 with some of the general differences which you will have to or you can apply the general relationships to the specific irrigation method because of the fact that in the case of Faroo is not the application of water is not similar to what you do in the other two surface irrigation methods, the border as well as the basin or the check irrigation method, the different name given to that. We had seen so far that how we can upgrade the relationship of the general infiltration curve which we had written down and we had incorporated the vetted perimeter and the furrow spacing to upgrade this relationship, okay and we had also looked at another raw relationship which is used for finding out what is the advance time and this relationship we had seen what are the various variables, what do they mean and we had also seen some of the order of magnitude for some family curves. Now today we will start with the most important parameter which is the time of infiltration opportunity that for how long? There is a relationship between the time of infiltration opportunity, the time of water application and the advance time as well as the recession time. Now here this T-O is the infiltration opportunity time, T-C-O we have looked at all these different variables earlier, T-C-O is the time of water application, you can also call this as the cut of time, the cut of time. Now this cut of time is the time up to which you are supplying the water, this is the advance time, T-R is the recession time, all these times are generally expressed in minutes. Now this general equation if you look at various components that T-C-O which is the time of water application, this is the one which is in the hand of the management. The farmer makes the decisions about this T-C-O for how long he wants to make the water available for the field. So this is something which is dependent on the management of the system, either the decision is taken by the farmer or it can depend on the availability of water, how the water is made available in the total network, it will be related to that but the ultimate decision is in the hand of the farmer, how for how long he wants to make this water available. So if you try to look at this T-C-O it can be taken to be equal to the net time requirement plus the advance time minus the recession time. So preferably if you want to take care of the net irrigation requirement this is one indicator which is available to you when you design the system that how much what should be the order of magnitude of T-C-O can be known from these three items, the net irrigation time, the advance time and the recession time. As far as the component of time is concerned you can use the infiltration equation, the modified infiltration equation to find out what is the net time requirement. So if you write this equation this is the net depth which is required, this is the same equation which we had written in the for Yn that is transformed to get this in the value of Tn. So the same equation can be used to find out what is the order of magnitude of the net time requirement to satisfy or to satisfy the requirement of Yn which is the net irrigation depth requirement that is known a priori that you know when you go in for the design or that irrigation you know that how much is the net depth of irrigation requirement and you can always decide to start the irrigation at that level when the net irrigation requirement is of that order of magnitude. Then this component of TR the recession time can be safely taken as 0 if you consider the graded they are open ended. So if you have open ended furrows which are having some grade you will find that the value of TR the recession time will approach 0. You can safely assume this to be 0 if you have the graded furrows which are open ended furrows. So you are left with the TO previous equation which we had started with, TO is can be approximated to dCO minus TT in this equation this term becomes 0 and left with this part of the equation and we have also seen that this TCO can be obtained from the order of magnitude of TCO can be obtained from this equation which in turn the TCO has also modified to TN minus TN plus TT. This TT is the time the advance time taken to reach for the water to reach the downstream end but you can also find out it depends when you start with either you might be knowing the length of the furrow in some cases you do not know the length of the furrow. So that case you might have to do some trial and error procedure you might have to adopt we will come to that later. Now let us assume that this TT is the advance time with respect to the length of the furrow the water how much time water reaches, what it takes to reach the downstream end of the furrow that is what TT is corresponding to and this TT we have also seen that you can you can predict this TT depending on the this general equation we had written earlier that you can use this relationship to find out what is the value of TT and if I if I put this this term equal to beta I can simplify and write this equation as this. Now this equation we have seen that you are having the there is a function and this is dependent on the family curve and these variables are available the J and F these two variables are available for different family curves. So once you know the family curve once you know the characteristics of the soil you can find out how much will be the advance time with respect to those and here this also incorporates the other characteristics of the furrow was the slope was the stream size. So having known this this general equation this will give you the time for a specific point for a specific section of the furrow. You can also use this general equation to find out what will happen on the average to do that you can take the differential of this difference and that is what is done in another equation which has been written for any segment of the furrow up to a particular length. So if we take that we want to take the average value up to a distance x then you can write this the average infiltration opportunity time this is what is the average infiltration opportunity time up to a distance of this is equal to TCO which is the cut off time minus the advance time the average advance time for this segment. So that is given in the form of this expression f times x times 3 not 5 to beta divided by x this is the total expression which is used for finding out the average infiltration opportunity time for any segment up to any length of the furrow. So if you want to find out the average infiltration time over the total length of the furrow you replace x with replace x with having found this time now let us go to those items what we are interested in is in the design we are interested in some specifics some efficiencies and the amount of wastage which we are incurring. One of the item is to find out those wastages you will have to find out what is the average infiltration which has which has been made available in the stretch of the furrow this can be obtained using the same equation but replacing the time the opportunity time which is the time for the length of the furrow that is what is TOL. So you can use this relationship to find out what will be the average depth of infiltration for the length of the furrow this can also be used for finding out the average depth