Example: If the temperature gradient is 2°C per 100 Km and if the specific heat capacity of the air is 0.25 Kcal/Kg.C .How much thermal energy per unit mass is convicted to the point P in 12h if the air is moving at a speed of 10Km/h?
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- The sphere is dropped in gasoline at 20 ° C.Ignoring its acceleration phase, what will it's terminal (constant)fall velocity be, from Fig. ?A ship 200 f t long with a wetted area of 5000 ft2 moves at 25 ft/s. Find the friction drag, assuming that the ship surface may be modeled as a flat plate, and ρ = 1.94 slugs/ft3 and ν = 1.2 × 10−5 ft2/s. What is the minimum power required to move the ship at this speed?A solid cone of angle 2θ , base r 0 , and density ρ c is rotatingwith initial angular velocity ω 0 inside a conical seat, asshown in Fig. . The clearance h is fi lled with oil ofviscosity μ . Neglecting air drag, derive an analyticalexpression for the cone’s angular velocity ω ( t ) if there isno applied torque.
- In principle, it is possible to use rotating cylinders as aircraftwings. Consider a cylinder 30 cm in diameter, rotatingat 2400 r/min. It is to lift a 55-kN airplane cruising at100 m/s. What should the cylinder length be? How muchpower is required to maintain this speed? Neglect end effectson the rotating wing.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 velocityAn airplane weighing 28 kN, with a drag area CDA ≈5 m2,lands at sea level at 55 m/s and deploys a drag parachute3 m in diameter. No other brakes are applied. (a) How longwill it take the plane to slow down to 20 m/s? (b) How farwill it have traveled in that time?
- Some animals have learned to take advantage of the Bernoulli effect without having read a fluid mechanics book. For example, a typical prairie dog burrow contains two entrances—a flat front door and a mounded back door, as shown in Fig. P3.5.6. When the wind blows with velocity V0 across the front door, the average velocity across the back door is greater than V0 because of the mound. Assume the air velocity across the back door is 1.07V0. For a wind velocity of 6 m/s, what pressure differences, p1 − p2, are generated to provide a fresh airflow within the burrow?A laminar flow wind tunnel has a test section that is 30 cm in diameter and 80 cm in length. The air is at 20°C. At a uniform air speed of 2.0 m/s at the test section inlet, by how much will the centerline air speed accelerate by the end of the test section?Using Buckingham-pi theorem, find an expression for the drag force (D) of a sphere of diameter (do) falling slowly with a velocity (V) in a large vessel containing a liquid of density (ρ) and viscosity (μ).
- The shock waves on a vehicle in supersonic flight cause a component ofdrag called supersonic wave drag Dw. Define the wave-drag coefficient asCD,w = Dw/q∞S, where S is a suitable reference area for the body. Insupersonic flight, the flow is governed in part by its thermodynamicproperties, given by the specific heats at constant pressure cp and atconstant volume cv. Define the ratio cp/cv ≡ γ . Using Buckingham’spi theorem, show that CD,w = f (M∞, γ ). Neglect the influence of friction.A tremendous force is generated when waterfreezes into ice and expands in volume by 9.0%. Suppose a 1.000-m3cube of liquid water freezes into ice that is 1.000 m on a side by1.090 m tall. How many 68-kg students would the ice be able tolift? Determine this by calculating the amount of force on the top1.000-m2face that would be required to squeeze 1.090 m3of iceback to 1.000 m3, assuming all of the volume change occurs alongthe vertical directionA laminar boundary layer is observed to grow on a flat plate such that the pressure is constant everywhere. If the boundary layer velocity profile is given by: where u is the velocity at a distance y from the surface, δ is the boundary layer thickness and Ue is the freestream velocity. (a) Show that θ/δ = 0.139, where θ is the momentum thickness. (b) Find the viscous stress on the plate in terms of the viscosity, the boundary layer thickness, and the freestream velocity.