Homework SourseIn a steady incompressible and fully developed flow between
In a steady, incompressible and fully developed flow between two parallel plates where the top plate is moving and bottom plate is stationary, the velocity field can be represented as v=(Vy/d)i. V is the velocity of the top plate, d is the gap between the plates and y is the distance from the bottom plate toeard the top plate. If the flow is rotational how much is the absolute ( without + or -) angular velocity in rad/s when the top plate is moving at a velocity 24.5m/s and the gap between the plate is .72m?
In a steady, incompressible and fully developed flow between two parallel plates where the top plate is moving and bottom plate is stationary, the velocity field can be represented as v=(Vy/d)i. V is the velocity of the top plate, d is the gap between the plates and y is the distance from the bottom plate toeard the top plate. If the flow is rotational how much is the absolute ( without + or -) angular velocity in rad/s when the top plate is moving at a velocity 24.5m/s and the gap between the plate is .72m?
Solution
Angular velocity w = 1/2*(del Vy / delx - del Vx /dely)
v = V*(y/d)i
So here, Vx = V*(y/d) and Vy = 0
We get, del Vx / dely = V/d
Thus, w = (1/2) * (0 - V/d)
Thus, w = -V / (2d)
= -24.5 / (2*0.72)
= -17.014 rad/s
