Thursday, 8 March 2018

LAGRANGIAN METHOD AND EULERIAN METHOD

LAGRANGIAN METHOD AND EULERIAN METHOD

We were discussing the basic definition of Buoyancy or buoyancy force, Centre of buoyancy, analytical method to determine the meta-centric height and conditions of equilibrium of submerged bodies and conditions of equilibrium off floating bodies in our previous posts.

Now we will start a new topic in the field of fluid mechanics i.e. Kinematics of flow with the help of this post.

Kinematics is basically defined as the branch of fluid mechanics which deals with the motion of particles without considering the effect of forces and moments which create the motion.

 
Fluid kinematics explains how fluids flow and how to describe the fluid motion. We will further discuss the way to find out the velocity at any point of time in the flow field. Once we will have information about the velocity, we can easily determine the pressure distribution and forces acting on the fluid.

There are basically two methods to describe the motion of fluid particles and these are as mentioned here.

Lagrangian method
Eulerian method

Lagrangian method

We need to trace the position and velocity of each individual particle in case of lagrangian method and further kinematic behaviour of each individual particle will be determined.

If the number of objects is small, for example billiard balls on a pool table, individual objects could be traced. But if a fluid lamp changes its shape, dimensions and state as it moves with respect to time, it will be very difficult to track the lump with the help of lagrangian method.

Motion of fluid particle A with time is displayed here in following figure.

Eulerian method
We do not trace individual particle with identity in this method. We will define the field variables such as velocity, pressure as function of space and time within the control volume.

Therefore in case of Eluerian method, velocity, acceleration, pressure, density will be described at a point in the flow field.

 
In order to describe the fluid motion by Eluerian method, a flow domain of definite volume or control volume will be defined through which fluid will flow in and out of control volume.

The kinematic behaviour or properties of fluid particle passing a given point in space will be recorded with time. The Eluerian method is generally used in fluid mechanics.

We will discuss another topic i.e. Types of fluid flow, in the subject of fluid mechanic, in our next post.

 
Do you have any suggestions? Please write in comment box.

Reference:

Fluid mechanics, By R. K. Bansal

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