hello friends this video on mechanical properties of fluids 529 is brought to you by exam feel calm no more your prom exam please make sure that you have watched all the videos from class 1 to 528 before going ahead with part 29 introduce another important term or another important concept don't as Reynolds number so what is a Reynolds number and what is the significance of Reynolds number let us learn about that Reynolds number is a dimensionless number whose value gives an idea whether the flow would be turbulent or laminar so now you understand the significance of Reynolds number we studied long back that broadly the types of fluid flow is classified into two types by this laminar flow or the steady flow and the other one is the turbulent flow so how do we know just from data that whether a flow is a laminar flow or a turbulent flow because a way both the flows I defined is something like you need to observe the motion of the particle right but if you consider in our real life if something is supposed to be fluid is flowing you are not able to visualize the flow of each of the particles always right so there has to be some mechanism or there has to be something with the help of which we can directly say that okay if this is this condition is true then the flow is laminar if this condition is false the flow is turbulent so Reynolds number gave us an approach like that it is basically a number the number itself will below whether the flow is lamina or the florists turbulent it is generally denoted by an e the subscript insures our e with the e it shows Reynolds the expression for Reynolds number is our E is equal to Rho in V into T divided by ETA here Rho is a density of the fluid V is the velocity of the fluid D is the diameter of the pipe to which the fluid flows and eta is the viscosity of the fluid now if we know all these values we can activate the value of Reynolds number and we can find whether the flow is laminar or turbulent if you see all these four bearings are something which will be knowing let us suppose if I tell you there is a fluid say let us call oil oil is going through a queue now the tube is something which you can visualize so we will know the diameter of Eugene quite obviously or we can measure the diameter of the tube we know that oil is flowing through the tube so oil is something whose density will be known to us while there something which is possibly will be known to us and sells we see that the oil is flowing through the tube we should also know which what philosophy oil is flowing through the tube so once we know all these four quantities we can calculate the value of two Reynolds number and we can get it be same wherever flow is laminar or turbulent so how does an ensemble distinguish between laminar and turbulent flow it says that if the value of balance number reaches thousand if it's valuable thousand the flow is laminar and once the value of y orn ensemble is greater than two percent the flow is turbulent that means laminar flow is denoted by less than thousand and third billing flow is denoted by greater than 2000 if the value of your notes number is greater than 2000 it is turbulent if the value is less than 1000 it is laminar so what is the binding lives between thousand and two thousand in that case the flow is unstable that means it is the flow is in an intermediate State the flow has some characteristics of laminar flow it has some characteristics of turbulent flow so he cannot classify the flow as either of them and we say that the flow is unstable okay so I don't think there is much complication in understanding you know its number it is very simple and straightforward now we will try to derive another expression or an alternative expression for Reynolds number so this expression of the null somewhere maybe in terms of the inertial force and the force of viscosity because he already however we have already expressed Renault number in terms of a velocity coefficient of viscosity and then a diameter of the tube but now we will derive another equation in terms of inertial force and the force of this kazantip now we have already expressed our we already know that expression for Reynolds number is tho into P into D divided by theta as I already told you what this will be handy now and not writing it again so let us concentrate other variation in this we will derive that main ensemble is equal to inertia force divided by the force of this positive so let us multiply both the numerator and denominator so multiply numerator and denominator by D so what do you get you get ie is equal to we'll see this way I'm sorry you multiply numerator and denominator if I feel that is velocity so you give for this parity divided by ETA V so this we can write it as Rho into v square divided by ETA into v ID where we did nothing just we rearranged the terms so you can write it in this one now now let us again multiply both the numerator and denominator by capital K that what is game it is nothing but area so what do we get we get an e is equal to 0 into T Square into a divided by ETA into V divided by D into a so now what we will do BBC since we had to prove that ie is equal to inertial force by troops of viscosity now we will prove that the numerator here this is nothing but the inertial force and the denominator which we have here is nothing but the force of this force P so that is what we will nodes now so now let us see what is inertial force so when I see inertial force what is inertial force the force which we talked about when we talked of Newton's laws that is for subsequently mass into acceleration that is the force by virtue of inertia so now what is mass mass mass is nothing but density into volume but we identity is recognized into volume and what this acceleration acceleration is nothing but change in velocity with time selectors do not velocity by P and mighty and volume by capital T so this we can write it as Rho into velocity into what is volume as we already discussed volume is Alinea into displacement so we can write volume as area in in displacement and what we'll get is placement stick and save it as displace you one who is enough if you just place and divided by time so this we can write as Rho into T into a if you displacement Italian taken what is to say my time taking displacement covered by time taken is nothing but there are also people so you can write it as Rho e square a so what is in actual force inertial forces who is penny in which is this numeric so we have proved that the numerator is in action force now let us look at the denominator this utilize this space so let us talk about force of this person T so what would be the force of viscosity when I talk of course of viscosity the coefficient of viscosity has to come in people we know that coefficient of viscosity that is kita is equal to stress that is shearing stress divided by shearing strain rate now what is shearing stress it is force per unit area and what is shear strain rate streamgages displacement the perfect it length displacement work it then one Pony time like a steal so this week I Drive a task force per unit area divided by what is displacement per unit time that is when or something so you can write it as P by M so this becomes F into L divided by L into C so what is this missus if that is equal to F into L divided by K into Z they are two what is the force of this quantity this F denotes the force due to viscosity so we can say that F is equal to income a C divided by M so what is this this is nothing but ETA into T divided by L what is this end in represents nothing but the direction of the two to which the fluid is flowing and in this case in this definition what was deep D was nothing but the diameter of the pipe through which it was coming so whatever n denotes here is what denotes here it is just that both are denoted by different alphabets so here we gave you type V divided by L into a so basically this is same as this denominator so we proved that Reynolds number is can be expressed as the ratio of inertial force in the force of viscosity thank you please visit example.com to watch free educational videos try3 online test get the best quality study materials study from the best tutors and mentors and much more thank you once again
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