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Question: problem 5 experime characterize the flow outside its central core...

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Problem 5 Experime characterize the flow outside its central core of radius R (i.e. for r> R), where A and B are constants. The flow is steady, axisymmetric, and two-dimensional. The fluid is Newtonian and has constant properties. Gravity may be neglected. ntal data from hurricanes show that the following velocity distribution can be used to for r> R a. Determine whether the flow in the hurricane is incompressible b. Determine whether the flow in the hurricane is irrotational. c. Assuming the pressure distribution in the hurricane is a function of r only, i.e. P- P(r) only, find an expression for P(r). The pressure in the core of the hurricane is constant, i.e. P-Pfor rsR The strength of the hurricane may be represented by the circulation Г(r). Consider a closed circular path of radius r surrounding the entire hurricane. The circulation is found by integrating the tangential velocity along this closed path, i.e d. 6-0 Alternatively, using Stokes theorem, the circulation can be found by integrating the in-plane vorticity field over the circular area of the hurricane (of radius r), as shown in the expression below. Find an expression for the hurricane strength Γ(r) and verify Stokes theorem. Clearly state any assumptions that are required.

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