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


Marshall, Franklin Lester (1967) I. Surface Deformations in a Draining Cylindrical Tank. II. Stability of a Laminar Film on an Inclined Plane. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/HFTH-5W53.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Mechanical Engineering)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Rannie, W. Duncan
Thesis Committee:
  • Unknown, Unknown
Defense Date:8 December 1966
Record Number:CaltechETD:etd-10012002-104737
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3849
Deposited By: Imported from ETD-db
Deposited On:02 Oct 2002
Last Modified:19 Mar 2024 20:43

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PDF (Marshall_f_1967.pdf) - Final Version
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