Consider the case in which the container and liquid of Prob. 7–76 are initially at rest. At t = 0 the container begins to rotate. It takes some time for the liquid to rotate as a rigid body, and we expect that the liquid’s viscosity is an additional relevant parameter in the unsteady problem. Repeat Prob. 7–76, but with two additional independent parameters included, namely, fluid viscosity μ and time t. (We are interested in the development of height h as a function of time and the other parameters.)

Data from Problem 7-76

Consider a liquid in a cylindrical container in which both the container and the liquid are rotating as a rigid body (solid-body rotation). The elevation difference h between the center of the liquid surface and the rim of the liquid surface is a function of angular velocity ω, fluid density ρ, gravitational acceleration g, and radius R (Fig. P7–76). Use the method of repeating variables to find a dimensionless relationship between the parameters. Show all your work.

FIGURE P7–76

Transcribed Image Text:

Too g Free surface Liquid @ R h