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Next: Partially Closed Valve Up: The Moving Shocks Previous: Shock-Choke Phenomenon   Index

Partially Open Valve

The previous case is a special case of the moving shock. The general case is when one gas flows into another gas with a given velocity. The only limitation is that the downstream' gas velocity is higher than the upstream'' gas velocity as shown in Figure (5.17).

The relationship between the different Mach numbers on the upstream'' side is

The relationship between the different Mach on the downstream'' side is

An additional parameter has be supplied to solve the problem. A common problem is to find the moving shock velocity when the velocity downstream'' or the pressure is suddenly increased. It has to be mentioned that the temperature downstream'' is unknown (the flow of the gas with the higher velocity). The procedure for the calculations can be done by the following algorithm:
(a)
Assume that

(b)
Calculate the Mach number My by utilizing the tables or Potto-GDC.

(c)
Calculate the downstream'' shock Mach number
(d)
Utilizing

calculate the new improved'' Mx

(e)
Check the new and improved Mx against the old one. If it is satisfactory, stop or return to stage (b).
 Earlier, it was shown that the shock choking phenomenon occurs when the flow is running into a still medium. This phenomenon also occurs in the case where a faster flow is running into a slower fluid. The mathematics is cumbersome but results show that the shock choking phenomenon is still there (the Mach number is limited, not the actual flow). Figure (5.16) exhibits some downstream'' Mach numbers for various static Mach numbers, My′, and for various static upstream'' Mach numbers, Mx′. The figure demonstrates that the maximum can also occurs in the vicinity of the previous value (see following question/example).

Next: Partially Closed Valve Up: The Moving Shocks Previous: Shock-Choke Phenomenon   Index
Created by:Genick Bar-Meir, Ph.D.
On: 2007-11-21