 Hello everyone, myself SV Kuttkur working as Assistant Professor in Mechanical Engineering Department, Vulture Institute of Technology, Solapur. Today we are going to start a new unit, Fluid Kinematics. At the end of this session, student will be able to describe fluid flow. These are the contents where today we are going to discuss. First what do you mean by fluid kinematics? Then basic fluid flow description approaches, which includes langrangian approach, Eulerian approach. Then we will differentiate between these two, what is the difference between langrangian approach and Eulerian approach. Basically fluid kinematics comes under the branch of the fluid mechanics. Fluid mechanics deals with the three aspects of the fluid. These are fluid static, fluid kinematics and fluid dynamics. Fluid static means when we are going to consider the study of the fluid, which is at rest and whereas fluid kinematics is defined as that branch of science, which deals with the motion of particle without considering the pressure forces causing the motion. And whereas in fluid dynamics, we are going to consider the pressure forces also. That is the difference between fluid kinematics and fluid dynamics moving towards the next. Now there are basically two fluid flow approaches are there for describing any fluid flow or to study any fluid flow. And these are nothing but the langrangian approach and Eulerian approach. Now let us discuss one by one first langrangian approach. In langrangian approach, the fluid properties are dated one by tracking the motion and properties of the fluid particle as the particle moves in time. Means we are going to label a fluid particle and we are going to study the changes in the properties of that fluid particle as it moves along with it within time. The fluid properties like density, velocity, pressure can be mathematically represented as function of time only, rho is the function of time, velocity is the function of time, pressure is function of time. And these all properties are associated with the single particles because we are going to track the single particle, we are going to label a particle and we are going to study the properties as that particle moves along with the time in the flow. And these properties are associated with the single particle. Whereas in Eulerian approach what we are going to do is that instead of following each fluid particle we can record the changes of the flow properties at a point in the space as time varies. Means we are going to fix one location and we are going to study or note down the properties as the different particles moves at that point. And mathematically the fluid properties like density, velocity, pressure can be expressed as rho is function of x, y, z and time. Whereas these x, y, z are the dimensional coordinates because as different particles are moving x, y, z, this velocity is the function of x, y, z and t and pressure also is function of x, y, z and t. These properties are of different particles but at the same point we are going to fix the location according to the concept of the Eulerian approach. This is all about the Langrange and Eulerian approach. Now we will discuss the study of the same with example. Now this is the example. Now here in Langrange and approach let us say if you want to major or if you want to study the movement of this missile we are going to fix the observer. An observer fix to the missile and that he is going to note down along with this missile whatever the speed is there or whatever we are interested parameter is there that we are going to study whereas in Eulerian approach that man will be stay here and he is going to observe as that missile will move forward but he is fixed where the observer is moving along with the missile that is the basic difference between the Langrange and Eulerian approach. Now think on that which method is easier to describe the flow of water through the pipe. Now you know the basic two types that is Langrange and Eulerian approach out of these two methods which method is easier to describe the flow of water through the pipe. The answer is Eulerian approach. Why? I will explain with this example. Now here this is the chimney whereas the smoke particles are coming out from the chimney and if you want to measure the temperature of the smoke particles in Langrange and Eulerian approach we are going to fix one particle and we are going to track that particle and we are going to measure the temperature of the fluid particle as it moves in the fluid flow. Therefore the temperature whatever the temperature we are going to measure is of that A particle alone means T of H and that is depend upon the time. This is with respect to time. And whatever the properties we are going to measure, whatever the temperature we are going to measure that is of individual particle as it moves along the time. That is by approaching what you can say in the Langrange method whereas in Eulerian approach we are going to fix the thermometer and we are going to measure the temperature at point O as the different particles as the different smoke particles are passes through this point. We are going to measure the temperature that is why the temperature is function of that location x0, y0 and time. But this temperature is of different particles that is all about the Langrange and Eulerian approach. Now we have to differentiate between Langrange and Eulerian approach. Let us see one by one with the parameters. First parameter is the reference point or observer. As I already told you in Langrange fluid motion and in Langrange approach we have to follow the fluid particles or we are going to fix the we are going to label the fluid particle and we have to move along with the fluid particle. Means the observer is not stationary in case of Langrange approach whereas in Eulerian approach observer is stationary means we are going to fix the point and we are going to observe the changes at that point itself. Now here in case of Langrange approach what is observed? The motion of single particles and whatever the equation whatever the mathematical expression we are going to write in Langrange approach that is of only single particle and whereas in case of Eulerian approach motion of fluid particles across the specific volume oblique time is we are going to consider. The best example is now here consider this if you want to apply the Langrange approach here the red car is following the blue car at every point to track the position velocity etcetera of the blue car means you are means this blue car is labeled by the red car and this will observe the properties like the position velocity etcetera and whereas if you want to apply the Eulerian approach here the number of here we are going to find out or here we are going to find the in we are here we are interested in to find the number or flow rate of the fishes that cross the fixed volume on this rectangular time this rectangular we are going to find out the number of fishes crossing per unit time or we are going to find out the flow rate of the fishes this is the Eulerian approach this is all about the difference between Langrange and Eulerian approach I will explain these are the on the basis of this we are going to differentiate between the Langrange and Eulerian approach the another example you can give as if you want to study the motion of the fluid particles along the river if we are traveling in a boat and we are drifting down a water that is the example of the Langrange fluid motion and if you are sitting at the corner of the riverbank and we are going to study the fluid particles passes through the at a particular point that is the example of that is the example of Eulerian approach and basically we are going to use in all cases Eulerian approach because it is almost difficult because there are plenty of particles are there and it is almost impossible to track each and every particle and you have to note down the all properties therefore Langrange method is generally used in the research applications and whereas in normal all the applications we are going to prefer the Eulerian approach that is all about the difference between Langrange and Eulerian approach these are the references thank you