I. Surface Deformations in a Draining Cylindrical Tank. II. Stability of a Laminar Film on an Inclined Plane

Author: Marshall, Franklin Lester

Year: 1967

Degree: Dissertation (Ph.D.)

Advisor: Rannie, W. Duncan

Committee Member: Unknown, Unknown

Option: Mechanical Engineering

DOI: 10.7907/HFTH-5W53

Abstract

I. The problem of draining of a liquid from a cylindrical tank through a hole in the bottom is considered. The flow is irrotational, and the free surface boundary conditions are linearized. Solutions are obtained and the shape of the free surface determined for any constant mass flow rate. At large mass flow rates, the free surface deforms appreciably when the mean depth is about 40 per cent or less of the tank diameter.

The initial acceleration distribution of the free surface and the transient behavior of the mass flow rate are determined for a flow started impulsively from rest as a result of a constant pressure head.

At large Froude numbers it is possible to compare the results with the recent experiments of Gluck, Gille, Zukoski, and Simkin, and the present analysis is consistent with the experimental observations.

II. The stability characteristics of a laminar film with a free surface flowing under the action of gravity down an inclined plane are examined. Approximate solutions of the Orr-Sommerfeld equation are obtained. These are valid as long as the wave speed of the disturbance is somewhat larger than the maximum velocity of the undisturbed flow. Curves of neutral stability as functions of Reynolds number of the undisturbed flow and wave number of the disturbance are found. These are valid over a larger domain of Reynolds number and wave number than the previous results of Benjamin.

The special case of a vertical wall and zero surface tension is also discussed. It is shown that undamped waves of the type predicted by Yih (and tentatively suggested by Benjamin) cannot exist, and a source of error in Yih's analysis is suggested.

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