Introduction Mach knowledge
Published on:2015-1-16 8:51:40 Hits:

Fluid flow velocity (v) and the ratio of the sound propagation velocity in the fluid (c), called Mach number (M), M = v / c. In gas dynamics, which is divided into a gas flow type of the standard version is a yardstick to judge the gas compressibility.

In the gas (steam), the pressure of gas relative to the speed of sound propagation. When the gas (steam) at a flow rate v flow in the downstream case, the pressure is down with the propagation velocity c + v; in countercurrent case, the pressure upstream propagation speed is c - v. As such,

When v> c, the change does not propagate downstream pressure upstream. Sonic nozzle uses this principle to achieve a constant critical flow. When the Mach number M> l, it is called a supersonic flow; M <1, called subsonic flows. In the supersonic and subsonic flow, gas (steam) performance characteristics are essentially different.

Fluid compressibility refers to fluid in the flow field relative density changes. Experiments show that, with the gas (steam) flow rate is increased, the gas (steam) stream pressure gradient increases, the density of the fluid can not be regarded as constant. Therefore, it can be used as a measure of Mach gas compression standard. Fluid in the flow field changes the relative density (ρ / ρ 0) and Mach What is the relationship? Isentropic process engineering often encountered (e.g., gas flow in the nozzle or leaves) is expressed as:


Where K - isentropic index;

M - Mach number;

ρ - density of the gas in a fluidized state;

ρ 0 - gas density (zero flow rate) under the state stagnation.

The above equation, the density of the gas in the flow field change is a function of Mach number and the nature of the gas and related. For the same gas, the greater Mach number, greater density. For example, the commonly used superheated steam is industrially ρ / ρ 0 and M relationship shown in the following table.

Superheated steam ρ / ρ 0 relationship with Mach








ρ/ρ 0







The above table shows that with increasing Mach number J, i.e. the flow rate increases, the density of the gas will decrease.

In the industrial measurement, if the Mach number is not, you can use the above formula calculated ρ / ρ 0, if within the allowable error range ρ changes can be ignored, as the case may be regarded as the compressible fluid incompressible fluid deal with.

Status tones (sound) and the speed and nature of the medium which is related to the project, the speed of sound can be expressed as:


Where M - medium isentropic index;

R - gas constant N · m / kg · K;

y - absolute temperature working condition medium K.

The velocity of sound in different gases varies. 0 ℃ in air at sonic velocity is 332m / s, in the carbon dioxide atmosphere, of 262m / s. In the same gas, the speed of sound increases with increasing temperature. Sound velocity should be calculated by the above formula according to the temperature and the nature of the medium under the operating state. Common physical properties of gases listed in the table below.

Physical properties of common gases (10132Pa, 20 ℃)

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