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intuitional

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please note in the process proving bernoulli we use the CONTINUITY equation.Consider a situation wherein a pitot tube is used to measure pressure/velocity in a steady flow(picture attached for reference).Here we use bernoulli for pressure measurement.we apply the bernoulli theorem for a streamline which has some finite velocity at one end while zero(stagnation point) at the other end.This violates continuity and hence we canot apply bernoullis theorem in the first place itself!can ayone explain the situation

PS-in almost all fluid mechanics books they just apply bernoullis directly as written,without any explanation of the above question.a name of a book explaining the situation properly would be very helpful too.

PS-in almost all fluid mechanics books they just apply bernoullis directly as written,without any explanation of the above question.a name of a book explaining the situation properly would be very helpful too.