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Two horizontal plates with infinite length and width are separated by a distance h in the z direction. the bottom plate is moving at a velocity u. the incompressible fluid trapped between the plates is moving in the positive x-direction with the bottom plate. align gravity with positive z. assume that the flow is fully-developed and laminar. if the systems operates at steady state and the pressure gradient in x-direction can be ignored, do the following: 1. sketch your system 2. identify the coordinate system to be used. 3. show your coordinates and origin point on the sketch. list all your assumptions. 5. apply the continuity equation to your system. nts of navier stokes equations of choice to your system 7. solve the resulting differential equation to obtain the velocity profile within the system make sure to list your boundary conditions. check units of velocity 8. describe the velocity profile you obtain using engineering terminology. sketch that on the same sketch you provided in (1). 9. obtain the equation that describes the volumetric flow rate in the system. check the units.

Which statements describe the movement of ocean currents around the globe? check all that apply. strong winds force warm water to sink to the ocean floor. the coriolis effect causes warm and cold water to mix. cool dense water sinks to the ocean floor. warm water replaces cool surface water. wind blowing parallel to the shore causes upwelling of cool water.

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