 Myself Sachin Deshmukh working as assistant professor in the department of civil engineering of Walch instead of technology solapur today we are going to study regarding model analysis at the end of this topic students will be able to find out the dimensions of model as well as prototype depending upon the dominating force or dominant force particularly to study this model analysis we must know what is a dimensional analysis which we have seen previously every quantity can be converted into different dimensions that is we often we call this as a MLT system ML and T and many times again we are adding temperature also in that now why to study this model analysis particularly in hydraulics the structures are very huge take the example of dam canals wears then cross drainage works these structures are very huge if the structures fails there is a lot of we can say loss of property loss of humans many things will happen which are not you can say tolerable that's why before construction we have to go for their models and we have to study the model and then we can reflect those dimensions in the prototype now see in this introduction that many problems in fluid mechanics cannot be solved purely in mathematical methods as they are in complex signature just I have told you model analysis which is an experimental method can be effectively used to solve such complex problems particularly this study is for two important purposes to get the information about the performance of the prototype what is the prototype first prototype is a working model I will tell you once again in the next you can say in the next slide and the second one is to help in design and to avoid costly mistakes because these mistakes are very we can say effective mistakes and loss will be there it will cause and to evolve an economic solution of a hydraulic problem model is a model is a small scale replica not always small scale but particularly we can say it is a small scale replica of a actual structure or a machine and prototype is the working model or you can say it is a actual structure or a machine and the model analysis is the study of models of actual machine now see this is one of the photographs this is a model now how huge it is how huge it is we know the models or we can see the models are very small it is not like that to study clearly effectively models may be in large size also this is the dam see here this is the downstream side this is the upstream side very small details already they have shown in this particular model so what are the different advantages of model analysis the performance of the machine can be easily predicted with the help of the dimension analysis a relationship between different variables influencing flow problem in terms of dimensional parameters is obtained the merits of alternative design if the design is not properly working then the alternative design can be adopted and we can say the most economical and safe design we can choose for this we have to go for different similarities of model and prototype there are three important similarities geometrical then kinematical and dynamic similarities geometric similarity is related with the dimensions that is the ratio of all corresponding linear dimensions in the model and prototype must be equal now lm is the length of model bm is the width of the model l and dm is the dimension diameter of the model area is the area or am is the area of the model bm is the volume of the model then all these dimensions for the prototype is similar with lp then bp dp ap vp are the corresponding values of the prototype that is length then width then you can say diameter area and volume now the ratio of this length of the prototype to the length of the model width of the prototype the width of the model diameter of the prototype to the diameter of the model is denoted as lr similarly ap that is area of the prototype area of the model upon area of the model is lr square we know area is l into l that is lr square and it is a volume now volume of the prototype upon volume of the model is equal to lr cube volume is lr cube now what is the kinematic similarity it is a similarity of motion between model and prototype thus kinematic similarity is said to exist between model and prototype if the ratios of the velocity and acceleration at the corresponding points this is very important at the corresponding points in the model as well as in the prototype in same magnitude the directions also should have should be parallel to that is now see it is the velocity of the prototype upon velocity of the model of one is equal to velocity of the prototype of the second upon velocity of the model of the second is equal to vr similarly acceleration ratio it is a r that is in the kinematic similarity now most important again in this that is a dynamic similarity where all the forces at only before also there are inertia forces always there then we can go for gravity force viscous force then elastic force pressure force and surface tension force these six forces are very important and we are taking always one force which is more dominating force or we can say it is a predominating in one criteria one we can say one for one example many times different forces are acting on that but one force is we can say it is more dominating that force we are taking into account right now in dynamic similarity it is the similarity of forces between model and prototype thus the dynamic similarity is said to exist between the model and prototype if the ratios of the forces acting at the corresponding points in the model and prototype are the same in magnitude similarly and the direction is also parallel then the force in the prototype upon force in the model equal to like this there are different forces inertia force viscous force gravity force surface tension force pressure force and elastic force the ratio is fr now types of forces inertia force that we can calculate by rho av square viscous force we can calculate that is mu reserve dynamic viscosity u upon d into area gravity force it is denoted as fs it is rho l rho area into wells then pressure force that we can calculate by fp is equal to p into area surface tension force it is sigma into that that is the length organ say diameter and elastic force that is elastic stress into area these forces are very important and always one of the force is predominating force in that particular example now from the these forces we are going to find out different numbers different numbers now go for Reynolds number denoted as r suffix e it is a ratio of inertia force upon viscous force so rho vd upon mu so where it is applicable Reynolds number when it is a viscous force particularly in the closed pipe when the pipe flow is there viscous force is a dominating force so we are taking this viscous force definitely some other forces are also there i am repeating but this viscous force is more dominating that's why the ratio of inertia force upon viscous force we are taking for Reynolds number second Froude's number in the Froude's number gravity force is a predominating force gravity force is predominating force so the ratio of inertia force to the gravity force and we get the equation as v upon under root dg third is Euler's number here pressure force is predominating force so pressure force upon inertia force it is p upon rho v square if we want to take inertia upon pressure force then you can go for 1 upon this particular equation then Weber's number where surface tension force is predominating force surface tension force is predominating force so surface tension force upon inertia force it is surface tension upon rho v square similarly the final number that is a Mach number it is a ratio of inertia force upon elastic force raise to half that is v upon under root k upon p so these numbers are very important for solving the problems for the dimensional analysis as well as model analysis following are the examples where the study model study is used dams rivers and harbors where we can see there is a wear and tear regularly the hydraulic machines structures and ships ship models also these are some of the photographs of models see here it's a model of a dam here is a model of a river it's a model of you can say storage also we can find the capacity from this particular model here in the laboratory itself they have constructed a model see here it is in the laboratory and this is one of the big model of dam downstream side of the dam upstream or side of the dam then we can go for this from the spillway water is taken into the downstream side every idea is get cleared from these pictures see here the dam then you can see it is a river and it's a non the upstream side its capacity we can find out how the river behaves okay the mentoring of the river is also we can see here the model of a particular section dam is constructed in uh laboratory very many pictures are these are some of the questions for you take a look on this and write down the answers these are its answers these are the reference books