1. The aerodynamic drag of a Formula 1 car is to be predicted at a speed of 100 km/hr in an environment where air temperature is 25°C and the corresponding kinematic viscosity of air is v=1.60×105 m²/s. Automotive engineers build a 1/4 scale model of the car to test in a wind tunnel, where the air temperature is 10°C and kinematic viscosity of air is v=1.46×105 m²/s. A drag balance is used to measure the drag, and the moving belt is used to simulate the moving ground. Determine the speed of the wind tunnel that the engineers must run in order to achieve similarity between the model and prototype. (Ans: 365 km/hr). (Acknowledgement:http://www.invetr.com/uploads/2/1/8/2/21829402/565543954_orig.jpg)

1. The aerodynamic drag of a Formula 1 car is to be predicted at a speed of 100 km/hr in an environment where air temperature is 25°C and the corresponding kinematic viscosity of air is v=1.60×105 m²/s. Automotive engineers build a 1/4 scale model of the car to test in a wind tunnel, where the air temperature is 10°C and kinematic viscosity of air is v=1.46×105 m²/s. A drag balance is used to measure the drag, and the moving belt is used to simulate the moving ground. Determine the speed of the wind tunnel that the engineers must run in order to achieve similarity between the model and prototype. (Ans: 365 km/hr). (Acknowledgement:http://www.invetr.com/uploads/2/1/8/2/21829402/565543954_orig.jpg)

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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A light parachute for military purposes is being designed. Its diameter is 7.3 m, test load, parachute and rig weight is 1023 N. For this weight, the limit descent speed Vt = 6.1 m / s, which is taken as a basis in the design of the parachute. The 1/12 scale model will be tested in the wind tunnel and the temperature and pressure of the tunnel are the same as that of the prototype. (15.5 ºC and standard atmospheric pressure) a) Calculate the resistance coefficient of the prototype. (Hint: At the limit descent speed, the weight is balanced by the aerodynamic resistance.) b) At what speed should the wind tunnel be run to achieve dynamic similarity? c) Calculate the aerodynamic resistance of the model parachute in the wind tunnel. Density of air at 15.5 ºC and standard atmospheric pressure ρ = 1.22 kg / m3 viscosity, µ = 8.16x10-6 kg / m.s will be taken.
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Drop-load (I)This exercise is part of a series of problems aimed at modelling a situation by progressively refining our model to consider more and more parameters. This progressive approach is very close to what professional scientists do! Context We want to lower a suspended load in a controlled way so that it hits the ground with a speed whose modulus is not too great. To do this, the suspended load (B) is connected by a rope passing through a pulley to another mass (A), which can move on a horizontal surface. Information The masses of the charges A and B are known.The pulley is a ring of mass mp and radius R that can rotate without friction.The surface on which mass A is placed is horizontal.There is no friction between mass A and the surface on which it is placed.The string attached to mass A is perfectly parallel to the surface on which the mass rests. SchematizationDraw a diagram of each object that interests us. Draw x- and y-axes for each object. Draw and name each force…
2 A prototype car is designed for cold weather operation in Denver (-10°C, 83 kPa, altitude 1600m, µ = 1.741 × 10-5 Pas). It's drag force is to be tested in a 1:7 model in a wind tunnel at 150 mph under standard sea level conditions. If the model and prototype satisfy dynamic similarity what prototype velocity, in mph, is matched? Is this a reasonable test? 1 mile = 1609 m HINT: p = pRT
1. A model submarine is tested in a sea water tank at a speed of 30 m/s. The prototype speed should be 21.6 km/hr. (a) Determine the geometric scale between the model and the prototype (b) Determine the model speed if it is tested in a pressurized air wind tunnel with 12/s. kinematic viscosity v = 8 × 10-7 m² /s. For sea water use v = 1.124 × 10-6 m² /s.
The drag on a 2-m-diameter satellite dish due to an 69-km/hr wind is to be determined through a wind tunnel test using a geometrically similar 0.4-m-diameter model dish. Assume standard air for both model and prototype. (a) At what air speed should the model test be run? (b) With all similarity conditions satisfied, the measured drag on the model was determined to be 152 N. What is the predicted drag on the prototype dish? (a) Vm = (b) D = i i km/hr N
2. A student team is to design a human-powered submarine for a design competition. The overall length of the prototype 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, as shown in the Fig. 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 in order to achieve similarity? Take for water at T = 15 °C and atmospheric pressure, p = 999.1 kg/m³ and µ = 1.138 × 10-³ Pa.s. Take for air at T = 25 °C and atmospheric pressure, p = 1.184 kg/m³ and µ = 1.849 × 105 Pa.s. Wind tunnel test section V Poo, P Model Shield FD Drag balance Strut
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Air flows across a thin airfoil at a velocity of 90 m/s. For the same Reynolds number based on the actual chord length, L = 1.40 m, what velocity of water is required for a 1/2 scale model test? Assume a temperature of 15°C for both fluids. air U = 90 m/s L = 1.40 m