Question

A symmetrical wedge with a 12° included angle is placed in an air flow in which the Mach number is 2.3 and the pressure is 60 kPa. If the centerline of the wedge is at an angle of 4° to the direction of flow, find the pressure difference between the two surfaces of the wedge.

Answer 1

Answer:

Explanation:

The detailed steps and appropriate diagram is as shown in the attached file.

Answer 2

Answer:

The symmetric and deflected wedge is shown in figure below.

The given parameters are

UPPER SURFACE of WEDGE

Mach no. (M) = 2.3

Wedge angle = 120

Pressure upstream (p1) = 60 kPa

Angle from the centerline of wedge = 40

Hence angle of deflection as shown in figure () = 20

Let us assume that the shock angle is  

From the oblique shock relation we have

cot() = tan[(+1)M2)/2(M2sin2 - 1)]

Solving for the above values given above for upstream side of the wedge, we get

= 27.290

Pressure ratio is given by

p2/p1 = 2M2sin2 - ( -1)/( + 1)

where p1 and p2 and upstream and downstream side pressure

Solving the above equation for the above given values we get

p2/p1 = 1.131

p2 = 1.131 x 60 = 67.86 kPa

Explanation: