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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 flows offer a good opportunity to apply the ideas of vector calculus. We consider c wo-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. Recall that a differentiable vector field V is irrotational if its curl is zero at all points of a domain; that is, . Show that for a two-dimensional vector field implies V=(u, v), *V=0 implies that vx-uy=0. Recall that a differentiable vector field V is irrotational if its curl is zero at all points of a domain; that is, . Show that for a two-dimensional vector field implies V=(u, v), *V=0 implies that vx-uy=0. Recall that a differentiable vector field V is irrotational if its curl is zero at all points of a domain; that is, . Show that for a two-dimensional vector field implies V=(u, v), *V=0 implies that vx-uy=0. 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 flows offer a good opportunity to apply the ideas of vector calculus. We consider c wo-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. Recall that a differentiable vector field V is irrotational if its curl is zero at all points of a domain; that is, . Show that for a two-dimensional vector field implies V=(u, v), *V=0 implies that vx-uy=0. 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 flows offer a good opportunity to apply the ideas of vector calculus. We consider c wo-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. Recall that a differentiable vector field V is irrotational if its curl is zero at all points of a domain; that is, . Show that for a two-dimensional vector field implies V=(u, v), *V=0 implies that vx-uy=0. 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 flows offer a good opportunity to apply the ideas of vector calculus. We consider c wo-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.
