Kinematic Analysis of Fluid Flow: Position and Velocity Description – Lagrangian and Eulerian Approach

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To analyze the flow we should know the basic principles applicable to it. The principles are as simple as the basic laws of motion, classical mechanics, and the fundamental principles of energy, mass, and the conservation of momentum.

In the kinematic analysis of the fluid flow, we are concerned about the position, velocity, and acceleration of fluid particle and sometimes further derivatives of the position of fluid particles. In kinematic analysis we study the flow without being bothered about the force causing it. As discussed in the earlier article on different approaches for fluid flow analysis, for analysis fluid flow can be described by the Lagrangian Method and also by the Eulerian Method.

Lagrangian Approach for Kinematic Analysis

For kinematic analysis of fluid flow using the Lagrangian approach, we trace the fluid particles or elements and find their position, velocity, pressure, and other properties with the passage of time. The position of a particle at any point of time is determined by its position at the reference time. For the three dimensional analysis of flow the position of a particle is defined by three coordinates, and each position coordinate is a function of the three coordinates of the initial position and the time passed from the initial position.

Eulerian Approach for Kinematic Analysis

In the Eulerian Approach for kinematic analysis of fluid flow we no more concentrate our attention to particular fluid particles and run behind them. Rather we now go to any point in the flow field and try to define and find the flow properties at that point for any particular instant of time. Any number of particles may pass and go through that point, but we look for the properties, primarily velocity, of the flow at that point and do not attach it to a particular particle.

The properties of the fluid flow at the concerned point will be a function of the definition of that point, its coordinates, and the time at which we are interested to note them. The basic fluid property for kinematic analysis is the velocity of flow. For three-dimensional flow, it has three components and each component is a function of the position of the point and time.

Velocity Vector and Flow Dimensions

The flow considered for analysis may be one, two or three dimensional. One dimensional flow, like the flow in a straight pipe, will have velocity vector as a function of only one coordinate. The flow of water through a wide straight irrigation canal can be considered as two-dimensional flow for kinematic analysis, and the velocity in such flow will be a function of two coordinates. In the three-dimensional flow, velocity vector will be a function of three coordinates.

This post is part of the series: Analysis of Fluid Flow

For the efficient design of the hydraulic systems in civil engineering it is very important to first analyze the flow of fluid through the system. This article series tells what the concepts for analysis of fluid flow are and how these concepts are used in the context of the fluid flow analysis?

  1. Kinematic Analysis of Fluid Flow: Position and Velocity Description
  2. Accelerations in Fluid Flow
  3. Dynamics of Fluid Flow: Energy Equation for Ideal Fluid Flow
  4. Bernoulli’s Equation Explained
  5. Applications of Bernoulli’s Equation