Suppose that glycerin is flowing (T = 20 degrees Celsius) and thatthe pressure g

Question

Suppose that glycerin is flowing (T = 20 degrees Celsius) and thatthe pressure gradient dp/dx is -1.6 kN/m3 . Whatare the velocity and shear stress at a distance of 12 mm from thewall if the space B between the walls is 5.0 cm? What are theshear stress and velocity at the wall? The velocitydistribution for viscous flow between stationary platesis:    u = -(1/2)(dp/dx)(By-y2)

Explanation / Answer

given: pressure gradient dp/dx= -1.6 kN/m3 B = 5 cm The velocity distribution for viscous flow betweenstationary plates is:    u =-(1/2)(dp/dx)(By-y2) shear stress = *du/dy => = *(-(1/2)(dp/dx)(B-2y)) => = -(1/2)(dp/dx)(B-2y) (a)at y = 12mm velocity, u = -(1/2)(dp/dx)(By-y2) => u =-(1/2)*-1.6*103*(.05*.012-0.122) =>u = 0.3648 m/sec shear stress, = -(1/2)(dp/dx)(B-2y) => = -(1/2)*-1.6*103*(0.05-2*0.012) => = 0.0208 N/m2 (b)at the wall velocity, u =-(1/2)(dp/dx)(By-y2) =>velocity, u =0 m/sec shear stress, = -(1/2)(dp/dx)(B-2y) shear stress, = -(1/2)*-1.6*103*(0.05) =>shear stress, = 4 N/m2

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