A highly viscous Newtonian liquid (p =1300 kg/m3; μ = 6.0 N · s/m2) is contained in a long, vertical, 150-mm-diameter tube. Initially, the liquid is at rest, but when a valve at the bottom of the tube is opened flow commences. Although the flow is slowly changing with time, at any instant the velocity distribution is essentially parabolic; that is, the flow is quasi-steady. (See Video V6.13.) Some measurements show that the average velocity, V, is changing in accordance with the equation V = 0.1 t, with V in m/s when t is in seconds. (a) Show on a plot the velocity distribution (vz vs. r) at t = 2 s, where vz is the velocity and is the radius from the center of the tube. (b)Verify that the flow is laminar at this instant.
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