 But before we do that, establish a relationship between 2 s elements which are advance, time, infiltration, depoculation. This relationship will be a general purpose relationship which will be used for all these surface irrigation methods. Even the border irrigation method which we have considered earlier, this will be applicable to that. This will give you a general understanding that how these items, the advance, time, infiltration and the depoculation are related to each other and these relationships you can exploit for the design purposes. So this will be a very important way of looking at the overall process. First take the Kosti-Kov relationship which we had defined earlier and this gives the infiltration depth, the accumulated infiltration depth with respect to opportunity time and these 2 parameters which we had defined, C and alpha are the empirical constants or these parameters. We had also seen that how we can derive these parameters from the absorbed infiltration data which is taken in the field. So these are basically defining the type of soil for each type of soil, these parameters are known and T is nothing but is the infiltration opportunity time. In other words if I write T, I can write this T in terms of Y and these 2 parameters, I can approximate this T which is the infiltration opportunity time, cho, this T here as we have used this T is nothing but infiltration opportunity time which means that at the surface of the ground for how long the water was available and for how long the infiltration opportunity was prevailing. So accordingly the depth of infiltration can be determined depending on what is the time of infiltration or what is the time for which at least that assumption is valid that the amount of water is more than the infiltration opportunity or the infiltration capacity. Those things we have seen and since in irrigation when we are applying irrigation water we are ensuring that the depth of irrigation is always more than the infiltration opportunity of the infiltration capacity prevailing at that particular time. But we can make an approximation that this time can be approximated to the time of irrigation. So when we find out this time the T, T now may be taken as the required time of, that assumption we are making is that the time of infiltration opportunity is equal to the time of irrigation. So indirectly we can, we can find out that time if we know the characteristics of the soil this relationship is known which we have already looked at. Now let us assume that the soil is we make 2 more assumptions, first the soil is uniform that means the soil characteristics are not changing that particular field which is in question and we also make another assumption that the initial moisture content are uniform. Now making these 2 assumptions let us take that the distance z, we take z as the vertical distance, the distance z from the soil surface to the depth of the soil when the infiltration will take place the wetting front will move. So if you want to express that wetting front in the form of distance z then this distance z can also be expressed, it can be expressed as a function of proportional to with some proportionality constant if k I define as a proportionality constant if k is then I can express z with respect to y, if I substitute y from the Cauchy-Koff equation this can be expressed as this c t to the power alpha into k, now this these are 2 constants I can express this as new constant which is k dash t to the power alpha, let us take 2 more quantities t t is time for advance curve required for advance curve to reach the end of the field and if t n is the time to infiltrate the net irrigation requirement which is y n. So to achieve the net irrigation requirement if you need the time t n that is the time which is required to get this net depth of irrigation and t t is the time of advance of the waterfront to reach the downstream end. Now here comes the various options available to you it depends on your type of soil as well as the length of the field, what will be the value of t in terms of t n or what is the proportion of t t of t n which is required for the waterfront to move in the downstream direction and to reach the downstream end of the field. For example right now we will assume that we will make assumption we will take one case where we will assume that this t t is one-fourth the time of net infiltration that if that infiltration is one unit it will take one-fourth the time for the advance curve to reach the downstream end. So if we make that assumption there can be various cases it might it depends on the characteristics of the soil it depends on the length of the field that what will be the t t because the movement is a function of how much of the water is infiltrating with the soil as the water is moving in the forward direction and is also a function of what is the length of the field. So these are this is only one possibility there can be many possibilities depending on how you have fixed the other parameters. So let us make assumption that assume we are making assumption that t t for the present case which we are going to consider is one-fourth the t n time taken for the net irrigation depth to be achieved is 4 times the time taken for the advance curve to reach the downstream end. So with this assumption we divide the total time taken which is the t n into 4 different parts in such a way that delta t 1 each one of these are the various intervals which we are going to consider and each one is equal to t n by 4. Let us try to have a look what we have done so far I will try to sketch this that this is your