Explanation Given information: The diameter of the circle is d = 82.5 m . The output power is P 1 = 1.5 MW . The wind speed of the generator is v = 12 m / s . The output power is P 2 = 10 MW . The density of air is ρ = 1.21 kg / m 3 . The efficiency for the designs η = η 1 = η 2 . Calculation: Calculate the length of the slipstream ( Δ l ) as shown below. Δ l = v Δ t . Here, v is the velocity of the air and Δ t is the time. Calculate the area of the turbine ( A ) as shown below. A = π d 2 4 Calculate the mass rate of flow ( d m d t ) as shown below. mass = density × volume = density × area × length Δ m = ρ A Δ l Substitute v Δ t for Δ l . Δ m = ρ A v Δ t Calculate the input power of the turbine ( Δ T ) as shown below. Δ T = 1 2 ( Δ m ) v 2 Substitute ρ A v Δ t for Δ m . Δ T = 1 2 ρ A v Δ t × v 2 = 1 2 ρ A v 3 Δ t Δ T Δ t = 1 2 ρ A v 3 d T d t = 1 2 ρ A v 3 Calculate the output power ( P ) using the relation as shown below

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The study of the flow of gases and liquids, usually in and around solid surfaces, is known as fluid dynamics in physics and engineering. Fluid dynamics, for example, can be used to evaluate the movement of air through an airplane wing or the surface of a…

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Chapter 14.3, Problem 14.79P

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Question 1 You are working as an engineer in a bearing systems design company. The flow of lubricant inside a hydrodynamic bearing (µ = 0.001 kg m¯¹ s¯¹) can be approximated as a parallel, steady, two-dimensional, incompressible flow between two parallel plates. The top plate, representing the moving part of the bearing, travels at a constant speed, U, while the bottom plate remains stationary (Figure Q1). The plates are separated by a distance of 2h = 1 cm and are W = 20 cm wide. Their length is L = 10 cm. By applying the above approximations to the Navier-Stokes equations and assuming that end effects can be neglected, the horizontal velocity profile can be shown to be 1 dP u(y) = 2μ dx -y² + Ay + B y= +h Ꮖ 2h=1 cm 1 x1 y = −h moving plate stationary plate 2 X2 L = 10 cm Figure Q1: Flow in a hydrodynamic bearing. The plates extend a width, W = 20 cm, into the page. (a) By considering the appropriate boundary conditions, show that the constants take the following forms: U U 1 dP A =…

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