use the following equation to calculate sonic velocity:

**V _{s }(sonic velocity) = 91.2 (k T/M)^{0.5}**

Where:

V_{s} = sonic velocity (m/s)

k = ratio of specific heats in the gas (C_{p}/C_{v})

T = absolute temperature (^{o}K)

M = molecular weight of gas

I attached a simple spreadsheet to calculate sonic velocity in imperial unit and metric unit, respectively. Please download if you need.

**Reference:**

- Bahadori, Alizera,
*Oil and Gas Pipelines and Piping Systems*, Gulf Professional Publishing, 2017. - Branan, Carl,
*Rules of Thumb for Chemical Engineers*, Gulf Professional Publishing, 2005. - Coker, Kayode A,
*Fortran Programs for Chemical Process Design, Analysis, and Simulation*, Elsevier Science & Technology Books, 1995.