All Problems Quiz4

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Oct 30, 2023

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Your Answer Correct Answer Dirigibles attached to the ground by wires are often used for surveillance along the border. Winds up to 16 mph (7.15 m/s) are common and the drag forces are high. In order to determine the drag on a dirigible, a 1/15 scale model is built and tested in a water tunnel. For the dirigible shape, the drag force depends on the Reynolds number. Determine the water speed required to model the prototype. The drag measured on the model is 1.92 kN. Determine the corresponding drag on the prototype assuming that the model and prototype are dynamically similar. Assume standard conditions (1 atm, 20°C) for both the air and water properties. D= 523.993249516935 N
Solution For dynamic similarity, the dimensionless pi groups for the model and the prototype must have the same value. For the dragon the dirigible, the two pi groups are the drag coefficient and the Reynolds number I} = Cp and I, = Re The pi groups for the model and prototype are equal for dynamic similarity Hl,m = H1 and H2,m = H2 The drag coefficient is then a function of Reynolds number _ @ pVe Cp = ¢ (Re) or —%pvzfl = ¢<—” ) The Reynolds numbers is the same for model and prototype: P Vnln _ pVC Hom T The velocity of the water required to match the Reynolds number of the dirigible in air is Ay vV, = m P Cm B The velocity of 16 mph corresponds to 7.15 m/s. The density and viscosity of the air and water at standard conditions are from Tables B.2 and B.4. ke Ns Airp = 12045, 4 = 1.82x107° — m- m ke Ns Water: p = 9982 —5 4 = 1.003x 107 —- m- m The velocity for the model must then be kg 1204 — Vo= VoLl oggsm, w5 o P n 9982 = 182x107° = For the same Reynolds number, the drag coefficient is the same for both the model and the prototype. The relation is 2 _ D SV S0 Vit The drag on the prototype will then be kg 2 2 2 1204 = 7152 LV L —192x10° N- — < =) 152 = 524N 50 K& 7132
Your Answer Correct Answer ¥ Your answer is incorrect. A 1/12 scale model of an airfoil is tested in a wind tunnel at a velocity of 125 ft/s, a temperature of 70 F, and at 6 atmospheres pressure. The chord length of the model airfoil is 1.6 ft. Determine the Reynolds number for the tests. Determine the air speed of the prototype when flown at the same dynamic conditions in air at standard conditions. V= 142 ft/s
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Solution A 1/12 scale model of an airfoil is tested in a wind tunnel at a velocity of 125 ft/s, a temperature of 70 F, and at 6 atmospheres pressure. The chord length of the model airfoil is 1.6 ft. Determine the Reynolds number for the tests. Determine the air speed of the prototype when flown at the same dynamic conditions in air at standard conditions. Solution The dynamic conditions are the same if the Reynolds numbers are the same. The model Reynolds number is given as Vi P Em Hm Re, = where ¢, is the model chord length. The density is determined from the ideal gas relation, where the temperature is in °R. 6 14696)& . 144 f2 slu; p=L =T _ 001397 2 RT 1716 —2— 529.7°R fr slig "R The Reynolds number for the model is then 1258.0.01397 2 .1 6t v, 17 S 3 Re, = —oetn = = = 7.31-10° " 3.82:107 = The air speed of the prototype at the same Reynolds number is determined from V = Re £ pt At standard conditions, the air properties are p = 0.002329 % andy = 3.82- 1077 llf)lzs The air speed of the prototype is then 382107 22 V=Re £ =731-10° ———"— =625% pt 0.002329 = 19.2 ft %
Show Attempt History Your Answer Correct Answer ¥ Your answer is incorrect. A model of a pipe network that transports octane (SG = 0.7) at 56 F is used to study pressure drops. The network pipes are 2.4 ft.in diameter and the velocity is 4.7 ft/s, with a pressure drop of 3.4 psi for a 270 ft. length of piping. The 1/3 scale model uses water at 60 F. Determine the velocity of the water and the pressure drop for a modes length corresponding to the 270 ft length of piping in the network that maintains dynamic similarity. Vi = 0.154 ft/s Appy = 0.0355 psia
Solution A model of a pipe network that transports octane (SG = 0.7) at 56 F is used to study pressure drops. The network pipes are 2.4 ft.indiameter and the velocity is 4.7 ft/s, with a pressure drop of 3.4 psi for a 270 ft. length of piping. The 1/3 scale model uses water at 60 F. Determine the velocity of the water and the pressure drop for a modes length corresponding to the 270 ft length of piping in the network that maintains dynamic similarity. Solution For dynamic similarity between the model and the prototype, the Reynolds numbers must be the same Po Vi m Ve i " The characteristic dimension for the Reynolds number is the pipe diameter. The velocity of the water to match the Reynolds number of the octane flow must then be _ yLl D Fe Vm = Vo5 The density and viscosity of the octane are found using the specific gravity (0.7) and Figure B.1 for viscosity. The density and viscosity of water are taken from Table B.1. 1 | Ns Ib Octane:p = 0.7+ 1936 2 = 135522 )/ = 6.0x 107 — = 13x 107 — ft? ft* m? ft 1 b Water: p = 3 u& = 2344 %107 —15 fe* ft* The velocity for the model must then be slug 5 Ibs o 1.355— 2344 x 1077 — v, = v P ot 3. g0t P D 1 S 1938 ‘I‘L"E 13 10_5 b s The pressure drop is represented by the pressure coefficient (or Euler number, Table 7.1), and is a function of Reynolds number. The pressure coefficient is given by The Reynolds numbers are the same, and so the pressure coefficients for the model and prototype are equal Ap AP 2 1 2 3PV 9m Vi The pressure drop for the model is then slug £1\2 o V2 o 1938 (1781%) PV st (yqny? = 69.6 psi The higher velocity causes the pressure drop of the model to be greater.
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Show Attempt History Your Answer Correct Answer Dirigibles attached to the ground by wires are often used for surveillance along the border. Winds up to 36 mph (16.1 m/s) are common and the drag forces are high. In order to determine the drag on a dirigible, a 1/12 scale model is built and tested in a water tunnel. For the dirigible shape, the drag force depends on the Reynolds number. Determine the water speed required to model the prototype. The drag measured on the modelis 9.72 kN. Determine the corresponding drag on the prototype assuming that the model and prototype are dynamically similar. Assume standard conditions (1 atm, 20°C) for both the air and water properties. D= 2670.972958669355 N
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Solution Golf balls must meet a diameter standard of not less than 4.267 cm. A ball hit by a professional golfer can reach a speed of 80 m/s and an angular rotational speed of 9400 rpm. Determine the diameter of a model of a golf ball to use in a wind tunnel with amaximum speed of 33 m/s. The lift and drag of a golf ball are functions of the Reynolds number and a dimensionless group that includes the rotation speed. Determine the dimensionless groups that maintain dynamic similarity and use them to determine the diameter and rotational speed for the model. Solution The dimensionless groups are the Reynolds number and a group that includes the rotational speed of the golf ball. The dimensions of rotational speed w are s°1. A dimensionless group that combines the rotational speed, the diameter of the golf ball, and the velocity is @D == For dynamic similarity, the Reynolds numbers for the prototype and the model are the same. The appropriate dimension for a golf ball is the diameter. The Reynolds number is VpD Re = m The relation between the Reynolds numbers for the model and the prototype is then Vu Pin Do VpD Re, = Re or fi— = + Assuming that the air properties are the same for both the prototype and the model yields the relation for the model diameter at the wind tunnel maximum speed as Y% 103 em D, = Dy~ = 4267Tcm- — The dimensionless group that contains the rotational speed is the same for the model and prototype. onDn _ oD V. TV The model rotational speed is 4267 cm 332 Wy = ® %% = 9400 rpm - = 1600 rpm

