 Good morning friends, in the previous classes we have learned how to design the razor using the Keynes method, modulus method and the NRL method. Now let us see another topic today that is the feed metal volume. What is this feed metal volume? One must remember that the razor or the feeder should take care of the casting shrinkage as well as its own shrinkage because during the solidification casting undergoes shrinkage and the razor also undergoes shrinkage. So the razor has to take care of the casting shrinkage as well as its own shrinkage. Now little volume of the liquid metal from the razor solidifies during the process of the feeding hence the entire volume of the razor will not be available for the purpose of the feeding. So this is clear right. So if we are designing a razor with a particular amount of volume of the liquid metal this entire liquid metal will not be available for the purpose of the feeding because part of that will be freezing before it could what say feed the casting. Thus a feeder must compensate solidification shrinkage as shown by the following expression. Alpha into Vc plus Vr is equal to eta f into Vr where Vc is the volume of the casting, Vr is the volume of the razor, alpha is the percentage volumetric shrinkage of the cast metal. So different what say shrinkages for different metals we will be seeing in the next slide. Now eta f is the razor efficiency which is defined as the ratio of feed metal available to the total volume of the razor. So that is the definition for the razor efficiency. Here we can see alpha into Vc plus Vr is equal to eta f into Vr. Here we can see this is the volume of the casting and this is the volume of the razor. This is multiplied by the percentage volumetric shrinkage means this is the total shrinkage of the casting as well as that of the razor. Now this total shrinkage is to be compensated by the razor. Now what is the razor? This is eta means this is the razor efficiency multiplied by the volume of the razor gives us the amount of liquid metal that is available for the purpose of feeding the casting as well as the razor. Now these are the volumetric shrinkages of different cast metals. Pure aluminum volumetric shrinkage is 6.6 percent, aluminum 12 percent silicon alloy and the volumetric shrinkage is 3.8 percent, aluminum 4.5 percent copper alloy and the volumetric shrinkage is 6.3 percent, grey cast iron 0 to 1.8 percent, white cast iron 4 to 5.5 percent, plain carbon steels 2.5 to 4 percent, copper the volumetric shrinkage is 4.5 percent, tin bronze the volumetric shrinkage is 5.5 percent, aluminum bronze the volumetric shrinkage is 4 percent, magnesium the volumetric shrinkage is 4.2 percent, zinc and its volumetric shrinkage is 6.5 percent, lead and its volumetric shrinkage is 3.2 percent, gold and its volumetric shrinkage is 5.5 percent. So these are the values of alpha the volumetric shrinkages for different cast metals or the alloys. Now let us see another definition that is the razor efficiency. What is this razor efficiency? The razor efficiency is the ratio of the total feed metal available to the total volume of the razor. So this total feed metal available for the purpose of feeding is always less than the total volume of the razor because part of the liquid metal in the razor solidifies before it could feed the casting. That is why this feed metal volume is always less than the total volume of the casting. So open cylindrical razors have a low efficiency less than 15 percent whereas a cylinder what is a razor with an exothermic cover and sleeve its what is a razor efficiency will be more than 70 percent. The maximum efficiency of a razor depends on its shape and use of the feed aids. What is its shape and what are the feed aids? Are we using any feed aids? First of all what are these feed aids we are going to see very shortly these feed aids. Next one razor efficiency can be improved by achieving directional solidification and modifying its design. What is this directional solidification? Let us quickly review before that let us take a problem. Design an open side razor without any feeding aid like insulating sleeve, exothermic cover, etc. for a casting of dimensions 25 into 25 into 5 centimeters using modulus method. Check its adequacy when A the material of the casting is plain carbon steel and in the second case the material of the casting is pure aluminum. Means we have to design the razor for this simple casting whose what is a length is 25 centimeters width is 25 centimeters and the thickness is 5 centimeters using modulus method. The methods that we have learned in the modulus method and the NRL method that is the main guideline. So, afterwards we need to check whether what we have designed is correct or not. What we have designed is sufficient or not because different cast metals have different shrinkages. Unfortunately in the modulus method and also in the NRL method the material of the casting or what is a percentage shrinkage, percentage volumetric shrinkage does not come into picture. Only the Keynes method takes care of the material of the casting. That is why when we are designing using what is a modulus method and NRL method we need to cross check whether what we have designed is sufficient or not. So, that is the adequacy. Adequacy means will it be sufficient or not solution. Now volume of the casting we see is equal to 25 into 25 into 5 centimeters that is equal to 3125 cubic centimeters. Surface area of the casting is equal to 25 into 25 such phase are 2 multiplied by 2 plus 4 into 25 into 25. These phase are there are 4 such phases. So, we are multiplying by 4 that is equal to 1750 square centimeters. So, this is the