Question

Freestream pressure for a Mach 4 supersonic windtunnel is 1949 Pa when expanded from a reservoir pressure of 3 bar. Calculate the pressure at the face of a pitot tube placed in such a facility. Why is the gas at rest on the Pitot tube face at a lower pressure than the gas at rest in the reservoir?

Answer 1

Given static pressure P = 1949 Pa, M =4, gamma = 1.4 (for air)

From isentropic relations,

P₀ = 295926.8392 Pa

Given Reservoir P_0r = 3 bar = 300000 Pa.

We can see the loss of total pressure from reservoir to freestream inlet. In supersonic windtunnel, to increase the mach number we have a vacuum chamber at the end of the tunnel. So, the incoming flow has to expand from really high pressure to really low pressure. From the Thermodynamics we know that as pressure decreases the temperature also decreases and this process takes place while in contact with the atmosphere from outer wall of the wind tunnel. So, this process results in a irreversible process. Irreversibel process results into loss of energy of the fluid which leads to loss of total pressure.