aerodynamics Aerodynamics () is the study of the motion of atmosphere of Earth, air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dynamics and its subfield of gas dynamics, and is an ...

, the normal shock tables are a series of tabulated data listing the various properties before and after the occurrence of a normal shock wave. With a given upstream

Mach number The Mach number (M or Ma), often only Mach, (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound. It is named after the Austrian physicist and philosopher Erns ...

, the post-shock Mach number can be calculated along with the

pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...

density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...

temperature Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...

, and

stagnation pressure In fluid dynamics, stagnation pressure, also referred to as total pressure, is what the pressure would be if all the kinetic energy of the fluid were to be converted into pressure in a reversable manner.; it is defined as the sum of the free-strea ...

ratios. Such tables are useful since the equations used to calculate the properties after a normal shock are cumbersome. The tables below have been calculated using a

heat capacity ratio In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant vol ...

\gamma

, equal to 1.4. The upstream Mach number,

M_1

, begins at 1 and ends at 5. Although the tables could be extended over any range of Mach numbers, stopping at Mach 5 is typical since assuming

\gamma

to be 1.4 over the entire Mach number range leads to errors over 10% beyond Mach 5.

Normal shock table equations

Given an upstream Mach number,

M_1

, and the ratio of specific heats,

\gamma

, the post normal shock Mach number,

M_2

, can be calculated using the equation below. :

M_2 = \sqrt

The next equation shows the relationship between the post normal shock pressure,

p_2

, and the upstream ambient pressure,

p_1

. :

\frac = \frac - \frac

The relationship between the post normal shock density,

\rho_2

, and the upstream ambient density,

\rho_1

is shown next in the tables. :

\frac = \frac

Next, the equation below shows the relationship between the post normal shock temperature,

T_2

, and the upstream ambient temperature,

T_1

. :

\frac = \frac

Finally, the ratio of stagnation pressures is shown below where

p_

is the upstream stagnation pressure and

p_

occurs after the normal shock. The ratio of stagnation temperatures remains constant across a normal shock since the process is adiabatic. :

\frac = \left(\frac\right)^\frac\left(\frac\right)^\frac

Note that before and after the shock the isentropic relations are valid and connect static and total quantities. That means,

p_\neq p_ + p_

(comes from Bernoulli, assumes incompressible flow) because the flow is for Mach numbers greater than unity always compressible.

The normal shock tables (for γ = 1.4)

References

{{reflist

External links

University of Cincinnati shock relations calculator

Parkin Research Normal shock calculator
Aerospace engineering Aerodynamics

Normal shock table equations

The normal shock tables (for γ = 1.4)

See also

References

External links