Consider a flow with a pressure and temperature of 2332 lbft

Consider a flow with a pressure and temperature of 2332 lb/ft2 and 498 deg. R, respectively. A Pitot tube is inserted into this flow and measures a pressure of 8065.2 lb/ft2. What is the velocity of this flow? Is the flow supersonic? Use appendix B.

Solution

Pitot tube measures total pressure.

Total pressure = Static pressure + Dynamic pressure

P_t = P_s + 1/2*rho*V²

We have density rho = P / RT.............for air, R = 1716 ft-lb/slug-R

= 2332 / (1716*498)

= 0.00272886 slug / ft³

Dynamic pressure = 1/2 * rho*V²

= 1/2* 0.00272886 * V²

8065.2 = 2332 + 1/2* 0.00272886 * V²

V = 2049.85 ft/s

Speed of sound = (kRT)^0.5........where for air, k = 1.4, R = 1716 ft-lb/slug-R

= (1.4*1716*498)^0.5

= 1093.8 ft/s

Since 2049.85 > 1093.8, the flow is supersonic.