Pitot tubes mach number

There are certain limitations on the range of usefulness of pitot tubes. With gases, the differential is very small at low velocities e.g., at 4.6 m/s (15.1 ft/s) the differential is only about 1.30 mm (0.051 in) of water (20°C) for air at 1 atm (20°C), which represents a lower hmit for 1 percent error even when one uses a micromanometer with a precision of 0.0254 mm (0.001 in) of water. Equation does not apply for Mach numbers greater than 0.7 because of the interference of shock waves. For supersonic flow, local Mac-h numbers can be calculated from a knowledge of the dynamic and true static pressures. The free stream Mach number (MJ) is defined as the ratio of the speed of the stream (V ) to the speed of sound in the free stream ... 

Pitot tube. When a pitot tube is used for the measurement of the velocity of a compressible fluid, the usual hydraulic formula may be employed for all velocities less than about one-fifth that of the acoustic velocity in the medium. The error at this arbitrary limit is about 1%. For higher velocities a correction should be made, which applies up to a Mach number of 1. 

Since the manometer of the pitot tube measures the pressure differenee p — po, Eq. (8.52) gives the local velocity of the point where the impact tube is located. Normally, only the first Mach-number term in the equation is significant. 

The static reading on a Pitot tube is accurate to 0.5% for Mach numbers up to 0.5. For Mach numbers befween the values of 0.5 to 0.7 the accuracy increases to 1.5%. Above a Mach number of 0.7 fhe error can increase as much as 10% due to the formation of shock waves on and around the tip of the probe. Above a Mach number of 1.0 both the total and static readings vary significantly for the actual values [27]. The Mach number in the above example is calculated as follows ... 

Example 8.16. A pitot-static tube immersed in an airstream shows an impact pressure of 151bf/in absolute and a static pressure of lOlbf/in absolute. What is the Mach number of the flow ... 

From App. W.5 this would correspond to a free-stream Mach number of 1.36. However, this is not correct, because, as discussed above, the transition from a supersonic flow in a pitot tube takes place by means of a normal shock. Thus, in this casej the impact pressure is not the reservoir pressure of the flow but the reservoir j pressure which exists downstream of a normal shock at the free-stream Mach number. The reading of the manometer P, J is therefore PJPr - This free-streani Mach... 

Air is flowing steadily in a nozzle. At some point in the nozzle, the Mach number is 2.0 and the absolute pressure 4,0 psia. We now insert a pitot-static tube which has a differential-pressure gauge. What will the gauge read ... 

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