Problem 7-34: A student team is to design a human-powered submarine for a design competition.
The overall length of the proto¬ type submarine is 4.85 m, and its student designers hope that it
can travel fully submerged through water at 0.440 m/s. The water is freshwater (a lake) at T =
15°C. The design team builds a one-fifth scale model to test in their university’s wind tunnel (Fig.
P7-34). A shield surrounds the drag balance strut so that the aerodynamic drag of the strut itself
does not influence the measured drag. The air in the wind tunnel is at 25°C and at one standard
atmosphere pressure. At what air speed do they need to run the wind tunnel to achieve similarity?
Answer: 30.2 m/s
Problem 7-35: Repeat Prob. 7-34 with all the same conditions except that the only facility
available to the students is a much smaller wind tunnel. Their model submarine is a one-twentyseventh scale model instead of a one-fifth scale model. At what air speed do they need to run the
wind tunnel to achieve similarity? Do you notice anything disturbing or suspicious about your
result? Discuss your results.
Problem 7-37E: The aerodynamic drag of a new sports car is to be predicted at a speed of 60.0
mi/h at an air temperature of 25°C. Automotive engineers build a one-third scale model of the car
(Fig. P7-37E) to test in a wind tunnel. The temperature of the wind tunnel air is also 25°C. The
drag force is measured with a drag balance, and the moving belt is used to simulate the moving
ground (from the car’s frame of reference). Deter¬ mine how fast the engineers should run the
wind tunnel to achieve similarity between the model and the prototype.
Problem 7-47: A periodic Karman vortex street is formed when a uniform stream flows over a
circular cylinder (Eig. P7^7). Use the method of repeating variables to generate a dimensionless
relationship for Karman vortex shedding frequency as a function of free-stream speed V, fluid
density p, fluid viscosity p, and cylinder diameter D. Show all your work. Answer: St = f (Re)
Problem 7-58: When small aerosol particles or microorganisms move through air or water, the
Reynolds number is very small (Re <<1). Such flows are called creeping flows. The aero¬ dynamic
drag on an object in creeping flow is a function only of its speed V, some characteristic length
scale L of the object, and fluid viscosity /a (Fig. P7-58). Use dimensional analysis to generate a
relationship for Fj, as a function of the independent variables.