this is your total field the upstream end the downstream end okay say that this is the root zone depth which you are interested in irrigating. This root zone depth the total time taken you are divided in you are trying to consider what will happen each time in towel which you have well considered each one is equal to one-fourth the total time requirement. So if that is the case let us look at what will be the depth of water infiltrated in the first time interval the first time interval is delta t 1 depth of infiltration is if I say that in general the depth of infiltration if you want to take in any one interval will be a function of what is the initial depth in the soil and what is the depth infiltrated during this time interval. So if y i is the infiltration during that at the end of the interval and y not is the infiltration which was already available in the beginning then during that interval you have the increment depth in the depth of infiltration is delta y i. So similarly the depth of soil which will become wet which we will call as delta z 1 you are saying that this is our total z this root zone is the z which we are which we are considered this is the total depth. So in the first interval this will be the depth of soil which will be wetted in the very first interval if we assume that z 0 to start with let us make an assumption that z 0 is 0 to start with if it is known you can take that value but if it is not known then if it is it was totally dry you can always take it to be 0 not a very appropriate assumption. So once you assume this you also need the value of alpha used in that equation the Caustic of equation. Let us assume that the value of alpha is also known this for the present problem let us take this to be 0.5 then if these two things are known then the very first interval delta t 1 you can write this delta z 1 is equal to z 2 minus sorry z 1 minus z 0 and z 1 is nothing but you have said that 0.5 minus 0 in this particular present case which is nothing but z 1. So in this particular case if this is delta similarly write the expressions for other interval or delta t 2 time interval I mean find out what will be delta z 2 is z 2 minus z 1, z 1 is nothing but this much depth is not it this is z 1 is equal to delta z 1. So to find out the next step I am trying to reduce this z 2 minus the previous step which has been considered earlier in the previous interval so z 2 minus z 1 which will be equal to q dash into t 2 to the power 0.5 minus delta z 1 because z 1 is equal to delta z 1. Now t 2 is 2 times t 1 so if you substitute that your z 2 will be q dash into t 1 minus z 1 power 0.5 into 2 to the power 0.5 minus delta z 1 which is nothing but delta z 1 this part is delta r 1 into 2 to the power 0.5 minus similarly you can write the other forms also delta z 3 will be delta z 1 into 3 to the power 0.5 minus 2 to the power 0.5 delta z 5 will be 5 to the power 0.5 minus 4 to the power so this general relationship can be established and if you plot this onto this you will find that at the end of this will be the this will be the general trend if we take that this is a linear variation you can find that over the length of the field this will be the variation which will be encountered because of the fact that the water is moving from the upstream end to the downstream end and the water is taking one-fourth the time since the time is equal to the time to reach the downstream end when the water will reach just the downstream end the infiltration will be minimum there similarly the other segment you will find that the size of the segment the depth of infiltration will keep on reducing that is what you will see in the relationship and in each case this will be the of the infiltration for each of the smaller segment example this is for t is equal to 2, t is equal to 3, t is equal to 4 and if you go beyond this if you go beyond this take another segment you will find from this this is for t is equal to though you have gone beyond the roots on depth these equations you will if you just analyze these equations you will find that this trend will be shown each successive z or delta z which is lowered down will be having smaller and smaller depth and that is quite understandable because we have been studying this so far that what happens when you go and the when you have the infiltration for a longer period so that is what is reflected here that the initial infiltration will be at a higher rate the later infiltration will be at a lower rate. Now if you want to satisfy the downstream end of the field also you will have to provide the water beyond the roots on depth that means for additional time period only then this component the lower part of the field can also be satisfied or in other words what you can say is that if you want to satisfy the the needs of the downstream end also you have to ensure that at least the water should be available there for t n time what is the net time for which the infiltration should take place so that to get the achieve the net irrigation requirement okay. So that is what you will you can write in the form that to infiltrate depth y n of the field there should be opportunity time at the lower end also equal to t n but you also know that t 4 is equal to how much 4 times t 1 and correspondingly z 4 is k dash 4 t 1 or delta z 1 into 4 to the power 0.5 the same thing so to achieve this the infiltration opportunity at the in order to achieve this requirement the opportunity time at the upstream end has to be has to be t 5 which is equal to t n plus t n by 4 is also equal to 5 times t 1 the corresponding z 5 is delta z 1 into 5 to the