Show that the radius r of the moon’s orbit can be determined from the radius ( R ) of the earth, the acceleration of gravity ( g ) at the surface of the earth, and the time ( Γ ) in SI and U.S Customary units.

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Chapter 12.2, Problem 12.81P

To determine

Show that the radius r of the moon’s orbit can be determined from the radius (R) of the earth, the acceleration of gravity (g) at the surface of the earth, and the time (Γ) in SI and U.S Customary units.

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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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