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Feedback    Next: The Limitations of the Up: Normal Shock Previous: Prandtl's Condition   Index

# Operating Equations and Analysis

In Figure (5.3), the Mach number after the shock, My, and the ratio of the total pressure, P0y/P0x, are plotted as a function of the entrance Mach number. The working equations were presented earlier. Note that the has a minimum value which depends on the specific heat ratio. It can be noticed that the density ratio (velocity ratio) also has a finite value regardless of the upstream Mach number.

The typical situations in which these equations can be used also include the moving shocks. The equations should be used with the Mach number (upstream or downstream) for a given pressure ratio or density ratio (velocity ratio). This kind of equations requires examining Table (5.1) for or utilizing Potto-GDC for for value of the specific heat ratio. Finding the Mach number for a pressure ratio of 8.30879 and k=1.32 and is only a few mouse clicks away from the following table.

This table was generated by Potto-GDC (in HTML)

Normal Shock Input: Py/Px k = 1.32
Mx My Ty/Tx ρy/ρx Py/Px P0y/P0x
2.7245 0.476422 2.111 3.93596 8.30879 0.381089 To illustrate the use of the above equations, an example is provided. Solution

Analysis:
First, the known information Mx=3, Px=1.5[bar] and T=273 K. Using these data, the total pressure can be obtained (through an isentropic relationship Table (4.2), i.e. P0x is known). Also with the temperature, Tx the velocity can readily be calculated. The relationship that was calculated will be utilized to obtain the ratios for downstream of the normal shock.  Normal Shock Input: Mx k = 1.4
Mx My Ty/Tx ρy/ρx Py/Px P0y/P0x
3 0.475191 2.67901 3.85714 10.3333 0.328344 Now the velocity downstream is determined by the inverse ratio of ρy = 993.6 / 3.85714 = 257.6 [m/sec].

Uy=993.6/3.85714=257.6[m/sec]

P0y = ( P0y / P0x ) * P0x = 0.32834 * 55.1 [bar] = 18.09 [bar]

Subsections    Next: The Limitations of the Up: Normal Shock Previous: Prandtl's Condition   Index
Created by:Genick Bar-Meir, Ph.D.
On: 2007-11-21