 relationship between the advanced curve type of soil which is applicable to all the methods and then we had started with the irrigation systems and we said that we will start looking at those relationships which have been built up with the experience of the farmers and through their field trials, the experimental data. These are general purpose relationships which have been introduced with the idea of giving some levels of these parameters, may be the upper bound, what will be the recommended lengths of the fields under different conditions of the system, so some of these relationships we will try to have a look, for example a relationship between the value of maximum stream size which should be picked up for a particular condition and it has been seen that it is basically dependent on what is the slope or is the prevailing slope, so that parameter has been taken into your account, this S is the ground slope that is given in percentage and Q maximum is the maximum stream size litters per second, this is a very crude relationship in fact if you look at from the point of view that is not having any parameter which is soil dependent, so from that angle and since you know that the maximum stream size should be basically based on is some parameter which is related with which is dependent on what type of soil is the prevailing soil but since it is a very approximate relationship which is only giving an indicator value that what is the range, you should not be very much of the range, so looking into the ground slope you can pick up a value of stream size which is reasonable, for example using this relationship you might get that for a slope of 0.1 you are getting a maximum stream size of 6 litters per second, 0.5 will give you 1.2 litters per second, similarly slope of 2 percent will give you a stream size of 0.3 litters per second. Now comes the other conditions, for example in the case of furrows you do not go after the slope of 2 percent, the 2 percent slope can be very erosive slope under some conditions, so along with these relationships are not to be used in isolation, these are only giving you some order of magnitudes which have to be used very judiciously and you can make use of these relationships if you are aware of the other constraints. The maximum slope let us look at some of the furrow grades which are normally the recommended grades, these slopes again they have come out they have been suggested with respect to the trials, field trials as well as the experience of the farmers, there are many factors which will influence these suggested furrow grades, if you start from the beginning when you are trying to bring some area under irrigation, when you are trying to lay the field it will be basically a function of what is the prevailing slope. So the natural slope which is prevailing in the area that will be the major constraint or major condition which will decide what is the grade to be adopted. In many situations you will find that if the natural slopes are excessive if you go in for the formation of those areas or the grading of those areas you might turn the soil upside down, the soil which is fertile soil might be taken away and replaced with the soil which is exposed soil which has come from the lower layers that soil is not very fertile. So you will try to avoid that situation where the exposure of the soil might be possibility, the grades are very excessive. Similarly the grades which are generally adopted in furrows they should not be more than 1.0%. Now this is the maximum limit though it can be exceeded depending on the soil type what type of soil is in question, if the erosion is not a problem, if the furrows are cultivated furrows the erosion will be again less, so you can but this is the general limit which is applicable to most of the soils that one should not cross these limits. Similarly from the point of view of the other conditions which can be prevailing conditions you might find that the minimum grade, this is the maximum grade, the minimum grade should not be less than 0.1% because if it is less than 0.1% then it will be a flat area, you might find problem in moving the water in the furrow. So from that consideration the minimum grade is the limitation that if the grade is, there should be some grade so that the water can move in the forward direction. Similarly in the case of changing conditions as we were discussing in the last class, that if you have conditions varying from arid areas to semi-arid areas or to humid areas you will find that the slopes will be, the grades will be also affected from those concentrations. So in arid areas let us look at some of these, if you have arid areas, the rain is naturally will be very small in these areas. You might be able to go up to slopes of around 3%, again soil will be a constraint what type of soil you are using but you might be able to achieve such a slope also provided your steam sizes are very small, those are the other conditions if your steam sizes will be small then it will have its own repercussions, repercussions can be that your length of the furrow might be reduced drastically because of the fact that there will be lot of infiltration taking place in the upstream end of the furrow. So all those conditions will be the other condition which will govern what slope can be achieved, what steams when it has to be looked at along with the other parameters of steam size of the soil type. The humid areas on the extreme you might find that the slopes may be as low as 0.5 percent. So they should not be, this will be the limiting slope that you should try to avoid the slopes more than 0.5 percent, at the same time you will like to give some minimum grade so that you can have the water which gets accumulated in these humid areas it should be, these slopes should be able to drain off that water quite comfortably. So the minimum slopes might not be less than 0.05 percent, this becomes the range which is only a recommendation that the actual slopes when if you want to find out you will have to go in for the actual designs where you will have to look at the other parameters in combination with these parameters and the suggests or select those parameters accordingly. That is what the design is all about, if you have to you have to ensure that the efficiencies are proper, the efficiencies will be proper if the wastage is less and then the erosion is avoided, sedimentation is avoided, all those things have to be taken care of. Similarly along with these slopes or the grades the field sizes important parameters