**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.

**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 :

**Gas sonic velocity = V**_{s}
= (K g R T)^{0.5}

With :

V

_{s} = Sonic velocity (ft/s)

K
= C_{p}/C_{v} around 1.4 for most diatomic gases
g = 32.2 ft/s

^{2
}R

^{ }= 1544 mol

^{
} T = Absolute temperature (°R)

The formula can also be expressed in SI units :

**Gas sonic velocity = V**_{s}
= (K.R.T)^{0.5}

With :

V

_{s} = Sonic velocity (m/s)

K
= C_{p}/C_{v} around 1.4 for most diatomic gases
R

^{ }= 289.9 J/kg/K

^{
} T = Absolute temperature (°K)

**3. Critical pressure ratio**

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

Critical pressure ratio = P_{2}/P_{1}
= [2/(K+1)]^{K/(K-1)}

Critical pressure ratio = P_{2}/P_{1} = 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.

Source

[1] Rules of Thumbs for Chemical Engineers, Brannan,
Gulf, 2005