 Welcome to this lecture number 16 in which the topics covered are well flow for special conditions followed by partially penetrating wells, it will be followed by horizontal wells and collector wells and lastly the lecture will end with multiple well systems. Now we will start with the first topic of this lecture that is well flow for special conditions. So in this topic, so the depending upon the three parameters that is upon aquifer, well and pumping conditions, so different types of well flows can be observed and again, so this is as you see, so this aquifer well as well as pumping conditions, so these are three such vital parameters, so which may make the things quite intensive and quite complicated. So therefore, we will not be able to focus very much into these parameters. So at least so here, so the but researchers have obtained solutions for the problems consisting of different aquifer conditions, different well conditions as well as different pumping conditions for the following special situations or circumstances. That is, solutions have been obtained by various researchers for the following situations involving any or all of the above three conditions. So these three conditions means the aquifer conditions, the well conditions as well as the pumping conditions. So based on this for different situations, so the which are listed here, so the solutions have been obtained by various researchers. So these different situations are listed here, the first one is the constant well discharge and we already have discussed many of these constant well discharge situations and this is followed by varying stroke cyclic stroke intermittent discharge situations and next we will go to the next situation is sloping aquifers or sloping aquifer situations followed by variable thickness aquifer situations followed by two layered aquifer situations followed by an isotropic aquifer situations followed by aquifer conditions, aquifer situations rather aquifer situations varying with depth. So next it is, so these are corresponding to the aquifer conditions, then the well that is the large diameter wells, large diameter wells situations followed by collector well situations followed by wells with multiple sectioned well screens, sectioned well screen situations etcetera. So here we should not restrict, we should not be under the impression that, so these are the only ten situations which we may encounter, after all it is groundwater which is the subsurface water and then so the situation may depend upon the various this one, it may depend upon the various aquifer conditions or well condition or pumping conditions or combination of any of these three. So therefore, so these are the ten major situations which the researchers have considered and then obtained solutions. So these solutions are fully analytical solutions, they are analytical come field or experimental solutions or it is fully experimental solutions or combination of others. So this is actually, this is how well flow for special conditions involving the either aquifer or well or different kind of pumping conditions is handled. With this we will go to the next topic of this lecture that is partially penetrating wells. So here we should note that some of the wells do not penetrate for the entire thickness of the aquifer. So here such wells are known as partially penetrating wells. So the wells which do not or rather which are not dug or say drilled till the bottom confining layer of the aquifer are called partially penetrating wells. They are very simple and straight forward concept. So in case of this partially penetrating wells, unlike the fully penetrating well wherein, so there is radially inward flow all along the all around the circumference of the well. So whereas in case of this partially penetrating wells the flow is even more slightly, I should say slightly more complicated in the sense. So there is flow not only through the inner surface of the inner cylindrical surface of the well but also through the bottom that horizontal surface of the well or say the bottom of the well. Therefore, in this case unlike the fully penetrating wells wherein we assume that the stream lines the flow is radially inward and in the horizontal direction of course there has to be some slope but for simplicity we do assume that the flow is horizontal radially inwards and horizontal whereas in this case so the especially on the bottom the flow will be in the upward inclined direction whereas in the in case of the through the sides that is the cylindrical curve this inward surface of the partially penetrating well the flow will be generally or mildly sloping horizontal as well as radially inward flow and so the following sketch will represent these three is one. So let us say this is a let us consider for simplicity one water table aquifer so sticking to the convention of green for water table so this is water table and then there is this ground level and in this case let me show a fully penetrating well as well as a partially penetrating well. So this is the bottom confining layer and here in this case let us say so this is a fully penetrating well of course say this there will be an opening here obviously and there is also another well which is partially penetrating. Let us say it just is dug only up to say this much fraction and then below this even though it is an aquifer so this is a unconfined aquifer and then similarly so this is here so this is a fully penetrating well in an unconfined aquifer whereas this is partially penetrating well in an unconfined aquifer let me show here with the break line so in this case now let us say suppose these are the flow lines into this fully penetrating well which are almost horizontal whereas in case of this partially penetrating well so of course here also for the through the cylindrical surface the flow lines are radially inward and almost horizontal whereas through the bottom also there will be some ground water and in this case so this is the both are this discharging wells which is represented by this q, later q. So here so therefore we do get the upward flow or in the inclined direction inclined upward flow through the bottom of this partially penetrating well so here so we can write down so this is a ground water contribution only through cylindrical side surface of the well whereas in this case GW stands for ground water, ground water contribution through that is side cylindrical surface and that is the bottom surface of the well so through the side cylindrical surface it will be mostly radially inward and mostly horizontal flow whereas through the bottom it is an upward inclined flow so therefore so here we can denote this as so this is in case of an unconfined aquifer. Now let us also consider a confined aquifer a partially penetrating well in a confined aquifer partially penetrating well in a confined aquifer of course it is not much different from partially penetrating well in an unconfined aquifer only thing is so in case of confined aquifer so it is the flow takes place under pressure and suppose this is the say this is the ground level and then this is the water table and let us also consider say suppose this is the bottom confining layer of the confined aquifer and then say let us say this is the top confining layer and say let us say this is the so this is the equiclude or the impervious layer which distinguishes this unconfined aquifer which is at the top and the confined aquifer so this is the unconfined aquifer and this is the confined aquifer and in this case so the so this is the original water table or piezometric surface original piezometric surface denoted by this letter wt and then so here with this full had the well been fully penetrating may be let me show it here so this is the original piezometric surface so this is also the same original piezometric surface let me abbreviate this as OPS and here this is original piezometric surface and this is a fully penetrating well this is the partially penetrating well and in this case this is a and here we have so this is a fully penetrating well in a confined aquifer and obviously so this is the the central line of the well partially penetrating well this is the central line of the fully penetrating well and so these are the so this is the both are discharging wells and in this case so what