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Contrary to popular belief, the shape of a hyperbolic natural draft cooling tower has nothing to do with the airflow through it.

The airflow through the tower is generated by the difference in density of the warm, humid air inside the tower, versus the relatively cool, dense ambient air outside the tower.

This density difference causes a natural "draft" also known as the chimney or stack effect. If the temperature of the air outside the cooling tower is less than the temperature of air inside the cooling tower, the dense air outside forces the hot, humid air inside to travel upwards and thus provides the natural ventilation. For this reason you can see openings at the bottom of the hyperbolic cooling towers (Natural Draft Cooling Towers).

Plant cooling water is sprayed over "fill" which is usually a grid of thin PVC sheets arranged in a honeycomb, placed near the lower end of the tower, just above the air openings at the bottom. The water is cooled by the natural draft of the ambient air traveling up through the fill, while the water cascades down the fill.

Originally, natural draft cooling towers were cylindrical in shape. As the design of these types of towers evolved, and the towers were made increasingly larger, the cylindrical shape was changed to hyperbolic, since a hyperbolic shape offers superior structural strength and resistance to ambient wind loadings. For a structure of the size of some of these towers, the wind loading can be substantial.

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Q: Why Cooling tower are hyperbolic in shape?
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