which must be considered and they are suggested field sizes which are available in literature on the basis of the field trials as well as on the basis of the experience of the local areas and in general you will find that if you increase the field length in the case of furrow irrigation it will be the furrow length because field is composed of many parallel furrows. So increasing the field length what it what it results in and is increase in the FR and FR we had defined as the ratio of advance time to the you will also if you just look at the various relationships we have derived so far if you increase the FR what it amounts to, if the FR is more there will be more of deep percolation that is what we have seen earlier in the previous lecture that when the FR increases I had given you a table also, if the FR increases what happens? You are basically your advance time is increasing that means the length the higher the length of the field the larger the length your TT will be larger the Tn may or may there is something which is the requirement so far a larger TT FR will be larger, if the FR is larger the disparity of infiltration will be much higher and you will have more of deep infiltration or the percolation loss will be more. So this increases percolation loss and which in turn will result in reduced efficiency. From these type of relationships which have been put forward ultimately you will find that you have been given recommendations in different forms, one form of recommendation is may be in the form of a relationship or a table which is giving you for different slopes or different slopes and for different average depth of application, the application or the irrigation application requirement is not a fixed requirement, it might be different, it might be varying, it is something which is dependent on the management and the farmers at what time they want to irrigate and accordingly the amount of water which has to be applied as irrigation water, depth can vary, it also is a function of different types of schemes whether it is a rotation, a rotational irrigation scheme or the on demand irrigation scheme, we will look at those things later but it is true that the depths of applications can vary. So for different depths you might find that there are different relationships, these depths are also dependent on what type of soils are the prevailing soils, you might have clays, you might have loamy soils or sandy soils, so under each of these soils the actual depth of irrigation and just taking some representative values or the values which are normally used as depths, these are the depths in centimetres, all these are in centimetres, 7.5 centimetres, 15 centimetres and so on, these are the possible, these are the normal depths which are used in irrigation, so the suggestions or the suggested parameters can be of this type that for a specific slope under different conditions of soil for different depths of applications will be the recommended length of the furrow, this is giving a recommended length of furrow meters, I am just picking up some of the values just to show you that how much variation can be there from one type of soil to another type of soil and from one slope to another slope, then let us have a look at these two more values for a slope of 0.5 if you want. Now you will see the variation when you have for an increased slope you could get for the same type of soil and for the similar depths you could get, you could use the longer lengths of the furrows, when it became more steep, for example for 2 percent slope, if we look at the recommended maximum lengths these are basically let me put here these are the maximum lengths, so your length should be preferably below this these lengths, there will be many other constraints which might force you to reduce the lengths than these lengths, these are just the recommended maximum lengths which can be used under some of these conditions. Now you see here that when the slope has increased and the grade has increased the lengths are again reduced, all the cases is the same, I have just picked up 3 slopes, in the beginning the slope was 0.5, the lengths were more for the clay soils less than that for the lomi soils and even lesser for the sandy soils which is quite understandable because of the variable infiltration rates under these the infiltrations rates are maximum under sandy soils so you cannot afford to have very longer lengths otherwise you will have lot of deep percolation losses but when the slope increased to 0.5 percent for the same soils the lengths the possible lengths which you can adopt they are they are much higher lengths but the trend is same when you go from clay to loam to sand again the for those slopes you cannot your your lengths are reducing in order of magnitude. Now within the within the same soil if you see here from 0.05 to 0.5 to 2 percent increased first and again it reduced. Now this is this reduction is on account of the erosion problems. The erosion plus also the velocities which are the movement the rate at which the water is moving it might have problems of erosion plus the accumulation of water the surface runoff also can be another problem which can be very detrimental in terms of loss is because those surface runoff is again a form of loss the water is just getting passed over the furrow is not getting infiltrated into the soil there is of no use is basically is again a loss. So whether is the loss because of deep percolation or whether because of surface runoff it has a loss. This is these recommendations are on the basis of those evaluations that so that your efficiencies can be maximum under these prevailing conditions. So if you are starting with a design these recommended values can be taken as the starting values these can be taken as treated as the first assumptions of the design parameters that is what these recommended values should be used for. So once you have these starting values or if the data is not available you cannot do anything you might have to do your designs approximately on the basis of these you select the parameters and look at the combination of various parameters and select a value which is a reasonable value and even you can find out under various conditions what will be the efficiencies which you are producing either you can go in for the evaluation of those are those some segments of the furrows the actual test runs and find out what will be the efficiencies and then on the basis of those efficiencies select a set of parameters which give you the best efficiencies