During the course, we have learned about the Bernoulli equation as well as rotational and irrotational flows. Answer the following problems c. Give explicit one example of velocity field (v = … i + … j meter/second) for rotational flow and one example for irrotational flow. d. Is Bernoulli equation valid only for rotational flows or it is also valid for irrotational flow? Explain your answer.

Problem s): Consider incompressible Newtonian fluid flow between parallel plates (Fig. 7) that are horizontal and a distance A apart. A constant pressure gradient is applied in the x-direction (dp/dx). The flow is fully developed laminar and steady. The plate width is denoted by B. a) Simplify the governing equations TILST b) Define the boundary conditions inte c) Determine the velocity profile Continuity Equation f + P8x P8y ə əx Momentum Equations au 2x² Pgz (pu) + др əx + μl ap + M ay (pv) + 2- (07) - = əz ap + az d²v əx² a²w 2 dx² + + + อิน dy² dv dy² a²w ay² + + a²u ลิน az + a²w az² ди pl at dv at dw at + u + 11 + u ди əx dv əx aw əx + v + v ди + v ду dv ду + w dw + w du Fig. 7: Flow between parallel plates with a constant pressure gradient az du + w əz dw az Fixed 1 1 1 u(y) Fixed max A

A subtle point, often missed by students of fluid mechanics (and even their professors!), is that an inviscid region of flow is not the same as an irrotational (potential) region of flow. Discuss the differences and similarities between these two approximations. Give an example of each.

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