will happen is in case of a full for full penetration so the drawdown curve will be somewhat like this whereas for the same this one the drawdown curve for partially penetrating well in the same confined aquifer I am sorry so I am sorry I use the wrong color this one so whereas in case of this partially penetrating well the this one the drawdown in this case if you denote this drawdown by the letter sp representing the drawdown for partially penetrating well and whereas in this case so the drawdown for fully penetrating well in this case we can write down the relationship that is sp that is the drawdown is greater than s and so in the in case of this one so the stream lines will be like this whereas in case of fully penetrating well so obviously the stream lines are almost horizontal and radially inwards like this so in case of partially penetrating well so the drawdown so this is a higher drawdown as compared to a fully penetrating well okay so this is a drawdown slightly lower so this is the higher drawdown for partially penetrating well and drawdown slightly lower so this is for fully penetrating well okay and here so like this so the area of the circle of influence they all may be more or less the same but only thing is in case of partially penetrating well so the drawdown will be more for the simple reason that the area which is absorbed which is drawing water is more because this area which draws water is the not only the cylindrical curved surface but also the bottom surface of the well which in most of the cases is horizontal so therefore since the area is more so then obviously the amount of water extract is also more and then so therefore the drawdown in case of partially penetrating well is more so with this we will complete the second topic of today's lecture and today we will go to and then this next we will go to the third topic which is on horizontal wells and collector wells and here so these horizontal wells play a very major role in especially in providing the large amount of ground water that is required generally in case of municipal water supply schemes so here so for the simple reason that the horizontal wells so they are basically there the flow into the well is along the axis of the horizontal well whereas in case of this vertical penetrating wells the flow is perpendicular to the well axis the ground water flow is perpendicular to the well axis whereas in case of horizontal of this one the horizontal wells so the actual flow is perpendicular to the horizontal well axis but the combined flow is along the horizontal well axis so here so therefore they play a very vital role in providing the adequate ground water supply so here horizontal wells play a vital role in providing the required large volume of ground water especially in case of municipal water supply schemes so here this and then of course there is infiltration galleries are type of this one so this is infiltration galleries and collector wells are also some form of horizontal wells and in this case suppose this is the horizontal well and then followed by in this case there is a water table so here this is the water table and here this is the aquifer the here so this is the impervious layer so this is the impervious layer so this is the aquifer is here so here also this is aquifer and then this is the horizontal well so this is the and here this is the seepage area or say which is also generally referred to as simply seepage area and this is the water table and here we can say so this is the the break line I am showing here so this is one this one wherein the formation of this at the ground water layers is almost in the horizontal direction so it can also be in the whereas this ground water this rocky formations geological formations may be mostly in the vertical direction also in such case so the horizontal well will be somewhat different in this case let us say this is a say this is an impervious layer here say this is the and then the here this is the aquifer and here let us say this is the water table so in this case the general formation of the geological formation direction is in the vertical this one so again here also we can show a horizontal well which will be so this is horizontal well so this is a horizontal well in an area with almost horizontal geological formations similarly this is a horizontal well so this is here this is the horizontal well in an area having almost vertical geological formations or geolayers so so this horizontal wells as you can see so depending upon the in this case obviously the the area that is a seep area is much more and so therefore because the gradient in this case is quite less as compared to vertical wells so therefore the the Darcy's law will be more applicable and then obviously that is the reason why the the output by this horizontal wells is much more than a regular vertical well and let me also bring it to the notice of what are known as the collector wells so this collector wells is well which consists of a number of a radially symmetrical horizontal wells which join a well which is generally for so now let us consider the collector well in this case say this is suppose this is the the top view and here this is the of course here if you want to you can be a brake line so this is the pumping unit so through which the water is pumped so this is the sectional view sectional front view and so these are so that is horizontal wells horizontal well components of a collector well so this is the sectional front view and then the same thing let us draw the the top view so in the top view so it will be here this will be so all this they are radially emanating so here we can show the the axis so there can be any number of this radial horizontal well horizontal wells which together constitute what is known as a collector well so in this case so this is the top view of this collector well and so here so this is and this is horizontal well components which are generally so this is they are referred to as screen pipes and so together so it will form a collective well so this is here this is the so this is the clear water well and obviously so this is the clear water well and so this is a collector well which is may which is basically a combination of a number of horizontal wells generally located at the same level and so here we can say this is so this is section so this is a sectional top view of a collector well so these so here they play a very vital role in ensuring adequate ground water supply generally in municipal water supply schemes so now we will go to so this completes a third topic and the last topic of today's lecture is on multiple well systems as a name itself says so there are number of wells which are involved in this multiple well system and here so so this is a multiple well system as a name itself it is self explanatory so there are a number of this wells which consists this multiple well system and here so this is a let us consider so this is here we can write down so when cones of depression in nearby pumping well pumping wells overlap with one another they constitute a multiple well system so basically a multiple well system has nearby wells and then so these wells each one of them will have a cone of influence cone of depression and then these cone of depressions of these nearby wells so they will overlap with one another so let us show with this one that is a multiple well system with say three wells where in the cone of depression cone of depressions of each of these wells is overlapping this case let us say this is the suppose these are the three wells let us consider that these this is the common bottom impervious layer and each of these wells are discharging wells so this is Q1 this is Q2 and then this is say Q3 and each of them let us say the suppose this is the cone of depression for this well and so there will be another cone of depression for the other then similarly the third cone of depression for the so a resultant cone of depression will be something like this so this is the resultant that is composite drawdown curve curve for all three wells so this is these are the individual drawdown curves for each of the wells and then so this is the resultant so like this so this multiple well systems we have will stop at this and in the next lecture we will discuss the further topics thank you.