Page 67 - Aerodynamics for Engineering Students

50 Aerodynamics for Engineering Students

increase, aggravating the stall. Such a characteristic is an unstable break. This type of
characteristic is commonly found with highly swept wings, although measures can be
taken to counteract this undesirable behaviour.

Exercises
1 Verify the dimensions and units given in Table 1.1.
2 The constant of gravitation G is defined by

where F is the gravitational force between two masses m and M whose centres of
mass are distance r apart. Find the dimensions of G, and its units in the SI system.
(Answer: MT2L-3, kg s2 m-3)
3 Assuming the period of oscillation of a simple pendulum to depend on the mass of
the bob, the length of the pendulum and the acceleration due to gravity g, use the
theory of dimensional analysis to show that the mass of the bob is not, in fact,
relevant and find a suitable expression for the period of oscillation in terms of the
other variables. (Answer: t = cfi)
4 A thin flat disc of diameter D is rotated about a spindle through its centre at a
speed of w radians per second, in a fluid of density p and kinematic viscosity v. Show
that the power P needed to rotate the disc may be expressed as:
P= &Dy(L)
wD2

Note: for (a) solve in terms of the index of v and for (b) in terms of the index of w.
Further, show that wD2/v, PD/pv3 and P/pw3D5 are all non-dimensional quan-
tities. (CUI
5 Spheres of various diameters D and'densities n are allowed to fall freely under
gravity through various fluids (represented by their densities p and kinematic
viscosities v) and their terminal velocities V are measured.
Find a rational expression connecting V with the other variables, and hence
suggest a suitable form of graph in which the results could be presented.
Note: there will be 5 unknown indices, and therefore 2 must remain undetermined,
which will give 2 unknown functions on the right-hand side. Make the unknown
indices those of n and v.
V
(Answer: V = fi f , therefore plot curves of- a
against (:) fi for various values of n/p)

6 An aeroplane weighs 60 000 N and has a wing span of 17 m. A 1110th scale model is
tested, flaps down, in a compressed-air tunnel at 15 atmospheres pressure and 15 "C