Where points 1 and 2 lie on a streamline, the fluid has constant density, the flow is
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Most nonlinear DEs, even many nonlinear firstorder DEs, cannot be solved in closed form. (Sometimes even when they can be solved this way a numerical technique is still easier).
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div V != 0 would mean that fluid was collecting or dispersing, which it can't if it is incompressible
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It is that branch of science which deals with the motion of the fluids.
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