of infiltration for any length in that case you will have to substitute the appropriate time here up to that distance. Then you are interested in what is the gross depth. Gross depth can be obtained let us call it y g gross depth can either be obtained by if you know what is the net depth and the efficiency. The efficiency to be used is the application efficiency and distribution pattern efficiency but quite in this part the application efficiency for the surface irrigation systems can be approximated to 0 because it is approximated to 100 percent because we are not losing any water from the device when it comes up to the surface we are not losing any water the way we have defined the sufficiency so in other methods the sufficiency might be much less so this will be this can safely be now this is one way of finding out what is the gross requirement provided you know the distribution efficiency the distribution pattern efficiency which is not always known because that you will have to you might have to in evolve a evaluation procedure before you can find out what is the A D or you lose a value which is already found out for that particular area under those conditions this is not necessary that you always know this you can also find out the equivalent gross depth from the other parameters which is the stream size the time of the time of cutoff or for how long we have supplied that water and the spacing between the furrows and the length of the furrow this will the various items y g will be millimeters if q is in liters per second and t c o is in minutes this is in meters and this is in meters so once we have found out the equivalent gross depth of application you are basically now interested in knowing what is the equivalent surface runoff if you call it as d r o depth of runoff surface runoff that will be equal to the gross depth minus the average depth and then you are also interested in another item that how much there is one one form of loss which will be prevalent in the furrows the other form of form of loss is the deep percolation the equivalent depth of deep percolation just call it this is by average minus the net depth of variation so once you can find out these two items you can also find out all the other efficiencies which you are interested in which you have dealt with and that is how you can evaluate a specific system which you have evolved and you can change some of the parameters see how these values change is not always necessary they are also graphical procedures the graphical there are some charts which have been formulated they are available you can directly use those charts and all these charts are based on these relationships so once you use those charts you can arrive at some of the preferable parameters and you can use those parameters to make this let us take one actual data and see that what we will just go through the one example program example data to show you that how you actually perform how you actually use these relationships to arrive at the specific values I will quickly go through this the data given in this you have the data available on what is the family curve it has value of 0.3 then the data on furrows the various data on furrow one is the length length is 275 meters which is the given length available then slope is 0.004 meters per meter the width of the spacing between the furrows is 0.7 meter other the characteristics of the soil are given the form of n value 0.04 and the requirement the net irrigation depth is given as 75 millimeters so that is the requirement and another parameter which is available is the stream size the stream size which is available is 0.6 liters per second so with this data now you want to design the system or at least check the system for the various type of efficiencies and losses which are incurring that if you have this these parameters fixed to these values will be the end result. Now the first thing which you will like to know is that what is the advance time for this family curve and to do that you know the family curve the corresponding values of A, F and G parameters they are known as 0.9246, B is 0.72, C is 0.6.7.0 and F is 7.61 is 1.904 into is power minus 4. Now having known this you can find out what will be the value of Tt for the length of 275 meters and that Tt is comes to 44 minutes. Having known this, this is a parameter which is now available to you with respect to the characteristics of the soil and the ferro characteristics because while evaluating the beta you have used the Q and S also as well as the other parameters of F and G. Then you can find out the adjusted vector parameter, this is B and this adjusted vector parameter is 0.4 meters. You can also find out the net infiltration time Tn you have the relationship for that which is based on the modified infiltration opportunity curve which is we have already written this minus C and this gives the time requirement the net for this net infiltration time to get a depth of Yn you need 999 minutes. Then you can find out the design cutoff time which is Tco which was Tt plus the net time and this is the summation of 999 and the advance time which was found to be 144 minutes. So this is the total design cutoff time that means you should cut off the water only after this time. You can also find out the gross depth from this equation Q is known, Tc0 is known, W is known, L is known and this comes to be 200 millimeters. Now you can see here that with respect to the other parameters the gross depth is way above the net irrigation depth. Net irrigation depth is only 75 millimeters whereas you are required to apply 200 millimeters of depth. So now you can also find out the average infiltration time and we have seen that this relationship we have seen the relationship which is written earlier in this relationship you can substitute the value of X as L and all the other values are known and you can find out what is the average infiltration opportunity time for the whole length and it works out to be 1095 minutes. Now the average infiltration depth can also be found out using this oscillationship and this works out to be 80 millimeters and now having obtained all these different values you can compute what is the surface runoff DRO which is the variation between YG and Y average, YG is 200 millimeters and Y average is 180. So you are losing 122, 120 millimeters of water through the surface runoff. The deep percolation is only 5 millimeters. This is the average infiltration depth and this is the net infiltration depth so on the average you are losing around 5 millimeters of deep percolation. Similarly you can also find out the distribution pattern efficiency which is nothing but YG into 100 which works out to be 37.5 percent only. This these details have given you insight into what is the level of efficiency which you have obtained if you fix these parameters or if you adopt these parameters and how much losses you are incurring in. Basically the efficiency is also dependent on the losses only. So looking at these values you can decide whether it is acceptable to you or not. If it is not acceptable then you can change some of the parameters depending on what is what is within your reach. For example you might not be able to change the grade if you do not want to incur any more money. You might be able to only