surface area of the casting. Now modulus of the casting what is the modulus ratio of the volume to the surface area. So, VC by SCSE what is a here C stands for the casting that is equal to 3125 divided by 1750. Thus the modulus of the casting is equal to 1.7857. So, this is the modulus of the casting. Next one now we need to find out the modulus of the razor. Now in the during the what say when we have learnt about the what say design of the razor using the modulus method we have seen that the modulus of the razor should be 1.2 times the modulus of the casting. Thus MR the modulus of the razor is equal to 1.2 multiplied by MC the modulus of the casting that is equal to 1.2 into 1.7857 that is equal to 2.1429. So, this is the modulus of the razor. Now, but for a cylindrical razor that to when the diameter of the razor is equal to height of the razor we have seen that the modulus of the cylindrical razor is equal to d by 6 this we have already learnt when we are learning about the modulus method. Thus this 2.1429 is equal to d by 6 or d is equal to 6 into 2.1429 that is equal to 12.8 centimeters. This is the diameter or the height of the razor. So, diameter of the razor is equal to 12.8 centimeters and also the height of the razor is also the same 12.8 centimeters. Now, this is the what say design of the razor or the dimensions of the razor we have obtained by the modulus method. Now, we need to cross check whether this design is sufficient for feeding the casting or not or what we need to check thus the what say liquid metal present in this razor of a size 12.5, 12.8 and 12.8 what say size will it be what say will it have sufficient to liquid metal to feed the casting or not. So, we need to cross check case 1 material of the casting is plain carbon steel the case 1. Now, this is the what say expression we have learnt previously alpha into Vc plus Vr is equal to eta f multiplied by Vr where this what say this expression on the left hand side represents the total shrinkage whereas, the expression on the right side represents the total liquid metal available for the feeding or we can say the expression on the left side indicates the demand this much liquid metal this much shrinkage is there or this much liquid metal is required. On the other hand the right side expression tells us this much liquid metal is available for the purpose of the feeding. So, one side we can see this is the demand and the other side we can see the supply. So, always in the design of the razor the supply should be more than the demand then only that razor is what say sufficient for feeding the casting. Now, we need to find out these two expressions and check. Now, in this expression what is Vc it is the volume of the casting 3, 1, 2, 5 cubic centimeters Vr is the volume of the razor that is equal to 1572 cubic centimeters. Alpha is the volumetric shrinkage that is for the plain carbon steels it is say 2.5 to 4 percent. We are taking the maximum what say volumetric shrinkage and eta f is the razor efficiency for an open razor without any feeding aid what say razor efficiency is 15 percent. Thus alpha into Vc plus Vr is equal to alpha means 4 percent means that is 0.04 into this is the volume of the casting 3, 1, 2, 5 plus 1572 the volume of the razor is equal to 188 cubic centimeters means the left side expression or the demand for the liquid metal is 188 cubic centimeters. Similarly, let us calculate this right side expression eta f into Vr eta f into Vr eta f means what is that that is the efficiency of the razor that is 15 percent. So, 0.15 into Vr volume of the razor 1572 that is equal to 236 cubic centimeters. Now, the demand is 188 cubic centimeters whereas, the supply of the liquid metal is 236 cubic centimeters right supply is more than the demand. Hence, there is no chance for the shrinkage because there is more liquid metal to what say compensate the shrinkage. So, there hence the size of the razor is adequate means it is sufficient. Now, let us see the second case material of the casting is pure aluminum again the same expression we need to calculate this left side this is alpha into Vc plus Vr right side eta f into Vr. So, this is the demand for the liquid metal and this is the supply of the liquid metal or available liquid metal. Now, again Vc is the volume of the casting that is 3125 cubic centimeters Vr is the volume of the razor that is equal to 1572 cubic centimeters alpha is the volumetric shrinkage for pure aluminum it is 6.6 percent and eta f is the razor efficiency since the razor is an open one and without any feeding aid it is 15 percent. Now, in this expression alpha into Vc plus Vr is equal to alpha that is equal to 0.066 into 3125 plus 1572 that is equal to 310 cubic centimeters. Now, let us calculate the right side expression eta f into Vr is equal to eta f is point what say 15 percent that is 0.15 into 1572 that is equal to 236 cubic centimeters. Now, let us see this is the what say total shrinkage or this is the demand for the liquid metal. This is the supply this much liquid metal is available for the purpose of the feeding this is the demand this is the supply means here the supply is less than the demand this much 310 cubic centimeters shrinkage is there but the available liquid metal is 236 cubic centimeters only means the shrinkage will be more than the what say liquid metal that is available for feeding hence the size of the razor is not adequate this is not sufficient means the casting requires still a bigger razor. So, that is how we can cross check what we have designed is sufficient or not what we have means the design of the razor is adequate or not we can check using this expression. Now, let us see