Problem Description

The present problem is solved using the potential flow past a half-body. As shown in the theory section, the magnitude of the velocity at any point is given by

To determine the actual wind speed at any point along the surface, variables b, r and θ need to be determined. Note that b is the distance between the source and the stagnation point (see theory section).

The stagnation point (i.e., point B) is given by

     θ = π   and   r_stagnation = b = m/2π U

and the stream function at this point is

     ψ_stagnation = πbU

The stream function that passes through the stagnation point and along the hill, is then obtained as

     ψ = πbU = U r sinθ + b U θ

which can be rearranged to give

     r = b(π - θ)/sinθ    or    y = b(π - θ)

The above expression gives the radius location along the hill. Note that as θ approaches 0 (i.e., towards inland), y approaches πb. For this problem, πb becomes 300 ft. Thus, b equals 300/π.

At the proposed site (i.e., point A), θ_A is π/2, and the radius (r_A) is determined to be πb/2. The velocity at point A is then calculated as

     V_A = 59.27 mph

The velocity for all angles is given at the left. Notice, the velocity is zero at the front stagnation point, and rises to a maximum at about 120 degrees. the downstream final velocity will be the same as the initial velocity, 50 mph.