Question

In a supersonic flow, the indicated Pitot pressure \(p_t\) is measured by a Pitot probe for calculating the flow Mach number, which of the following relation is used

• A. compressible Bernoulli’s equation
• B. Prandtl – Glauert rule for supersonic flows
• C. Prandtl relation for normal shock
• D. Rayleigh supersonic Pitot formula

Hint:

Rayleigh Pitot formula relates static and total pressures across normal shocks in supersonic flows.

Answer 1

The Correct Option is D

The correct relation used to calculate the flow Mach number from the indicated Pitot pressure \(p_t\) in a supersonic flow is given by the Rayleigh supersonic Pitot formula. This formula is specifically designed to handle the flow conditions encountered in supersonic speed scenarios. When a Pitot tube is used to measure the total pressure in a supersonic flow, the Rayleigh formula relates this pressure to the Mach number of the free stream flow.

The derivation and application of this formula are crucial for understanding how changes in mach number affect the flow conditions and pressure readings for supersonic velocities. The Pitot formula accounts for significant changes in density and pressure through a shock wave, which are characteristic of conditions seen in supersonic flows.