Mechanics of Fluids

steadily south-east at 6 m · s −1 ina14m· s −1 north-east wind.
For these conditions use inviscid flow theory to determine the
positions of the stagnation points and the difference between
the maximum and minimum pressures. (Assume an air density
of 1.225 kg · m −3 .)
9.22 Show that flow from a two-dimensional source of strength m
at (a, 0) deflected by an impervious wall along the y-axis is
described by
ψ = (−m/2π)arctan{2xy/(x 2 − y 2 − a 2 )}
9.23 Water leaves the guide passages of an inward-flow turbine at
a radius of 1.2 m. Its velocity is then 20 m · s −1 at an angle of
70 ◦ to the radius. It enters the runner at a radius of 900 mm.
Neglecting friction and assuming that the flow is entirely twodimensional,
calculate the drop in piezometric pressure between
the guide passages and the entry to the runner.
9.24 A kite may be regarded as equivalent to a rectangular aerofoil
of 900 mm chord and 1.8 m span. When it faces a horizontal
wind of 13.5 m · s −1 at 12 ◦ to the horizontal the tension in
the guide rope is 102 N and the rope is at 7 ◦ to the vertical.
Calculate the lift and drag coefficients, assuming an air density
of 1.23 kg · m −3 .
9.25 A rectangular aerofoil of 100 mm chord and 750 mm span is
tested in a wind-tunnel. When the air velocity is 30 m · s −1 and
the angle of attack 7 ◦ the lift and drag are 32.8 N and 1.68 N
respectively. Assuming an air density of 1.23 kg · m −3 and an
elliptical distribution of lift, calculate the coefficients of lift,
drag and vortex drag, the corresponding angle of attack for an
aerofoil of the same profile but aspect ratio 5.0, and the lift and
drag coefficients at this aspect ratio.
Problems 413