A fluid of constant density is flowing in laminar flow at steady state in the horizontal x direction between two flat and parallel plates. The distance between the two plates in the vertical y direction is 2y0. (a)Sketch the system above, define your coordinates and origin point and draw a shell control volume (b)Using a shell momentum balance, derive the equation for the velocity profile within the fluid and the maximum velocity for a distance L in the x direction. One boundary condition is dvx/dy=0 at y=0. Make sure the units for the expression are those for velocity. (c)Describe your profile using engineering terminology. Sketch the velocity as a function of y. (d)What is the maximum velocity? What are the units for velocity? (e)Derive the expression for average velocity? What are the units for velocity? (f)What is the ratio between maximum and average velocities? (g)What is the volumetric flow rate? What is the unit for volumetric flow rate? (h)Calculate shear stress? What is the unit for shear? (i)What is the drag force operating on the plate? Check that the unit for drag force is N.
A fluid of constant density is flowing in laminar flow at steady state in the horizontal x direction between two flat and parallel plates. The distance between the two plates in the vertical y direction is 2y0. (a)Sketch the system above, define your coordinates and origin point and draw a shell control volume
(b)Using a shell momentum balance, derive the equation for the velocity profile within the fluid and the maximum velocity for a distance L in the x direction. One boundary condition is dvx/dy=0 at y=0. Make sure the units for the expression are those for velocity.
(c)Describe your profile using engineering terminology. Sketch the velocity as a function of y.
(d)What is the maximum velocity? What are the units for velocity?
(e)Derive the expression for average velocity? What are the units for velocity?
(f)What is the ratio between maximum and average velocities?
(g)What is the volumetric flow rate? What is the unit for volumetric flow rate?
(h)Calculate shear stress? What is the unit for shear?
(i)What is the drag force operating on the plate? Check that the unit for drag force is N.
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