Consider a low-speed open-circuit subsonic wind tunnel with...

Consider a low-speed open-circuit subsonic wind tunnel with an inlet-to-throat area ratio of 12. The tunnel is turned on, and the pressure difference between the inlet (the settling chamber) and the test section is read as a height difference of $10 \mathrm{~cm}$ on a U-tube mercury manometer. (The density of liquid mercury is 1.36 $\times 10^{+} \mathrm{kg} / \mathrm{m}$ '.) Calculate the velocity of the air in the test section.

Key Concepts

Bernoulli's Principle

This principle states that in a steady, incompressible, inviscid flow, the sum of the pressure energy, kinetic energy, and potential energy remains constant along a streamline. It links the pressure difference measured by a manometer to the velocity of the fluid and is fundamental for determining airspeed in wind tunnels.

Manometer Pressure Measurement

A manometer is a device used to measure the pressure difference between two points in a flow system by observing a height difference in a liquid column. The height difference, combined with the density of the manometer fluid and gravitational acceleration, provides a means of calculating the pressure drop in the system, which is directly related to the flow velocity.

Dynamic Pressure and Velocity Relation

Dynamic pressure is the kinetic energy per unit volume of a fluid and is given by 0.5 times the fluid density multiplied by the square of its velocity. In wind tunnels, the measured pressure difference can be equated to dynamic pressure under appropriate assumptions, allowing for the calculation of the air velocity in the test section.

Continuity Equation and Area Ratios

The continuity equation, which expresses the conservation of mass in a fluid flow, indicates that the product of the cross-sectional area and the velocity remains constant along a streamline in steady incompressible flow. In wind tunnels, knowing the area ratio between sections is important for understanding how the flow accelerates or decelerates due to changes in cross-sectional area.

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