the methods of improving the razor efficiency one is the directional solidification second one is the by using the blind razors third one is the modification of the razor design. So, first we will see the directional solidification under that this directional solidification can be achieved by using insulating sleeves that directional solidification can be achieved using chills directional solidification can also be achieved using exothermic materials. First of all quickly review what is this directional solidification here you can see this is the casting and this is the razor and here we can see one more casting and a razor is somewhere here. Now, here we can see and this is the razor and this white color indicates the liquid metal whereas this gray color indicates the solidified metal. Now, the solidification is progressing in this direction and this is the razor and here there is liquid metal and the solidification is progressing in this direction. You can see slowly more and more material will be solidified more and more material will be solidified and it is going towards the razor this is the directional solidification. Now, let us see the second case here we can see the razor is somewhere here, but you see this is the solidified metal the gray colored one is the solidified metal whereas the white one is the liquid metal and here we can see the red colored one say is this that is the center line of the casting. Now, the solidification is progressing perpendicular to the center line of the casting. Now, what happens the razor is somewhere here the razor is what say it has sufficient metal to feed the casting, but before it could feed the casting this is slowly coming. See this portion is coming towards the center or the axis similarly the bottom portion is progressing towards the axis finally what will happen somewhere there will be shrinkage will be there and the razor though it has got the sufficient liquid metal it is not able to supply the liquid metal to that shrinkage area why because the there what say solidification is progressing perpendicular to the axis of the casting. So, this is the progressing progressive solidification always the directional solidification is good for the casting if we want there should not be any what say shrinkage cavity then there must be perfect directional solidification whereas sometimes because of the geometry or because of the what say pouring temperature or the material of the casting sometimes this progressive solidification dominates compared to the directional solidification. Generally in any solidification there will be directional solidification there will be progressive solidification also, but the progressive solidification should be less the directional solidification should be more, but if the progressive solidification is dominating certainly that would reduce the efficiency of the razor though sufficient liquid metal is there it is not able to flow into the casting because the solidified metal is obstructing the flow of the liquid metal into that portion where there is shrinkage. So, that is why directional solidification is very important. So, when we are designing the razor we have to see that there is directional solidification. So, we have to remember that excessive of progressive solidification leads to shrinkage defect. So, now let us see how to achieve this directional solidification. Again we can see here casting force geometry does not permit directional solidification here we can see this is the casting the casting has got three sections one section A another section B and another section C and this is the razor now you can see the section A has got the largest thickness whereas the section C has got the moderate thickness and the section B has got the minimum thickness. Now what will happen the liquid metal from the razor it has to feed the casting in this direction. Now solidification has to start from here slowly it has to progress towards the razor then only it will be able to feed the casting. Now what is happening in this case the thickness of the first section A is larger than compared to the other two sections. So, the thickness of the center section the middle section is minimum. So, this portion freezes quickly then what happens this portion does not quick as fast as the section B. Now because it has frozen the liquid metal has to come and it has to feed this portion now the liquid metal is not able to flow into section A the first section why because the center section has already solidified. Now how can we ensure the directional solidification certainly this casting does not permit directional solidification. Now let us see how to achieve the directional solidification using insulating sleeves we can achieve the directional solidification what are these insulating sleeves here we can see the same casting where what say the directional solidification is very difficult to achieve. So, we are taking the same casting now what we are doing here this section is covered by the insulating sleeve. Now what happens because of that there will be less heat transfer to the mould walls because of that this portion takes longer time for solidification by the time this before this portion is solidified this portion will be solidifying. So, first the section A will be solidifying because of the presence of the insulating sleeve next only the second section will be solidifying next section C will be solidifying now the liquid metal from the razor is able to flow into the initially into the section A next section B section C slowly the solidification is progressing towards the razor. So, by using the insulating sleeves we can achieve the directional