aerodynamics Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dyn ...

, the normal shock tables are a series of tabulated data listing the various properties before and after the occurrence of a

normal shock wave In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a med ...

. With a given upstream

Mach number Mach number (M or Ma) (; ) 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 Moravian physicist and philosopher Ernst Mach. : \mathrm = \frac ...

, 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 e ...

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...

, and

stagnation pressure In fluid dynamics, stagnation pressure is the static pressure at a stagnation point in a fluid flow.Clancy, L.J., ''Aerodynamics'', Section 3.5 At a stagnation point the fluid velocity is zero. In an incompressible flow, stagnation pressure is equ ...

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 volu ...

\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
Aerospace engineering Aerodynamics

Normal shock table equations

The normal shock tables (for γ = 1.4)

See also

References

External links