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The sum of static pressure and dynamic pressure is said to be constant along a streamline. Except for energy conservation reasons I don't understand why that is.

Static pressure is proportional to the cross sectional area. Dynamic pressure is inversely proportional to the square of the cross sectional area (since speed is inversely proportional to the cross sectional area and dynamic pressure is proportional to the square of the speed).

When the cross sectional area decreases by half, the static pressure decreases by half, the speed doubles and the dynamic pressure increases four times.

What did I miss?

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  • $\begingroup$ I think what you are looking for is a continuity equation. All continuity equations have the same basic form: $\partial_{t}$(some type of density) + $\nabla \cdot$(some type of flux) = (sources) + (sinks/losses). A flux is basically your density times a velocity, in terms of dimensional analysis. $\endgroup$ Oct 25, 2014 at 15:56

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"Static pressure is proportional to the cross sectional area" - this is wrong. According to Bernoulli law this is not so. The force due to pressure is indeed proportional to the cross section area (times pressure), but it is not of energy dimension.

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