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Related Questions
A model of an aircraft is being tested in a wind-tunnel.  If the model was replaced by one that is half the size but is otherwise identical, what would be the ratio of the drag on the large model to the drag on the small model for exactly the same flow conditions.  Give your answer to two decimal places.  The model is in a region where drag coefficent is independent of Reynolds number.
Problem 5Given: A prototype ship is 50 m long and designed for a cruising speed of 10 m/s. The drag is to be simulated by a 1-m-long model that will be towed in a towing tank.Required: Using Froude scaling, determine the tow speed and the ratio of the model to prototype drag and power (i.e. Vm/Vp and Pm/Pp . Recall: Power=Force*Velocity
A student needs to measure the drag on a prototype of characteristic length d, moving at velocity U, in air at sea-level conditions. She constructs a model of characteristic length dm such that the ratio d,/dm drag under dynamically similar conditions in sea-level air. The student claims that the drag force on the prototype will be = a factor f. She then measures the model identical to that of the model. Is her claim correct? Explain, showing your work (no credit for just guessing).
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
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 × 10-³ Pa.s. V Por P Wind tunnel test section Model Shield FD Drag balance Strut
2) A prototype ship is 50 m long and designed for cruising speed of 10 m/s. The drag is to be simulatedby a 1-m-long model that will be towed in a towing tank. Using Froude scaling, determine the tow speedand the ratio of the model to prototype drag and power.
Problem 3: Let's say you want to predict the aerodynamic drag of a new car based on the use of a model that is one- fifth scale of the actual car/prototype car. We want to predict the drag of the car when it has wind velocity 75 miles/hour with an air temperature of 40°C. The model is placed in a wind tunnel at 10°C. Determine the wind tunnel velocity necessary to achieve similarity between the model and the prototype.
If the model is 2 times larger and its velocity is 6.25 larger than the prototype, what will be the ratio between the model and prototype drag force? (Provide your answer using 3 decimal points) Answer: 0.495 Please provide a Handwritten solution in detail..
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.
A student wants to estimate drag force on a golf ball of diameter D moving in air at a speed of U at atmospheric conditions. The student has access to a wind-tunnel and develops a replica of the ball that is 5 times smaller in diameter sets the wind speed 5 times larger than the actual golf ball. Compared to the force on the replica, the estimated drag force on the actual golf ball will be
A 1:4 scale torpedo model has been built. The prototype is expected to move at a speed of 6m/s in water at 15°C. What should be the velocity in the model if, a) the test is done in a stream channel at 15°C; and b) the test is done in a wind tunnel at 27°C and a pressure of 20 atm?
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.
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)
The drag force of a new sports car is to be predicted at a speed of 65 mi/h at an air temperature of 25 C. Automotive engineers build a 0.333333333333333 scale model of the car to test in a wind tunnel. The temperature of the wind tunnel air is also 25 C. Determine how fast (in mi/h) the engineers should run the wind tunnel to achieve similarity between the model and the prototype.
A student team is to design a submarine for a design competition. The overall length of the prototype submarine is 4.85 m. The prototype submarine is expected to moves through freshwater in the lake at 0.440 m/s. The student team builds a one-fifth scale model to test in their university's wind tunnel. Calculate the wind tunnel air speed in order to achieve similarity with the prototype submarine. For water at T= 15 °C and atmospheric pressure, the density is p = 999.1 kg/m³ and the dynamic viscosity is µ = 1.138 x 10³ kg/m-s. For air in the wind tunnel at T= 25 °C and atmospheric pressure, the density is p= 1.184 kg/m³ and the dynamic viscosity is µ = 1.849 x 10-$ kg/m's.
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