A cubic approximate velocity profile was used in Problem 5.12 to model flow in a laminar incompressible boundary layer on a flat plate. For this profile, obtain an expression for the x and y components of acceleration of a fluid particle in the boundary layer. Plot ax and ay at location x = 3ft, where δ = 0.04 in., for a flow with U = 20 ft/s. Find the maxima of ax at this x location.
5.12 A useful approximation for the x component of velocity in an incompressible laminar boundary layer is a cubic variation from u = 0 at the surface (y = 0) to the freestream velocity, U. at the edge of the boundary layer (y = δ). The equation for the profile is u/U =
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Fox and McDonald's Introduction to Fluid Mechanics
- In chapter 12, we found the velocity profile for flow around a sphere using the creeping flow approximation. For the flow, derive the velocity profile for V, and Ve. Also, find the pressure distribution P. Finally, find the drag force acting on the sphere. (Hint: use the following integration ranges (1) 0<0<â and (2) 0<ô<2à). You can use all the assumptions that we made for this flow in the class.arrow_forwardfor a steady incompresible two dimensional flow, represented in cartesian coordinates (x,y), a student correctly writes the equation of pathline of any arbitrary particle as dx/dt =ax and dy/dt= by where a and b are constants having unit of second‐¹. if value of a is 5 determine the value if b.arrow_forwardfor a steady incomprssible two dimensional flow, represented in cartesian coordinates (x,y), a student correctly writes the equation of pathline of any arbitrary particle as dx/dt =ax and dy/dt= by where a and b are constants having unit of second‐¹. if value of a is 5 determine the value if b.arrow_forward
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