Why does CT in powerplants have hyperboloid shape?

The reasons are listed below

1. Strength factor
First and foremost, the hyperboloid shape impacts the strength of the entire structure. Since #CT are supposed to cool the working fluid down to a low temp., they release vapors into the atmosphere through the opening at the top of the tower.
Therefore, these towers have to be sufficiently tall (they can be as tall as 200 meters!), or else the released vapor may cause #fogging or #recirculation. To support such a high structure, it is extremely important that the base is considerably consolidated and spread over a large area so that it can support the tall, heavy structure above it. This is why CT have a large, circular base.

2.Facilitating Aerodynamic Lift

As hot fluid is cooled down by evaporation in cooling towers and hot water evaporates and begins to rise in the concrete structure, the #narrowing effect of the tower helps to enhance the speed of parallel layers of vapor without any disruption (referred to as #laminar flow).

3.Faster and More Efficient Diffusion into the Atmosphere If the narrowness at the center helps to speed up the updraft, then why is the open top so wide? The top of cooling towers widens because this is the point where hot air from inside the tower diffuses and mixes with the atmospheric air. Therefore, we want to maximize the area through which this diffusion takes place, so that more hot vapor is quickly mixed and the entire process of cooling is done more efficiently.