A Pitot tube can be used to determine the velocity of air...

A Pitot tube can be used to determine the velocity of air flow by measuring the difference between the total pressure and the static pressure (Fig. P15.41). If the fluid in the tube is mercury, whose density is $\rho_{\mathrm{Hg}}=$ $13600 \mathrm{~kg} / \mathrm{m}^{3}$, and if $\Delta h=5.00 \mathrm{~cm}$, find the speed of air flow. (Assume that the air is stagnant at point $A$, and take $\rho_{\text {air }}=1.25 \mathrm{~kg} / \mathrm{m}^{3}$.)

Key Concepts

Pitot Tube Measurement

A Pitot tube is an instrument used in fluid dynamics to measure fluid flow velocity. It works on the principle of converting the kinetic energy of the fluid flow into potential energy in the form of pressure. By measuring the difference between the stagnation (total) pressure and the static pressure, one can determine the dynamic pressure, which is directly related to the velocity of the fluid.

Bernoulli's Equation

Bernoulli's equation is a fundamental principle in fluid mechanics that relates the pressure, velocity, and height in a flowing fluid. The equation states that an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. This relationship is crucial for analyzing systems where pressure differences (like those measured by a Pitot tube) are used to determine fluid velocity.

Hydrostatic Pressure Difference

A hydrostatic pressure difference arises due to the weight of a fluid column and is calculated based on the density of the fluid and the height difference of the fluid column. In the context of Pitot tubes using a manometer filled with a specific fluid (such as mercury in this case), the measured height difference is used to compute the pressure difference between two points using the relation ?P = ?gh, where ? is the density of the manometer fluid, g is the acceleration due to gravity, and h is the height difference.

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