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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Here, a 1:10 scale prototype of a propeller on a ship is to be tested in a water channel. What would the rotating speed of the model be if the rotational speed of the p propeller is 2000 rpm, and if: (a) the Froude number governs the model-prototype similarity(b) Reynolds number governs the similarity
(b) A Formula 1 team tests their car in a wind tunnel at a scale of 50%, at a speed of Vwinarunnet = 50 m/s. The measured downforce at this speed is Foownforce.WT = 3000 N and the model reference area is Aref wT = 0.5 m?. 1. Find the downforce magnitude on the full-scale race car at the same Reynolds number. Assume constant air density p = 1.2 kg/m. II. It is said that F1 cars could travel upside down, as shown below. At what speed should the full-scale car travel to achieve this, if its mass is m = 740 kg? The acceleration of gravity is g = 9.81 m/s?. Downforce Weight
Ex. The force required to tow a 1:30scale model of a motor boat in a lake at a speed of 2m/s is 0.5 N, Assuming that the viscosity resistance due to water and air is negligible in comparison with the wave resistance, calculate the corresponding speed of the prototype for dynamically similar conditions. What would be the force required to propel the prptype at that velocity in the same lake? Ans.: 10.95m/s, 13500N
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.
An underwater device which is 2m long is to be moved at 4 m/sec. If a geometrically similar model 40 cm long is tested in a variable pressure wind tunnel at a speed of 60 m/sec with the following information, Poir at Standard atmospheric pressure = 1.18kg/m³ Pwater = 998kg/m3 Hair = 1.80 x 10-5 Pa-s at local atmospheric pressure and Hwater = 1 × 10-3 Pa-s then the pressure of the air in the model used times local atmospheric pressure is
A ship 350 m long moves in sea water whose density is 1030 kg/m3 . A 1:120 model of this ship is to be tested in a wind tunnel. The velocity of the wind tunnel around the model is 35 m/s and the resistance of the model is 65 N. Determine the velocity and also the resistance of the ship in sea water. The density of air is given as 1.24 kg/m3 . Take the kinematic viscosity of air and sea water as 0.012 stokes and 0.018 stokes respectively.
During World War II, Sir Geoffrey Taylor, a British fl uiddynamicist, used dimensional analysis to estimate theenergy released by an atomic bomb explosion. He assumedthat the energy released E , was a function of blast waveradius R , air density ρ, and time t . Arrange these variablesinto a single dimensionless group, which we may term theblast wave number .
Solve it correctly
A football, meant to be thrown at 60 mi/h in sea-level air( ρ = 1.22 kg/m 3 , μ = 1.78 E-5 N . m 2 ), is to be testedusing a one-quarter scale model in a water tunnel ( ρ =998 kg/m 3 , μ = 0.0010 N . s/m 2 ). For dynamic similarity,what is the ratio of prototype force to model force?( a ) 3.86 : 1, ( b ) 16 : 1, ( c ) 32 : 1, ( d ) 56 : 1, ( e ) 64 : 1
I need the answer as soon as possible
List and describe the three necessary conditions for complete similarity between a model and a prototype.
Wind tunnel test section km/h Model FD Moving belt Drag balance The aerodynamic drag of a new Volvo FH truck is to be predicted at a speed of 85 km/h at an air temperature of 25°C (p=1.184 kg/m³, u=1.849x10-5kg/m-s). Volvo engineers build a 1/2 scale model of the FH to test in a wind tunnel. The temperature of the wind tunnel is also 25°C. The drag force is measured with a drag balance, and the moving belt is used to simulate the moving ground. Determine how fast the engineers should run the wind tunnel to achieve similarity between the model and the prototype.

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