change the length which is again is not very difficult to take into consideration or the stream size which is again within your your command. You cannot possibly change the soil type. It is not possible once you have a soil type of a known nature it will behave in the same manner, okay. Let us go to the another important feature which has come out from experience and this is technique which is used in the forward irrigation system. It is only a technique of managing the water, the operation during the operation. You use the water in such a manner that you enhance the efficiency and this procedure is called the cutback system. In this system what you do is that you try to choose a high stream size to start with. When we say higher it has to be non-erosive. So you choose a high stream size so that you can wet the whole length of the furrow in some short period and then you reduce the stream size. By doing so it has been found that you enhance the efficiencies. Why it is so? You must have absorbed earlier that we had defined. Let us try to look at the system with respect to the FAR, the fractional advance ratio. If you remember we had given you some values of the FAR table. In the FAR table you must have noticed that the smaller the FAR, the smaller the FAR, the lesser is the amount of losses and when the FAR will be smaller when you are spreading the water throughout the total length in a relatively shorter period which means for the smaller FAR ratio this corresponds to larger inflow rates and when the inflow rates are larger for smaller FAR ratios we have seen that your deparculation losses are also smaller. So you have relatively lesser deparculation losses when you reduce the FAR ratio. That is what has been adopted in this particular cutback system that you try to use a FAR which is very small and you try to wet the whole furrow. Once you have done that then you reduce the stream size and you ensure that the net irrigation requirement is taken care of. So there are some equations which have been modified from the previous equations to account for this cutback system. Let us look at those relationships how they have been changed to account for all this procedure of cutback system but before we do that let us define some additional parameters which are relevant with the cutback system. These parameters are time of cutback which is we can define as Tcb. The equations which we are going to introduce they are with the condition Tcb is equal to time of advanced Tt that you cut back the stream size once the water reaches the downstream end, okay. The other condition is that the final flow, final stream size, the cutback stream size which let me call it Q2 is equal to half the initial stream size which is Q1. So one belongs to conditions, suffix, one belongs to conditions before the cutback and two after. Now the equations which are modified this is the relationship of adjusted wetted parameter. Adjusted wetted parameter is now the condition of perimeter after the cutback is designated as P2 and instead of using Q here we will use Q2 which is the cutback stream size otherwise the equation is same. Similarly the other equation which will need change will be the equation of required net infiltration time which will now will be only differences that adjusted wetted parameter appropriate parameter will have to be introduced. Similarly the average opportunity time for infiltration this parameter will be only the second term the equation which we had written earlier we will pick up the second term of that only and take the this equation. Now at TCO we are not concerned with because that has been taken care of before the cutoff period, okay. We are only concerned with this part which is giving the average infiltration opportunity time after the period after the cutoff that will be only represented by the second component of the second term of the equation which is now can be written as and similarly the equation for average infiltration under cutback conditions which is which will be now transformed to you have two components one before the cutback one after the cutback so this will be the relationship which will give you the average infiltration under cutback condition and similarly the relationship for the gross depth of application will also be modified this Q1 into the time TT plus Q2 will be prevailing during time Tn. So we have taken into consideration the effect of the timing corresponding to the corresponding discharges or stream sizes. Now once you have this particular change in the relationships you can again find out what will be the various quantities and just to show you how much variation it makes taking the same data which we have taken for the previous example, let us find out that if you cutback use the cutback system in a way that you cutback the stream size after 2 half the original stream size after the water has reached the downstream end of the furrow then what will happen? So to do that we know that is equal to the time of advance which was which we have found out in the previous case as 144 minutes. The adjusted vector parameter during the condition before the cutback we had found out to be 0.4 meter that we are calling it as B1 now and you can find out P2, P2 works out to be 0.36 meters this is the adjusted vector parameter after the cutback and similarly you can find out the Tn and Tn is basically will be equal to now is 1,165 minutes. So the time of cutoff works out to be 1,309 minutes. In comparison to the previous case the time of cutoff has increased slightly that means you are supplying water for a longer period but the same time is not at the same rate there is much less in terms of volume. To find out the others quantities the average infiltration time during advance period works out to be 47.6 minutes and the average infiltration correspondingly which you have given expression that it will be independent on plus the other term and this works out to be 80 millimeters which is the same as before but the gross application depth this is 127 millimeters. Earlier we had found out the gross application depth as 200 millimeters so this is drastically reduced and thereby the surface runoff which is dRO is only 47 millimeters instead of 120 millimeters of the previous case. The deep percolation has also reduced the deep percolation was the quite minimum has not reduced is the same. The major difference has been made by the surface runoff component and with the result the distribution pattern efficiency now will be 75 127 into 100. So this is increased considerably in the earlier case we had around 36 percent or so now we have 59 percent distribution pattern efficiency. So you can see that by just everything else is same by just changing the way you apply the water. By introducing a procedure by which you can reduce the supply the first steam size which has been used that has ensured that the whole surface is wet and if you keep the same steam size then you are wasting a lot of water through the surface runoff because the infiltration rates keep on reducing as we have seen the infiltration capacity curve show that the infiltration rates they reduce with time. So to account for that and to take advantage of that the system of cutback is very beneficial in the case of porous systems. Any questions? So we will stop there today.