The drag force on a submarine, which is moving on the surface, is to be determined by a test ona model which is scaled down to one-twentieth of the prototype. The test is to be carried in atowing tank, where the model submarine is moved along a channel of liquid. The density and thekinematic viscosity of the seawater are 1010 kg/m³ and 1.3x10-6 m 2/s, respectively. The speedof the prototype is 2.6 m/s. Assume that F = f(V, L. g. p.), using pi-theorem and similarityprinciple to:a) Determine the speed at which the model should be moved in the towing tank.b) Determine the kinematic viscosity of the liquid that should be used in the towing tank.

Let's refine the solutions for both parts of the problem using the concept of dimensional analysis…

Answered: The drag force on a submarine, which is…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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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 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). Determine how fast the engineers should run the wind tunnel to achieve similarity between the model and the prototype.
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1. (a) The motion of a floating vessel through the surrounding fluid results in a drag force D which is thought to depend upon the vessel's speed v, its length I, the density p and dynamic viscosity μ of the fluid and the acceleration due to gravity g. Show that:- D = pv²1² (1) (b) In order to predict the drag on a full scale 50m long ship traveling at 7m/s in sea water at 5°C of density 1027.7225 kg/m³ and viscosity 1.62 x 103 Pa.s, a model 3m long is tested in a liquid of density 805 kg/m³. What speed does the model need to be tested at and what is the required viscosity of the liquid?
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