A pitot tube on a SUPERSONIC aircraft no really measures P

A pitot tube on a SUPERSONIC aircraft (no. really!) measures P = 143.5 kPa (absolute), P_0 - P = 23.5 kPa. a. What is the flight Mach number, M_infinity? b. What is the altitude? (Use a standard atmosphere table.) c. What is the flight air speed, U_infinity? d. What T_0 would be measured?

Solution

P= 143.5Kpa

Po-P = 23.5Kpa

Po = 143+23.5= 166.5Kpa.

A) Since the flow is Supersonic,M>1

Therefore,for Compressible flow,

Po/P =(1+Y-1/2M^2)Y/Y-1

Y=1.4

166.5/143.5 =(1+.4/2M^2)^(1.4/.4)

1.160 = (1+.2M^2)^(3.5)

Therefore,by calculating the above equation we can easily find M.

C) Since we know the flow is Supersonic,M>1 airspeed cannot be calculated because Supersonic flow comes at the rest at the tip of the Pitot tube.

D) To/T = (1+ Y-1/2)M^2

This equation is valid for Compressible flow.

Y=1.4,M is calculated from above equation and T is local temperature I.e. 288.16K

By computing the values we can easily find out To.