1) Show that the Drag equation is homogenous in both SI units and basic units. 1 FD CD Apv²
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Show that the drag equation is homogenous in both SI units and basic units
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- 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.#4 1.11 For a small particle of styrofoam (1 lbm/ft) (spherical, with diameter d = 0.3 mm) falling in standard air at speed V, the drag is given by FD-3mVd, where is the air viscosity. Find the maximum speed starting from rest, and the time it takes to reach 95 percent of this speed. Plot the speed as a function of time. s) Answer: (Vmax=0.0435",t=0.0133 SIn the given image, both fluids are at 20°C. The specific weight of water is 9790 N/m³. If surface tension effects are negligible and a = 8.35 cm, what is the density of the oil, in kg/m³? Oil 6 cm Water Numeric Response CO 10 cm
- Is the dimensional consistency of the units in the expression v = 2ar? Choose the most appropriate response.Yes, both v2 and 2ar have m2/s2 units. Yes, both v2 and 2ar have m/s units.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?Dimensional analysis: O Is very helpful in determining speeds for dynamic similarity in model testing O Is an efficient way of storing and retrieving experimental data All responses are correct Helps in planning experiments Can be used to derive equations and non-dimensional numbers
- The wave resistance of a model of a ship at 1/19 scale is 2 lbf at a model speed of 7 ft/s. What are the corresponding velocity and wave resistance of the prototype? Fp = lbfGiven: The plane accelerates in its current trajectory with a= 100 m/s^2 Farag Angle theta= 5° W=105 kips F_drag= 80 kips m= 1000 lbs Find: F_thrust, F_lift Please include the KD. Fthrust Futel t Fueight 000 BY NC SA 2013 Michael SwanbomWhat is the volume of 92.4 grams of chlorine gas that is at a temperature of 46° C and a pressure of 694 mmHg? (Chlorine, R = 62.4 L- mm Hg/mole K and MW = 70.906 g/ mol) Computation: Show your Solution A lump of ice falls from an airplane as it comes into land. If the ice hits the ground with a vertical speed of 85m/s, what was the height of the plane when the ice fell off? (Assume that friction can be ignored.)
- The aerodynamic drag of a new sports car is to be predicted at a speed of 60 mph at an air temperature of 25°C. Automotive engineers build a one-third scale model of a car to test in a wind tunnel, shown in the figure below. 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). The aerodynamic drag on the model in the wind tunnel is measured to be 34.5 lbf when the wind tunnel is operated at the speed that ensures similarity with the prototype car. Estimate the drag force (in lbf) on the prototype car at the given conditions. For air at T = 25°C and atmospheric pressure, p=1.184 kg/m3 and u-1.849-10-5 kg/m-s. Wind tunnel test section Pm Pm Fo.m Moving belt Drag balance The drag force on the prototype car is estimated to be Ibf.Pide Use Buckingham's PI Theorem to determine non-dimensional parameters in the phenomenon shown on the right (surface tension of a soap bubble). The variables involved are: R AP - pressure difference between the inside and outside R- radius of the bubble Pide Soap film surface tension (Gravity is not relevant since the soap bubble is neutrally buoyant in air)using pure water at 20°C. The velocity of the prototype in seawater (p = A 1/18 scale model of the submarine is to be tested in the water tunnel 1015 kg/m³, v = 1.4x106 m²/s) is 3 m/s. Determine: a) the speed of the water in the water tunnel for dynamic similarity D) the ratio of the drag force on the model to the drag force on the prototype