Yes, vortex breakers are meant to be rigid, though for practical purposes they may flex a small amount.
We can not give you an answer for a thickness because it depends on a lot of information you are not giving us: density, velocity, flowrate, slurry, temperature, material, corrosion allowance, is the breaker spanning the walls of a cone, how long of a span, segemental baffles with stiffeners/supports, will it be a single plate or a cross, ....................
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A little knowledge is a dangerous thing.
No where near enough information given for any sort of half decent answer to be given but generally theyare under considerable stress and need to be very strong
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"Multa ferunt anni venientes commoda secum, Multa recedente adimiunt". (The years as they come bring many agreeable things with them; As they go they take many away).