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The drag on the hull of a ship depends in part on the height of the water waves produced by the hull. The potential energy associated with these waves therefore depends on the acceleration of gravity g. Hence, we can state that the wave drag on the hull is
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Chapter 1 Solutions
Fundamentals of Aerodynamics
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DESIGN OF MACHINERY
- 1 Consider a rapidly rotating (ie, in near geostrophic balance) Boussineq fluid on the f plane. A) Show that the pressure divided by the density scales as Φ ≈ fUL B) Show that the horizontal divergence of the geostrophic wind vanishes. Thus, argue that the scaling W ≈ UH = L is an overestimate for the magnitude of the vertical velocityarrow_forwardExplain the mechanism of drag and lift force generation for the wing using Newton's law. Here are the hints : If the wing does not exist, the velocity distribution is uniform at v=U_inf. Therefore, the x-directional velocity of the air is deceralated by the wing. This implies that the wing applied a force in the -x-direction to the air (Newton's second law). In other words, the air flow applied a force in the x-direction to the wing (Newton's third law). This is the mechanism of drag generation.arrow_forward(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 Weightarrow_forward
- A spherical dust particle of density ρp and radius R falls at a constant velocity V in an atmosphere of density ρa under its own weight. Find V if ρp/ρa = 1000, R = 0.5 mm, and the drag coefficient CD = F/(0.5ρaV2πR2 ) = 1, where F is the drag force acting on the sphere. Ignore the buoyancy force.arrow_forwardThe large block shown is x = 72 cm wide, y = 54 cm long, and z = 9.0 cm high. This block is passing through air (density of air p = 1.43 kg/m³) at a speed of v = 8.61 m/s. Find the drag force F41 acting on the block when it has the velocity vj and a drag coefficient I = 0.812. V2 Fa.1 N %3D Find the drag force F42 acting on the block when it has the velocity vz with a drag coefficient I = 0.893. F42 N Find the drag force Fa.3 acting on the block when it has the velocity vz with a drag coefficient I = 1.06. F4.3 = N ENarrow_forwardAeronautical engineers measure the pitching moment M0of a wing and then write it in the following form for use inother cases:M0 =βV2 AC ρ where V is the wing velocity, A the wing area, C the wingchord length, and ρ the air density. What are the dimensionsof the coeffi cient β ?arrow_forward
- A ship is 35 m long and is designed to move at 11 m/s. Laboratory experiments are carried out in a water tank with a 1 m long model. Find the velocity and the ratio of the resistive forces of the model. (r=1000 kg/m3)arrow_forwardA fighter aircraft is to operate at 200 m/s in air at standard conditions ( = 1.2 kg/m3). Amodel is constructed to 1/20 scale (length ratio) and tested in a wind tunnel at the sameair temperature (same air viscosity) to determine the drag force. The drag force FD is afunction of the air density and viscosity , the velocity V and the cross section length ofthe airplane D.arrow_forwardflat plate 30 cm by 50 cm slides on oil (μ = 0.8 N⋅s/m2) over a large plane surface. What force is required to drag the plate at 2 m/s, if the separating oil film is 0.5 mm thick?arrow_forward
- between two concentric spherical sheets there is air. The inner spherical sheet has a radius of 10 cm and is filled with ice at 0 ° C, the outer spherical sheet has a radius of 10.05 cm and is at a temperature of 15 ° C. What amount of heat will be transmitted from one sheet to another by conductivity ends in 1/4 hour ?. Considering that the air is pressurized, it is considered to be 15 N / m ^ 2 and at a temperature of 2 ° C. The diameter of the air molecules is taken equal to 3 x 10 ^ -10 m. the molar mass of air is taken equal to 29 g / mol; Boltzman's constant k = 1.38 x 10 ^ -23 J / Karrow_forward1)The model of the torpedo (a military vehicle that goes very fast underwater) as placed in a tank is moved by being towed at a speed of 14,4 m/s. In the prototype, the torpedo is expected to move at a speed of 4.2 m/s in water at 15°C. The kinematic viscosity of water at the same temperature is v=3.4x10^(-3) m2/s. a) Determine the scale of the model used. b) If the same prototype and the torpedo model, prepared in the same size, is moved in a wind tunnel where u air=1.975x10^(-4) Ns/m2 and p air=22.5 kg/m3 air with physical properties under 10 atmospheres pressure and 26 C° constant temperature are used. What is the speed of the torpedo?arrow_forwardWe want to predict the drag force on a remote-control airplane as it flies through air having a density of 1.21 kg/m³ and a viscosity of 1.76x10- Pa-s. The airplane's fuselage has a diameter of 200 mm and the airplane will fly through air at a speed of 32 m/s. A model of the airplane's fuselage will be tested in a pressurized wind tunnel. The diameter of the model is 75 mm and the density and viscosity of the air in the wind tunnel are 3.00 kg/m³ and 1.82× 10-5 Pa-s, respectively. a) The diameter of the airplane's fuselage will be used to define the Reynolds number Re, for the flow around the fuselage. Compute the Reynolds number for the flow around the airplane's fuselage (answer: Re, = 4.40x 10'). b) Find the speed of the air that should be used to test a model of the fuselage in the wind tunnel to correctly model dynamic conditions (answer: 35.6 m/s). c) The model is tested in the wind tunnel at four speeds that bracket the speed computed above. The measured drag forces on the…arrow_forward
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