solidification. Next one using chills also we can achieve the directional solidification what are these chills. Now let us take the same casting where directional solidification was found to be difficult previously we have seen somewhere here we have kept the insulating sleeve because of that it has taken longer time. So, before that because of that first section A has solidified faster then the directional solidification was possible. Now instead of using insulating sleeve we can place a chill here chill is a steel block and this chill absorbs heat rapidly. Now what is happening in this casting thus what is the thickness of this section A is larger than the B and C that is why this takes longer time for solidification before that section B can solidify. Now we have to see that section A takes lesser time for solidification after section A solidifies next section B should solidify after that section C should solidify. So, that is our what is a plan that is our aim. So, for that what we are doing we are placing a chill here chill means a steel block close to the mould wall then what will happen the solid what is a liquid metal comes in contact with this chill the steel block the steel block rapidly absorbs heat because of that this portion solidifies faster compared to the previous case where there was no feed aid. Now this takes lesser time compared to the other sections. Now the section B solidifies after that section C solidifies. Now the liquid metal is able to initially it is able to flow into A next into B next into C slowly the solidification is progressing towards the razor. So, by placing chill also we can achieve the directional solidification. Next one by using exothermic materials also we can achieve the directional solidification what are these exothermic materials these are the what is a mixtures of metal oxides oxides of nickel cobalt copper manganese iron and aluminum. Now these exothermic mixtures are placed on the top of the razor then what will what will happen an exothermic reaction will be taking place on the top of the razor. Now a typical exothermic compound is you can see Fe 2 O 3 plus aluminum when this mixture is placed on the top of the razor now you see this reaction will be taking place. Now right you can see here this is the exothermic material this much right and now when it is placed on the top of the razor the reaction will be like this 4 aluminum Al 2 O 3 plus 8 Fe plus heat. Now you see the temperature produced it is very high temperature is produced. Now what is the directional solidification first of all directional solidification means the point which is away from the razor must solidify first then the solidification slowly it should propagate towards the razor and the razor should be the one which will be solidifying at the last. Now we are increasing the razor to a very high temperature then what will happen because of the high temperature of the razor it will be taking longer time for solidification. So because of this longer time for solidification so more metal is available for feeding for a longer time that is how it is able to the feed the liquid metal to the casting and finally because of this high temperature of the razor finally it will be solidifying at the end so that is the directional solidification. So by placing exothermic materials on the top of the razor also we can achieve the directional solidification. Now there is another method of improving razor efficiency is by using blind razor. What is this blind razor yes this is the mold you can see here this is the pouring basin this is the sprue the molten metal will be flowing like this and this is the sprue well and this is the runner and this is the runner finally this is the cavity and here of course here there is a core and it flows around the core finally it rises through the razor. An open razor is exposed to the atmosphere because of that there will be more heat transfer. So to minimize this heat transfer we can use a blind razor here you can see this is a blind razor you can see. So this certainly this contains enough liquid metal but it is not exposed to the atmosphere because of that it will be in liquid state for a longer time because it is in a liquid state for a longer time it can feed the casting for a longer time finally it will be the one which will be solidifying at the last. So casting will be solidifying first and this will be solidifying last so that is the directional solidification. By what say by incorporating the blind razor also we can achieve the directional solidification. Next one by modifying the design of the razor we can improve the razor's efficiency modification of the design again there are 5 ways of modifying razor design one is the multiple razoring by using multiple razors we can what say increase the razor efficiency. What is this multiple razoring? A razor can feed the casting only up to a certain distance. So if we place a razor it may have what say sufficient volume of the liquid metal to feed the entire casting but it can feed only up to a certain distance. Beyond that distance though it contains more than sufficient liquid metal it cannot feed the casting. So this distance is known as the feeding distance of the razor. Based on the feeding distance multiple razors have to be incorporated if required. So once we know that there is a feeding distance once we know that a razor can feed only up to a certain distance which is known as the feeding distance and if the length of the casting is more than the feeding distance then what we have to do? We have to adopt multiple razors means we have to use 2 razors or 3 razors or even more depending upon the length of the casting. The