Concept explainers
The slope of the free surface of a steady wave in one-dimensional flow in a shallow liquid layer is described by the equation
Use a length scale, L, and a velocity scale, V0, to nondimensionalize this equation. Obtain the dimensionless groups that characterize this flow.
The dimensionless groups that characterizes the given flow.
Explanation of Solution
Given:
The slope of the free surface of a steady wave in one dimensional flow in a shallow liquid is as follows:
Calculation:
From Equation (I),
The length dimensional quantity which are having same unit of measurement are h and x.
The velocity dimensional quantity is u.
Consider the reference dimensional quantities as follows:
The length is
The velocity is
Dividing the dimensional quantity by its reference dimensional quantity yields non-dimensional quantity. The non-dimensional quantities are denoted with asterisk.
Divide the given dimensional quantities with their reference as follows:
Substitute
Here,
The dimensionless group is
Thus, the dimensionless groups that characterizes the given flow is
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