Chapter 20
Dimensional Analysis, Similitude, and Modeling
Dimensional Analysis
Dimensional analysis helps simplify fluid flow problems by using dimensionless groups, reducing complex variables into simpler terms that are easier to ...
The Buckingham Pi Theorem
Consider the flow through a pipe, where key variables include the pipe's diameter D, fluid velocity V, density ρ, and viscosity μ.
To ...
Determination of Pi Terms
To determine Pi terms using the Buckingham Pi theorem, consider the example of analyzing lift force on an airplane wing.
Relevant variables here include ...
Dimensionless Groups in Fluid Mechanics
The dimensionless groups in fluid mechanics are ratios of physical quantities used to describe and analyze fluid behavior independently of units of ...
Correlation of Experimental Data
A key use of dimensional analysis is to efficiently manage, interpret, and correlate experimental data.
Dimensional analysis alone cannot fully solve a ...
Modeling and Similitude
A scaled model of a dam is tested in a controlled environment to observe how it will manage water flow, turbulence, and pressure.
This setup predicts the ...
Typical Model Studies
Typical model studies analyze scaled-down systems to predict fluid behavior, focusing on interactions with free surfaces and flow around immersed bodies.
...
Design Example: Creating a Hydraulic Model of a Dam Spillway
A hydraulic model of a dam spillway is often created by scaling down the design, typically to a 1:15 ratio, to replicate key flow characteristics such as ...
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