feeding distance of a razor has to be calculated before finalizing the number of razors. Now the question is say there may be a long casting so how many razors does it require? How to know? First we need to find out the feeding distance. What is the feeding distance of each razor? Then we can find out how many razors are required to feed that casting. So by adopting multiple razors we can increase the efficiency of the razor. Now we are defining the feeding distance. The distance up to which a razor can feed the casting during solidification is known as feeding distance. Feeding distance has got 2 components. One component is the end effect and the other component is the razor effect. Let us see what are these end effects and the razor effects. End effect. Now this is a casting for example a casting without a razor. Practically it may not be a case. Generally we make a casting with razors. Let us consider a casting without razor. Now what is happening here? This portion the extreme portion is more subjected to solidification because it is more exposed to the mould wall. Similarly the other end is also more exposed to the mould wall. So here the solidification what say will be more here and this end. So this centre portion will be solidifying after some time whereas this extreme end the left end and the right end will be solidifying faster. Now what happens? Here because of that while it is solidifying this portion will be supplying the liquid metal because the central portion has got the liquid metal. So that acts as the razor for the end portion. So there is no shrinkage in this portion. Similarly there is no shrinkage in this portion. Now we can observe one thing. For the certain length of the casting without razor there was no shrinkage. Why? Because the central portion is acting as the razor. So the two ends of the casting have no shrinkage. This is due to the rapid solidification at the end and feeding from the inner portion of the casting. This phenomenon is known as the end effect. Means there is no shrinkage at the end. End effect promotes a distance of 2.5 T where T is the thickness of the section or the slab. Now let us see another casting. This casting has a razor. Previously we have seen that 2.5 times the thickness was there without any shrinkage. Now we are placing a razor. This is the razor. Now to this central portion this is supplying the liquid metal and because of that there is no shrinkage cavity. Previously there was shrinkage cavity without razor. Now there is no shrinkage cavity. Now this length is 2 T where T is the thickness of the slab or thickness of the section. Why? Now here there is no shrinkage in this portion, central portion. Here also there is no shrinkage and what is its length and if we measure it will be 2 T. And if we measure here it will be 2 T. Again a distance of 2 T in a distance of 2 T there is no shrinkage. Why? Because we have placed the razor. Because of the presence of the razor there is no shrinkage in that length. This is known as the razor effect. The middle portion of the casting has no shrinkage due to the presence of the razor. This is known as razor effect. Razor effect promotes a distance of 2 T. Now end effect we have already seen. End effect is 2.5 T and razor effect is 2 T. Then what is the total distance, feeding distance, total feeding distance due to end effect and razor effect is 2 T plus 2.5 T that is equal to 4.5 T. So this is the total feeding distance for a razor or when we use a razor so this much distance is covered by the razor and in this much distance there would not be any shrinkage. Now here we can see the illustration and concept of the feeding distance. Now feeding distance is the length of the casting where there would not be any shrinkage whether it is due to the end effect or due to the razor effect. Now the question is how to measure this feeding distance? Is it from the center of the razor or from the end of the razor? So the feeding distance here you can see this is the F T and this is the razor. This is the razor and this is the casting. Now the feeding distance is always measured from the edge of the razor you see from the edge of the razor to the furthest point in the casting or the casting section to be fed by that razor. It starts from the edge of the razor to the furthest point in the casting that is fed by the razor. So it starts from here and it ends here so this is the feeding distance. Now again we will see razor zone length RZL of a casting section without end effects. Suppose let us assume there is no end effect only razor effect is there. So here this is the razor this is a cylindrical razor then what happens to the razor zone? So razor zone will be a cylindrical portion. So this must in this much portion there would not be any shrinkage. So this is the razor zone. Now let us see another case end zone length EZL of the casting means if we again if we ignore the razor because of the end effect so this much portion there would not be any shrinkage. So this is the end zone or this is the end zone length. Now let us see a problem. A steel casting of size 40 into 25 into 10 centimeters is to be fed by a side razor calculate the feeding distance of the razor. So we need to calculate the feeding distance of the razor. It is a simple problem thickness of the casting T is equal to 10 centimeters this much. Now what is feeding distance 4.5 times the thickness of the slab or thickness of the casting that is equal to 4.5 into 10 that is equal to 45 centimeters so that is the feeding distance. It is a simple what is a example to calculate the feeding distance. Now feeding distance with two razors influence of end effect and razor