Dimensional analysis is a valuable technique in fluid mechanics for simplifying complex problems by reducing them into dimensionless groups. These groups capture the essential relationships between the variables involved, allowing researchers and engineers to analyze fluid flow without dealing with each variable individually. This approach reduces the number of independent variables, allowing for easier analysis and better understanding of physical phenomena.

In fluid mechanics, dimensional analysis is used to understand the behavior of fluids in systems such as pipelines, channels, and other structures common in civil engineering. Consider the example of fluid flow through a long, smooth-walled, horizontal circular pipe, which is typical in the design of water distribution systems or sewage networks. The pressure drop per unit length along the pipe depends on variables such as pipe diameter, fluid density, fluid velocity, and viscosity. According to dimensional analysis, the pressure drop can be expressed as a function of these variables:

Equation 1

This formulation involves five independent variables, which can complicate the analysis. To simplify this, we can use dimensional analysis to reduce the number of variables into two dimensionless groups, thus streamlining the problem. Two important dimensionless groups that emerge from this analysis are the Reynolds number, which characterizes the flow regime, and the friction factor, which correlates with the pressure drop.

Equation 2

Engineers use the dimensionless groups to generate a universal curve that applies to any smooth-walled pipe and incompressible Newtonian fluid. This curve would allow them to predict the pressure drop for different pipe sizes and fluids without performing numerous experiments for each possible combination.

Figure 1

This approach minimizes the time and cost required for experimentation and allows for more straightforward design decisions. Whether designing water distribution networks or analyzing pressure losses in irrigation systems, dimensional analysis is critical for any civil engineer.

Do Capítulo 20:

article

Now Playing

20.1 : Dimensional Analysis

Dimensional Analysis, Similitude, and Modeling

26 Visualizações

article

20.2 : O Teorema do Pi de Buckingham

Dimensional Analysis, Similitude, and Modeling

41 Visualizações

article

20.3 : Determinação dos Termos Pi

Dimensional Analysis, Similitude, and Modeling

14 Visualizações

article

20.4 : Grupos adimensionais em mecânica dos fluidos

Dimensional Analysis, Similitude, and Modeling

17 Visualizações

article

20.5 : Correlação de dados experimentais

Dimensional Analysis, Similitude, and Modeling

7 Visualizações

article

20.6 : Modelagem e semelhança

Dimensional Analysis, Similitude, and Modeling

19 Visualizações

article

20.7 : Estudos de modelo típicos

Dimensional Analysis, Similitude, and Modeling

11 Visualizações

article

20.8 : Exemplo de projeto: Criar um modelo hidráulico de um vertedouro de barragem

Dimensional Analysis, Similitude, and Modeling

22 Visualizações

JoVE Logo

Privacidade

Termos de uso

Políticas

Pesquisa

Educação

SOBRE A JoVE

Copyright © 2025 MyJoVE Corporation. Todos os direitos reservados