Which of the following quantities are necessarily constant:

(a) An incompressible fluid (? = constant) flows through a pipe of constant cross-sectional area. If the flow is steady, show that velocity u and volumetric flow rate q are constant.
(b) A chemically reactive gas stream flows steadily through a pipe of constant cross-sectional area. Temperature and pressure vary with pipe length.


a. ?=u A ?, if the ? is constant, the A is constant, and the flow is at steady state, which means it remains unchanged, then the velocity u is constant. Knowing that q=u A, then that would mean q is constant as well.
b. Due to the law of mass conservation, ? must be constant. ? will change due to reaction in the stream; the moles of A will go towards 0 as it travels to the end of the pipe. Due to the temperature and pressure changes in the pipe
both q and u will also vary.

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