Advanced Hydrodynamics
Take Home Exam
1391/04/25
Name:
Student #:
The take-home exam is due on 91/04/27, 10am. Absolutely no late
exams will be accepted. The solutions must be typed, and may be
turned in directly to the Mechanical Engineering Department or may
be e-mailed to:
s.niazi@hormozgan.ac.ir , or saeidniazi@hotmail.com
Note: write down all of your assumptions
Question 1
As an approximation so that we can simulate tornadoes, suppose we consider a singlecelled tornado that behaves as a columnar vortex. Let the columnar vortex travel at a
uniform velocity to simulate a tornado moving with a storm. Outside of the tornado core
of radius rc, the flow is assumed potential with a circulation Г∞. Let Station 1 be some
reference station in the irrotational field where the barometric pressure is 10.0 m of
water, the wind speed is 1.5 m/sec at a distance of 180 m from the centerline of the
columnar vortex that is moving with an average speed of 4.5 m/sec. The core radius is
7.5 m. Calculate:
a) The ambient circulation Г∞ at Station 1.
b) The tangential velocity at a 15 m radius.
c) The pressure at a 15 m radius.
d) If a house has a 10 m2 frontal area, what is the normal force on the frontal area if
the tornado's center passes within 7.5 m of it?
References
-
Modelling in Transport Phenomena: a conceptual approach. Ismail Tosun,
Second edition 2007, Elsevier
Theory of Wing Sections (Including A Summary of Airfoil Data), Ira H. Abbott
and Albert von Doenhoff
Low-Speed Aerodynamics, (From Wing Theory to the Panel Methods) , Joseph
Katz and Allen Plotkin