or you go in for the better relationships provided you have the data and as well as the computational facilities or even in some cases the other related data which is required for these computations which are based on better relationships which are closer to hydraulic relationships. So let us have a look at some of these relationships which are based on hydraulic relationships these hydraulic relationships which are used for design purpose of for irrigation design they are not again exact relationships because there is no need you do not justify using the exact relationships of hydraulic flows in these areas because of the three major reasons one is the lack of required data you require quite a good amount of data even that can be taken care of if the data requirement is there if you are going to get the best results no problem you can get the data you can afford to spend money on collection of the data but is not is not that only that is one aspect only the other is that even if you go in for the data collection still there is lot of spatial variability in all those parameters which are the parameters which are influencing these processes. So the spatial variability of the involved variables for example even if you take the infiltration properties of the soil in a particular field you are not certain that how much that those properties are changing from that point where we have done the infiltration analysis using the infiltrometer maybe that is only a point in the field if you go from that point to another point your infiltration characteristics are going to be different. Similarly the properties like the roughness coefficient is changing from point to point the soil might not be truly uniform so it is not worthwhile using very exact relationships if your data is known to have spatial variation okay so many of the relationships which have been put forward they are they are approximate relationships based on the hydraulic relationships to start with but using lot of assumptions on the way and they have ultimately been transformed into more empirical relationships you cannot say that they are based on the hydraulic relationships but with lot of assumptions wherever the assumptions were needed they have been incorporated and they do not remain to be as exact as you will like to be or when you use them in the experimental setups in the laboratory conditions that is not justifiable so most of these relationships which we are going to look at they are the approximate relationships and most of these have been put forward by the soil conservation services of USDA US department of agriculture then there are some other peculiar problems with the for irrigation we have formulated some equations for sorry for infiltration process they have to be they have to be revised why because in the case of furrow this is one segment of the cross section of furrow you have this is your water level in the furrow in this case the infiltration is taking place along this perimeter so the major difference is that the infiltration is taking place perimeter of the furrow and for all particular purposes you want to represent this as in the form of depth over there so it will be much better if we can find some equivalent depth our surface area of the field. So we will have to do some transformation to our equations so that we can we can convert this into equivalent depth what we should what we can one possibility is that we just assume that this this curvature can be flattened and then you find out the and that is what is is done basically in this particular case you try to make corrections to the existing equations so that you can you can incorporate this particular fact of having the furrows which are infiltrating water along the perimeter of that. Is the question is a good question that the infiltration now in this case we are the question is that whether the infiltration which is in this particular case in the case of furrow irrigation is not only vertical is lateral also so whether the two will be same or not yes they would not be same there will be some difference in the infiltration but we are approximating them to be what we are assuming is that if we this perimeter if we try to unfold this furrow how much would be the depth over accumulated over this length of time the parameters okay. So it will involve some assumption may be that it is giving you a value which is slightly less than what is actually happening there will be more infiltration in actual practice because of the lateral dryness of the adjoining parts of the soil but that is what is done in the actual practice if you want to take care of those additions the additional infiltration which is taking place you might have to improve upon those figures still to an extent but that is taken care of by taking the spacing between the furrows to an extent what we are doing is that we are saying we are having an area which is having furrows and we have laid down the furrows at a known interval the spacing between the furrows is known so if the spacing is more there will be less water area which is wetted the spacing is less the wetted area is much more but when you try to use the perimeter you are in any case you are increasing the length of the area so that is indirectly taken care of there when you are unfolding this. Integrates of the furrows there also there is a slight difference in environment of these integrates in the case of other irrigation the border irrigation as well as the level irrigation what you are doing is that you are taking the infiltration rates through the infiltrometer test whereas in this particular case it is not possible to use the infiltrometer test because of the fact that is not the is not the vertical infiltration so what we do is that we do the input inflow outflow analysis in a segment of the furrow so you take a representative segment of the furrow if we let us say that this is a furrow in plan and I take a segment this is my upstream location of the segment and downstream location of the segment so I install some some device at these two stations which will give me the measurement of the I can observe how much is the inflow how much is the outflow from this end so you can even install two partial forms any device which you feel normally the partial forms are used and there is furrows so if I know the inflow and the outflow I can find out how much is the amount of water which has infiltrated into this segment and that gives me the intake rates so to find out the intake rate use such a environment let us