A fluid of density p and viscosity u flows through a section of horizontal converging-diverging duct. The duct cross-sectional areas Ala, Alm and Aantlet are known at the inlet, throat (minimum area), and outlet, respectively. Average pressure Poutlet is measured at the outlet, and average veloc- ity Vines is measured at the inlet. (a) Neglecting any irrevers- ibilities such as friction, generate expressions for the average velocity and average pressure at the inlet and the throat in terms of the given variables. (b) In a real flow (with irrevers- ibilities), do you expect the actual pressure at the inlet to be higher or lower than the prediction? Explain.

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Dimensional homogeneity

The term dimensional homogeneity means that in an equation, the dimensions of each term on both sides are equal, which means the dimensions of the left-hand side (LHS) of an equation are similar to the dimensions of the right-hand side (RHS). For a dimensionally homogeneous equation, the powers of fundamental dimensions will be identical on both sides of the equation.