power 0.5 as we have done here the same thing okay that is what we have plotted here also this is basically the same thing which we have plotted that if you want what will happen at t is equal to 5 so that is what we have plotted already here. Now we will define two quantities which are very important quantities for our subsequent analysis and design purpose we can utilize these the first is that if you want to know the average depth of soil which has been wet by deep percolation will be the at average depth of soil is basically this part this portion which I can mark here this is the deep percolation could have been avoided but since we wanted to take care of the downstream areas we have indulged in this deep percolation so this deep percolation if you want to know that how much deep percolation you have indulged into you can express that as delta z 5 by that is the average deep percolation delta 5 is the maximum deep percolation if we assume that this relationship is linear and is varying from delta 5 on the upstream end to the 0 level at the downstream end then you can say the average deep percolation is delta 5 by 2 which can also be written as z 5 minus z 4 by 2 because delta delta 5 is nothing but z 5 is the absolute value or the total depth up to that level and z 4 is the depth up to the root zone level of the upstream end let me let me say that this is delta z 2 the next one is delta z 3 this is delta z 4 and delta z 5 okay these are the major values but for each one this is the z 1 up to this up to the next one is z 2, z 3, z 4 and z 5 so you can use it either way this is z 5 minus z 4 that is what is delta z 5 by 2 that is also you can write so this in fact is nothing but you can write this in the general form minus 4 to the power 5 into delta z 1 by 2 this is 1 which gives you that what is the average deep percolation and if you want to find out the average depth of soil which has been wet and you can express that as z 4 plus z 5 by 2 so the total depth which has been wet what is the average value of that is the average of the two extremes on one side is z 5 and the side is z 4 so the average of that will give you the total depth which has been wet this you can also express as 4 to the point 5 plus 5 to the power of now if you take the ratio of these two quantities ratio average depth of deep percolation of wet soil write this as z delta z 5 by 2 by z 4 plus which is 5 to the power 0.5 minus 4 to the power 0.5 by 5 to the power 0.5 plus delta z 1 is cancelled out so this is the ratio which is in this particular case is 0.056 now in this in this specific case what it amounts to is you can now formulate time of advance t t is one fourth the t n is one fourth the net infiltration time t n and for the alpha of 0.5 the average depth of the percolation is 5.6 percent this is only one one instance which has been analyzed similarly there are many other instances which have been analyzed by taking different values of alpha which means that by taking different characteristics of the soil and by taking different FR ratios which is the fractional advance ratio this ratio t t by t n we call it as FR or fractional advance so if these are known then you can formulate the relationships which can be used subsequently for your analysis and I will show you some values of the table which have been which has been provided through the similar analysis which we have done just now. This table looks like this I will just pick up some of the values out of this table so that you can get a feel of this table gives the expected percentage of deep percolation. On this side you have the fractional advance ratio FR here you have the alpha values for different soils may be ranging from 0.1 to 0.9 FR ratio of you can write it as t that means the time of opportunity is same as the time taken by the advance curve to reach the downstream end you will have the values look at the order of magnitude of these values that how much if you have this parameter fixed in such a way that your advance curve of the time taken to reach for the advance curve to reach the downstream end is equal to the opportunity of time requirement for the net infiltration to take place you will incur lot of losses and those losses will also vary from soil to soil the soil is a function of alpha so if your alpha is increasing the deep percolation losses are also increasing let us take another sample of when you have t by 4 out of which we have analyzed only 1 but for the others for example when alpha is 0.1 and you have FR ratio of t by 4 in this particular case the deep percolation losses will be 1.1 percent 2.2 percent 3.3 4.5 5.6 that is what we have analyzed for alpha is equal to 0.5 and for FR ratio of t by 4 or 1 by 4 and 6.7 7.8 0.9 and 10 percent let us take the other extreme of t by 10 that means you are you are flooding the total length in very short period is where FR ratio is t by 10 so in this particular case your deep percolation losses will be still smaller this table now can be utilized for picking up some of the parameters you can find out that if you want to accept only the deep percolation losses of a specific range you do not want the deep percolation losses to be more than 10 percent or more than 5 percent and you know what is the type of soil which is the prevailing type of soil you can pick up that alpha and you can find out what is the most preferable FR ratio which is which can be utilized and that can give you some indication towards what should be the time of irrigation should be selected and what will be the time of the accordingly the time of infiltration which will be available is