It is claimed that an oblique shock can be analyzed like a normal shock provided that the normal component of velocity (normal to the shock surface) is used in the analysis. Do you agree with this claim?

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Chapter17: Sound Waves
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It is claimed that an oblique shock can be analyzed like a normal shock provided that the normal component of velocity (normal to the shock surface) is used in the analysis. Do you agree with this claim?

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Step 1

Given

It is claimed that an oblique shock can be analyzed like a normal shock provided that the normal component of velocity (normal to the shock surface) is used in the analysis. Do you agree with this claim, as following below.

Step 2

Grant us draw the sketch for an oblique shock display the normal and oblique velocity vectors upward and downward and a small control volume around the shock.

Physics homework question answer, step 2, image 1

 

 

Step 3

Consider the diagram.

From the geometry of the control volume the upstream fluid properties (Velocity, Density, and Pressure) represented by the lower left face of the control volume is identical to the downstream properties signified by the upper right face of the control volume.

 

Then the consevation mass converts,ρ1V1 n A =ρ2V2 n Aρ1V1 n  = ρ2V2 n         ......1

From the sketch, we know that the tangential components of the velocity for an Oblique shock do not change across the shock.

Then the tangential velocities,

V1,t =V2,t

Consider the normal components.

Put in the conservation of momentum in the normal direction,

P1A-P2A =ρV2,n AV2,n-ρV1,n AV1,nP1-P2 =ρV2,n2 - ρV1,n2              ........2

 

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