PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow · Kinematics, conservation laws and ideal flow
Fluids and Continuum Physics, Ch Potential flow, complex potentials and lift
Problem
A vertical mooring mast of circular cross-section, radius a=0.25 m, stands in a horizontal wind of speed U=20 m s−1 blowing along +x. The air has uniform density ρ=1.2 kg m−3, and the flow in the horizontal plane through the mast is taken to be steady, incompressible, inviscid and irrotational; all points considered lie at the same height, so the ρgz term is the same everywhere. The polar angle θ is measured from the +x axis.
((a)) A region of the flow is described by the velocity potential ϕ=Bxy with B=18 s−1, x and y in metres and ϕ in m2 s−1. Verify that ϕ satisfies Laplace's equation, write down the velocity field, and find the flow speed at the point (x,y)=(0.050,−0.020) m.
((b)) For the ideal flow past the mast, find the surface pressure at θ=45∘, expressed as a difference from the far-field pressure p∞.
((c)) An engineer wishes to give the flow round the mast a circulation so that the mast experiences a transverse force of 900 N per metre of length along +y. What circulation Γ is required, with its sign on the convention used here (anticlockwise positive)?