Consider a Pitot static tube mounted on the nose of an experimental airplane. A Pitot tube measures the total pressure at the tip of the probe (hence sometimes called the Pitot pressure), and a Pitot static tube combines this with a simultaneous measurement of the free-stream static pressure. The Pitot and free-stream static measurements are given below for three different flight conditions. Calculate the free-stream Mach number at which the airplane is flying for each of the three different conditions

1. Pitot pressure=1.22×105N/m2 , static pressure=1.01 × 105N/m2 .

2. Pitot pressure=7222lb/f t2 , static pressure=2116lb/f t2 .

3. Pitot pressure=13197lb/f t2 , static pressure=1020lb/f t2 .

M∞ = 0.53

M∞ = 1.5

M∞ = 3.1

Explanation:

Find: For each case the free stream Mach number.

-Pitot pressure=1.22×10^5N/m2 , static pressure=1.01 × 10^5N/m2 .

Solution:

- The free stream Mach number is a function of static to hydrodynamic pressures. So for this case we have:

            P = 1.01 × 10^5 .. static pressure

            Po = 1.22×10^5   ... pitot pressure ( hydrodynamic )

- Take the ratio:

            P / Po = (1.01 × 10^5) / (1.22×10^5) = 0.8264.

- Use Table A.13 and look up the ratio P/Po = 0.8264 for Mach number M∞.

            M∞ = 0.53

Find:

-Pitot pressure=7222 lb/ft^2 , static pressure=2116 lb/ft^2

Solution:

- The free stream Mach number is a function of static to hydrodynamic pressures. So for this case we have:

            P = 2116 .. static pressure

            Po = 7222   ... pitot pressure ( hydrodynamic )

- Take the ratio:

            P / Po = (2116) / (7222) = 0.2930.

- However, since this is supersonic, a normal shock sits in front of the Pitot tube.  Hence, Po is now the total pressure behind a normal shock wave. Thus, we have  to use Table A.14.

            P1 = 2116 .. static pressure

            Po2 = 7222   ... pitot pressure ( hydrodynamic )

- Take the ratio:

            Po2 / P1 = (7222) / (2116) = 3.412.

- Use Table A.14 and look up the ratio Po2/P1 = 3.412 for Mach number M∞.

            M∞ = 1.5

Find:

-Pitot pressure=13197 lb/f^t2 , static pressure=1020 lb/ft^2

Solution:

- The free stream Mach number is a function of static to hydrodynamic pressures. So for this case we have:

            P = 1020 .. static pressure

            Po = 13197   ... pitot pressure ( hydrodynamic )

- Take the ratio:

            P / Po = (1020) / (13197) = 0.0772.

- Again, since this is supersonic, a normal shock sits in front of the Pitot tube.  Hence, Po is now the total pressure behind a normal shock wave. Thus, we have  to use Table A.14.

            P1 = 1020 .. static pressure

            Po2 = 13197   ... pitot pressure ( hydrodynamic )

- Take the ratio:

            Po2 / P1 = (13197) / (1020) = 12.85.

- Use Table A.14 and look up the ratio Po2/P1 = 12.85 for Mach number M∞.

            M∞ = 3.1

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