A 1/12th scale model of an aircraft was tested in a wind tunnel under sea level standard conditions. The following data was obtained. Air Speed (m s1) Angle of attack Lift Drag Pitching moment (N m) (degrees) (N) (N) 10 9.9225 0.8153723 -2.20813 15 37.20938 2.156077 -5.86508 92.61 4.690329 -12.0209 20 4 The wing area of the full sized aircraft is 83.0 m and the wing aspect ratio is 9.6. What value namic centre have?
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- 3. Problem Estimate the frictional resistance Rp for a container ship using the ITTC 1957 model-ship correlation line Equation (2): 0.075 CF [ log,,(Re) – 21 The ship has the following particulars: Full scale ship data length between perpendiculars Lep length in waterline length over wetted surface 195.40 m Lwz Los For the wetted surface S you can use the following formula by Kristensen and Lützen (2012) derived for container ships. 200.35 m 205.65 m breadth B 29.80 m draft T 10.10 m 37085.01 m3 S = 5 + Lw. T 0.995 displacement design speed Again, use the most up-to-date ITTC water properties sheet for density and kinematic viscosity. V 21.00 kna) Vortex shedding is a common fluid flow problem across bluff bodies. The design of buildings and bridges take into account the analysis of vortex shedding phenomena to avoid the occurrence of resonance, where the natural frequency of the body matches the vortex shedding frequency. In this analysis, the following parameters are found to be important: velocity of flow (V), density of fluid (p), hydraulic diameter of the duct (D₁), dynamic viscosity of fluid (u), width of body (B) and the vortex shedding frequency (n). Using the method of repeating variables, find the non-dimensional relationship governing the phenomena.A fighter aircraft is to operate at 200 m/s in air at standard conditions (p= 1.2 kg/m³). A model is constructed to 1/20 scale (length ratio) and tested in a wind tunnel at the same air temperature (same air viscosity) to determine the drag force. The drag force Fp is a function of the air density p and viscosity µ, the velocity V and the cross section length of the airplane D. a) Use dimensional analysis to prove that: F, and PV²D² pVD What are these two dimensionless numbers? b) If the model is tested at 50 m/s, what air density should be used in the wind tunnel? Comment the result and give a recommendation. c) If the model drag force is 250 N at 50 m/s, what will be the drag force of the prototype? Lift force 200 m/s Drag force
- A skateboarder weighing 51.24 kg goes over a smooth circular hilI. If the skateboarder's speed at point A is 21.12 m/s, what is his speed at the top of the hill (point B)? B A 10 m 450 Paint X Ute Use g=9.8 m/s? . Derive first the working equation before you substitute the given data to avoid disparity from the correct answer. Round off answer up to two decimal places. Include the unit/s. Abbreviation only.Lab 2-Measurement Asynch - Tagged.pdf Page 4 of 7 ? Part I: Taking Measurements & Estimating Uncertainties for a single measurement www.stefanelli.eng.br The mass of the object is_ 0 i Parts on a tripie peam palance 0 0 10 20 30 1 100 2 3 40 200 4 +/- 50 60 70 5 300 7 400 80 Qv Search 8 90 9 500 100 9 10 g www.stefanelli.eng.brA dam spillway is to be tested using Froude scaling with a 1:20 model. The model flow has an average velocity of 0.7 m/s. What is the velocity of prototype?
- A one-fourth scale model of a car is to be tested in a wind tunnel. The conditions of the actual car are V = 45 km/h and T = 0°C and the air temperature in the wind tunnel is 20°C. In order to achieve similarity between the model and the prototype, the wind tunnel is run at 180 km/h. The properties of air at 1 atm and 0°C: ? = 1.292 kg/m3, ? = 1.338 × 10−5 m2/s. The properties of air at 1 atm and 20°C: ? = 1.204 kg/m3, ? = 1.516 × 10−5 m2/s. If the average drag force on the model is measured to be 70 N, the drag force on the prototype is (a) 66.5 N (b) 70 N (c) 75.1 N (d ) 80.6 N (e) 90 NQuestion 5 a) A 1:20 scale model of a surface vessel is used to test the influence of a proposed design on the wave drag. A wave drag of 6.2 lb is measured at a model speed of 8.0 ft/sec. What speed does this correspond to on the prototype, and what wave drag is predicted for the prototype? Neglect viscous effects, and assume the same fluid for model and prototype. b) Discuss the modelling and types of similaritiesA model pump has an impeller diameter of 30 cm. During a manufacturer's test, this model achieved an efficiency of 80%. A prototype in the same family (geometrically similar) is 10 times larger than this tested model. Under the same operating conditions dynamically similar to those in the model test, what most approximately will be the efficiency of the prototype pump? O 74% OOOO O 64% O 84% O 94%
- A dimensional analysis is performed on the drag on a boat. When the effects of viscosity can be neglected, the Euler number based on the drag D experienced by the boat is a function of a Froude number. The effects of the dimensions of the boat can be represented by its length I. The drag on a model of the model is measured as 0.35N. If the ratio of / for a full-scale model to the value of/ for the model is 46, calculate the expected drag on the full-scale boat. Your answer should be to the nearest kN. The properties of the water in the model test matches those for the full-scale boat.6. A ball is thrown straight up in the air at time t = 0. Its height y(t) is given by y(t) = vot - 791² (1) Calculate: (a) The time at which the ball hits the ground. First, make an estimate using a scaling analysis (the inputs are g and vo and the output is the time of landing. Think about their units and how you might construct the output using the inputs, just by matching units). Solve the problem exactly. Verify that the scaling analysis gives you (almost) the correct answer. (b) The times at which the ball reaches the height v/(4g). Use the quadratic formula. (c) The times at which the ball reaches the height v/(2g). You should find that both solutions are identical. What does this indicate physically? (d) The times at which the ball reaches the height v/g. What is the physical interpretation of your solutions? (e) Does your scaling analysis provide any insight into the answers for questions (a-e)? Discuss. (Hint: Observe how your answers depend on g and vo).Given the following measurements of velocity for a falling object with m = 3kg: v, meters/seconds t, seconds 0 -1.424 -2.778 -4.068 -5.274 -6.426 -7.519 0 0.05 0.10 0.15 0.20 0.25 0.30 Use 4th Order Runge-Kutta to approximate the coefficient of drag, k, given the model: mv' = -mg - kv Approximate the terminal velocity and the time to reach terminal velocity of the falling object. Use g = 9.81m/s².