Since the expected velocity is supersonic, there will be a bow shock preceding the entrance to the pitot tube. In such cases, the shock wave in front of the nose of the object can be described as a normal shock. Its name comes from the orientation of the shock with respect to the flow direction. In order to analyze a flow moving through a normal shock the so called "normal shock relations" can be used.
For a flow passing through a normal shock we can always see the following:
-Total pressure drops
-Static pressure increases
-Mach number is always supersonic before the shock and subsonic past the shock
Indeed the shock can be seen as strong compression process.
In order to properly calculate the flow velocity, you will have to account for the total pressure loss through the shock wave in front of the pitot tube
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