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9 Nov 2019
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Is the flow of Step 16 irrotational? Is this flow incompressible? Let V be the velocity vector field for an ideal fluid flow defined in a region R. Prove that the level curves the stream function are orthogonal to the level curves of the potential function at all points of R (that is, streamlines are orthogonal to equipotential curves). Fluid dynamics deals with the motion of materials that flow. For this reason, fluid dynamics provides the equations that describe the motion of oceans, hurricanes, lava flows, and air around the wing of a supersonic jet. The usual starting point for fluid dynamics is ideal flow. As the name implies, ideal flows are often not very realistic (the physicist Richard Feynman claimed that ideal flow applies only to "dry water"). However, ideal We consider two-dimensional flows in which the velocity vector describing the motion of the fluid at a point (x, y) is V(x, y) = (u(x,y), v(x, yj), You can think of it as the east-west component of velocity and v as the north-south component (Figure 1). Two-dimensional models describe either very shallow flows or flows in which there is no variation in depth.
SHOW ALL WORK TO GET POINTS!!
Is the flow of Step 16 irrotational? Is this flow incompressible? Let V be the velocity vector field for an ideal fluid flow defined in a region R. Prove that the level curves the stream function are orthogonal to the level curves of the potential function at all points of R (that is, streamlines are orthogonal to equipotential curves). Fluid dynamics deals with the motion of materials that flow. For this reason, fluid dynamics provides the equations that describe the motion of oceans, hurricanes, lava flows, and air around the wing of a supersonic jet. The usual starting point for fluid dynamics is ideal flow. As the name implies, ideal flows are often not very realistic (the physicist Richard Feynman claimed that ideal flow applies only to "dry water"). However, ideal We consider two-dimensional flows in which the velocity vector describing the motion of the fluid at a point (x, y) is V(x, y) = (u(x,y), v(x, yj), You can think of it as the east-west component of velocity and v as the north-south component (Figure 1). Two-dimensional models describe either very shallow flows or flows in which there is no variation in depth.