say that Y if Y is the intake rate you can express it as length into Y is nothing but the equal in depth of infiltration is equal in depth of infiltration over the wetted surface area of the field and this is millimeters that is the length of the furrow segment considered meters P is the adjusted wetted perimeter this is again in meters then we have V in the volume of this is observed in liters similarly V out is outflow volume again in liters and V s is the volume of water there might be some volume of water which is at that particular time when you are taking the measurement there will be an storage between these two sections. So this is basically an inflow outflow analysis and the average value of infiltration if you take if you start the analysis at a particular time and take the final value after a very long time and what you are getting is average value over this period. So to find out the variation of the infiltration over this segment you will have to take some intermediate observations. So you take you keep on taking observations at some interval so that you can find out how this infiltration was varying over time. Now in this we have used two terms the inflow volume no problem you can you can measure the outflow volume you can measure length is known there are only two items you look at this equation again the adjusted wetted perimeter which will be difficult to find and V s which is the volume of storage water and storage between this section they have been uhh relationships which have been formulated for these two items so that they can be uhh used comfortably they can be evaluated without any problem within the known quantities which are easily observable. Let us look at the first uhh the adjusted wetted perimeter is given as this expression is basically obtained from the Manning's formula you can see the various uhh most of these relationships have been derived from the Manning's formula. Now this is the expression which has been found to give you the adjusted wetted perimeter and the various terms you already know Q is the the volumetric inflow in liters per second so Q is in liters per second N is the Manning's roughness coefficient and normally the value of N is in general taken as 0.04 and S is the the furrow slope basically is the hydraulic gradient is assumed to be equal to furrow slope and this is given as meters per meter the channel storage or the volume of water in storage which we have just mentioned V s the expression used for expressing V s is so in this expression also there are all the quantities which have been expressed they are the same as before and here is in the length of the furrow segment which is considered the zen meters. Now you remember the infiltration equation which we have earlier written in terms of time and these different parameters A, B and C this equation for the case of furrow irrigation design is modified to incorporate this is the wetted perimeter W is the furrow spacing meters so you can see that the impact of having a very large furrow spacing will be that your this Y will be reduced constantly so that is how the the impact of having furrows with a different spacing or even if the space is small still the Y will be much compared to be lesser than if you are using this expression of the same equation on a border irrigation on a border or on a level basin okay. Then let us look at some other expression which we are going to use one is for the advanced time the advanced time can also be computed on the basis of this equation this is the expression which is derived to express the advanced time and the various quantities which are used here T t we know that is the advanced time in minutes X is the distance down the furrow that means from the upstream end of the furrow what is the distance we are considering in the direction of the downstream length of the furrow in the long period in the middle of the direction of the furrow and this is meters then F and G are the advanced coefficients Q and S we have already seen they are the same parameters Q is the volumetric inflow rate in terms of in liters per second and S is the flow the furrow grade is the representative value of the hydraulic gradient, there is a these parameters these coefficients F and G they are available for different family curves along with the parameters A B and C. So these are the coefficients which are available in literatures they are the fixed values for different family curves I will provide the table of these coefficients these are basically to give you some order of magnitude for different family curves the intake family these intake family curves have been designed or they have been defined by the SCS the soil conservation service we have discussed that earlier and they have evaluated these curves for these coefficients along with F and G coefficients for example I will give you 1 or 2 values which will give you some idea about the order of magnitude of these this is the value of A when the intake family curve is 0.05 and this we had discussed earlier also that the intake family curve of 0.05 it means that this is a relationship this is a equation for which these parameters are applicable for a soil type whose basic infiltration rate stabilizes at 0.05 inches per hour is it inches per hour or not we will have to check that I am not sure but this gives the stabilized rate and that number they have adopted as the number associated to the intake family the intake curve and that the set of those curves they are calling intake family. So this indirectly it designates what type of soil you are using and all those characteristics of the soils are given in the form of the intake family curve characteristics the value of B is 0.618 C is taken to be constant C is basically introduced to change the shape of the curve in some cases if the soil characteristics are such that you are getting you are not able to represent the soil through a single parameter then you might be able to change the C and get the if there are 2 curvatures of the soil the infiltration capacity curve then this C parameter is helpful but in this particular case all the family curves are having the same C value. The F value is 7.16 for this intake family and the G value is 0.088 into minus 4. And this is given for the different types of soils and the number goes up to 2 for which the parameters are again given. This table will be made available to you and this is quite a useful table. I think with that we will stop today if there are any questions or we have to answer those. Thank you very much.