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A common procedure for measuring the velocity of an airstream involves the insertion of an electrically heated wire (called a hot- wire anemometer) into the airflow, with the axis of the wire oriented perpendicular to the flow direction. The electrical energy dissipated in the wire is assumed to be transferred to the air by forced convection. Hence, for a prescribed electrical power, the temperature of the wire depends on the convection coefficient, which in turn, depends on the velocity of the air

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The question relates to measuring airstream velocity using a hot-wire anemometer and Bernoulli's principle. The hot-wire anemometer gauges velocity based on convection heat transfer to the air, which increases as air velocity rises. Bernoulli's principle also allows for velocity measurement through pressure differences detected by a manometer, as described in the discussed equations and figures.

Step-by-step explanation:

Understanding Hot-Wire Anemometry and Bernoulli's Principle for Velocity Measurement

The student's question involves a physical understanding of measuring airstream velocity using a hot-wire anemometer and Bernoulli's principle. The hot-wire anemometer is a device that measures fluid velocity by utilizing the concept that electrical power dissipated in the wire is proportional to the forced convection heat transfer from the wire to the air, which depends on the velocity of the airstream. Therefore, as the air velocity increases, the convection heat transfer will also increase, cooling the wire and affecting its temperature.

Bernoulli's principle can also be used to measure fluid velocity. As explained in Figure 12.7, when fluid flows past a tube with an opening on the side (as in the case with the Prandtl tube, or pitot tube), the pressure at that point decreases compared to a point where the velocity is zero. This pressure difference can be measured with a manometer, and it is directly related to the fluid's velocity. The relationship is given by the equation P₁ = P₂ + ½ pv², where p is the density of the fluid and v is the velocity at tube 2.

To accurately determine air flow such as assessing if it's laminar, knowing the velocity of the air is essential, which can be ascertained through either the hot-wire anemometry or Bernoulli's principle-based devices.

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