effect for a steel plate casting with two razors. Here we can see this is the casting this is the casting and this is one razor and this is one razor. Suppose if we have placed two razors for this steel casting what will be the total feeding distance on one side there will be 4.5 T will be the feeding distance. Again this 4.5 T means it has got two components say 2.5 times T is the end effect and 2 T is the razor effect. So total this side of the razor there is a feeding distance of 4.5 T. Again this side there is a razor effect what is how much is it it is 2 T. So this is 2 T. Again for this razor again on one side there is razor effect how much is that that is 2 T. So in the center from this razor to this razor there is 40 distance of the feeding distance. Again from this razor from this end up to here 2.5 T 2 T is the razor effect and from here from the end up to here 2.5 T is the end effect. So the total feeding distance on this side is 4.5 T. Now what is the total feeding distance when we are using two razors it is 13 T. So remember that when we are using two razors for a steel casting the total feeding distance is 13 T. Now let us see one more problem design top razoring system for a steel slab casting of size 60 into 10 into 5 centimeters using NRL method Naval Research Laboratory method. Now this is the solution a single razor can feed a distance of 4.5 times the thickness of the casting. So here it comes to be 22.5 centimeters on each side. Hence the feeding distance on both the sides is equal to 45 centimeters. Thus a single razor is not sufficient in this case number of razors required in this case is equal to 2. The casting can be considered as two sections each of 30 into 10 into 5 centimeters. Actually the length of the casting is 60 centimeters but we are considering this as two sections each section's length is 30 centimeters. So this is the one section so other section is also of this much size only. So if we design the razor for this section so other section also will be requiring the same razor. Now the shape factor for each section is equal to L plus W divided by T. So that is equal to 30 plus 10 divided by 5 that is equal to 8. Now this is the NRL graph on the x axis we see the shape factor that is L plus W divided by T and on the y axis we see razor volume to casting volume ratio V r by V c. Now just now we have seen the shape factor is 8. So if we what say put this shape factor that is 8 on the x axis you see. So this is the shape factor you draw a line such that it touches the graph. So here it is touching. Now from here we draw a horizontal line towards the V r by V c. So this is the point where the line is touching the y axis. Now it is something between 0.4 and 0.6. If we more approximate it will be say 0.45 and something more. So it is shape factor for 8 is equal to 0.55. Now volume of the casting is equal to 30 into 10 into 5 that is equal to 1500 cubic what say centimeters. Volume of the razor V r is equal to now shape factor this is the V r by V c. V r by V c is equal to 0.55. So V r by this what say V r by V c ratio 0.55 into 1500 that is equal to 825 cubic centimeters. Now this is the NRL razor selection chart. Now so this is the volume we got volume of the razor is 825 cubic centimeters. Now here we can see on the x axis we see the razor volume and on the y axis we see the razor height. Now the razor volume is 825 cc cubic centimeters. So we have to identify 825 cc on the x axis. So this is the place we have approximated 825 cc. So from here we have to draw a line vertically like this. Now so these are all the different razor lines. This is the line corresponding to diameter 12.5 this line. This line is the one which corresponds to diameter 15. This is the line which corresponds to diameter 17.5 and this is the line which corresponds to diameter 20 and this is the line which corresponds to diameter 22.5. Now we have to draw a line upwards from this 825 razor volume. Then in this process that line will be intersecting all these razor lines. You see all these razor lines are what say intersected by this line. You see at this point it is intersecting at this point it is intersecting at this point at this point also finally at this point this vertical line is intersecting the different razor lines. Now what happens we have a rule that the diameter or the height by what say diameter ratio should be between 0.5 to 1 means the h by d ratio should not be less than 0.5. Similarly the h by d ratio should not be more than 1. Now you see here we this line has intersected the 5 razor lines here, here, here, here and here. Now all these 4 lines are in all these cases the h by d ratio is less than 0.5. You see as we come down the h by d ratio will be less than 0.5. Only in this case the h by d ratio is above 0.5 and less than 1. So though we we get the 5 values for the razor height only one is feasible this one. So all these 4 are to be discarded. Now what is the razor height in this case it is 7.5. You see this is 5 and this is 10 so this is 7.5. So finally only this value will be choosing. Now we get only one case that is the diameter is you see the diameter is for this line the diameter is 12.5 12.5 and this is the height that is 7.5. So the case one only one case 12.5 centimeters diameter and 7.5 centimeters height. And remember we have considered only half of the casting for half of the casting this is the required what is a razor required for the remaining half of the casting one more razor is required. So two such razors are required. So friends in this lecture we have learned how to design the razor and razoring system using NRL method. We will continue in the next lecture. Thank you.