not is not dependent on only these things will also be dependent on then which steam size you will be picking up what are the other parameters of the field what is the grade all those things we have not considered so far this is only the starting those parameters which are independent of the other aspects of the field they are only giving you the relationship between soil type which is through alpha and the advance time which is again dependent on the soil type to a certain extent and all these relationships can be utilized to start your your design considerations looking at which are the most suitable parameters which you should be start with okay. So this one analysis is as I had mentioned in the beginning that this is not only concerned with the furrow irrigation it is a general purpose analysis which can be made use of in all the surface irrigation methods. Next we will try to now start looking at the furrow irrigation method in particular first of all we will try to look at those relationships which are obtained through experience through field trials so these relationships which are based on field trials these relationships are very important in the absence of detailed data because you can also use the hydraulic relationships which are more exact but many a times you will find that the required data is not available so you have to you have to start at least looking at the designs with some some indicators which are available and since this is a very important area all over the world there are word organizations like FU which have compiled this information and made it available in many reports where is easily available where people have come out with under different conditions what will be the limiting design parameters from various concentrations and we have already considered in the case of border irrigation also the considerations the major considerations are of the things like that the steam sizes should be erosive you should not create problem for your fields then there is one consideration the other is that your efficiencies should be reasonable efficiencies so that will be basically dictated by what sizes you will choose will be the combination of discharge the steam size the size of the field with respect to the soil type and with respect to the slopes prevailing grades when you look at the grades there again you have to look at are those grades excessive which can create problems of erosion are those grades very flat which can also create problems of drainage so there are no specific rules and regulations which are applicable all over the places you will have to look at the climate you have to look at is it a humid area is it a arid area the rules will be different from the similar soils but if the area is humid on one extreme on the other extreme if the area is arid you might have to choose different parameters for example let us assume that if it is a humid area in the case of humid areas you will have lot of rainfall occurring and that too the intensity of the rainfall will be very high if you go in for slopes which are steep slopes may be that during the irrigation time you can control those those steam sizes you can control the rate of application of water but what will happen when the rain will occur there would not be any control at that time the slopes which are prevailing in the fields they will remain there so when the rain water will be generated the surface runoff will be generated that will create havoc that will create lot of erosion and all yours your fields might be distorted it might be be divide of all the fertile land which was there might damage the crop altogether so all those things are possible so when you look at those repanded parameters you will have to take into consideration many other conditions which are beyond the irrigation conditions these things are very important and we will look at all these these relationships which have been formulated on the basis of the experience of the farmer his farmer might not be having the scientific explanations of all these practices which he has been indulging into but through the experience through the common sense he has arrived at some of the combinations which are very scientific which are very realistic and those things have also been taken into consideration when the various researchers have looked into all these various possible details of these parameters they have taken into confidence or into consideration all those those experiences of the local farmers and those have also been brought out in all those publications wherever possible along with that the other recommendations are based on the experimentation which for example in the case of border irrigation we had seen that how we can do the evaluation runs so through those evaluation runs you keep on taking the observations and then you analyse those those data and come out with the recommended procedures for example in the case of the erosion you run those steam sizes in the fields and see that how much erosion is taking place you find out which are the steam sizes which are limiting steam sizes beyond which if you increase the steam size for those specific type of size under those slopes you will have the erosion problem so that is how you collect the data and you make the recommendations all those things we will we will discuss in the next class and along with that we will also look at the hydraulic relationship which have been formulated on the basis of the hydraulic principles and they can be used for the design wherever those data the required data are available okay. Any question at this stage? Thank you then.