Estimate the annual production of a 12 m diameter horizontal axis wind turbine operating at standard atmospheric conditions (r = 1.225 kg/m3 ) in an 8 m/s average wind speed regime. Rayleigh density distribution.
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Estimate the annual production of a 12 m diameter horizontal axis wind turbine operating at
standard atmospheric conditions (r = 1.225 kg/m3 ) in an 8 m/s average wind speed regime. Rayleigh density distribution.
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- Air at 1000C flows at an inlet velocity of 2 m/s between two parallel flat plates spaced 1 cm apart. Estimate the distance from the entrance to the point where the boundary layers meet.What is the power per unit area of a 10 knot uniform wind (in W/m²)?Estimate the annual production of a 12 m diameter horizontal axis wind turbine operating atstandard atmospheric conditions (r = 1.225 kg/m3 ) in an 8 m/s average wind speed regime. speed probality density is given by the Rayleigh density distribution.
- A wind stress of 0.2 N m-2 blows over an initially stationary freshwater lake, 20 km long, and moves water downwind in the upper 10 m of the 20 m deep lake. (a) Estimate the difference in lake level between the ends of the lake in the direction of the wind one would expect when the wind force is balanced by the opposing pressure force in the upper 10 m (assuming no Coriolis influence in the dynamical balance) (b) The current driven in the lower 10 m by the pressure force which is balanced by the vertical frictional forces characterized by a coefficient of vertical turbulent eddy viscosity Az=0.02 m2 s -1 .A 2 m diameter cylinder rotates at 1800 rpm in an air stream (p=1226 kg/m³) of 25 m/sec. Estimate the theoretical lift per unit length of the cylinder (in Newtons) AjoConsider a steel sphere (SG = 7.85) of diameter 2 cm,dropped from rest in the water at 208C. Assume a constant dragcoefficient CD = 0.47. Accounting for the sphere’s hydrodynamicmass, estimate (a) its terminal velocity and (b) thetime to reach 99 percent of terminal velocity. Comparethese to the results when hydrodynamic mass is neglected,Vterminal ≈ 1.95 m/s and t99% ≈ 0.605 s, and discuss.
- A wind turbine with two or four hollow hemispherical cups connected to a pivot is commonly used to measure wind speed. Consider a wind turbine with four 1-cm-diameter cups with a center-to-center distance of 22 cm, as shown in Fig. 1. The pivot is stuck as a result of some malfunction, and the cups stop rotating. For a wind speed of 20 m/s and air density of 1.25kg/m3, determine the maximum torque this turbine applies on the pivot.The 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 ENS Algebraic equations such as Bernoulli's relation, Eq. (1) of Ex. 1.3, are dimensionally consistent, but what about differential equations? Consider, for example, the bound- ary-layer x-momentum equation, first derived by Ludwig Prandtl in 1904: ди pu- du pv- ду + pgx + ax ду where 7 is the boundary-layer shear stress and g, is the component of gravity in the x direction. Is this equation dimensionally consistent? Can you draw a general con- cusion?
- Consider a business jet with the following characteristics:• Weight: 25208 kg• Wing area: 53.5 m^2• Wing span: 21.7 m• Cruise altitude: 10,000 m • Drag polar parameters (cruise): CD0 = 0.015, K= 0.08• Engine: Number of engines: 2 Max. thrust (at sea level, for 1 engine): 45 kN TSFC (for 1 engine): 0.41 1/h Calculate the velocity for minimum thrust required using the analytical expression (formula)? Calculate the velocity for minimum power required using the analytical expression (formula).? Calculate the maximum velocity using one possible graphical approach, and analytical approach?Assume that the Flettner rotor ship of Fig. has a waterresistance coefficient of 0.005. How fast will the shipsail in seawater at 20°C in a 20-ft/s wind if the keel alignsitself with the resultant force on the rotors? [Hint: This is aproblem in relative velocities.]Baseball drag data from the University of Texas are shownin Fig. A baseball weighs approximately 5.12ounces and has a diameter of 2.91 in. Hall-of-Famer NolanRyan, in a 1974 game, threw the fastest pitch ever recorded:108.1 mi/h. If it is 60 ft from Nolan’s hand to the catcher’smitt, estimate the sea-level ball velocity which the catcherexperiences for (a) a normal baseball, and (b) a perfectlysmooth baseball.