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Video 1
Hello everyone in the previous lecture we discussed Transient flows through horizontal and vertical columns or the transient flows without the influence of elevation head and with the influence of elevation head we have considered and we got analytical solutions. These equations are called Green and Ampt equations. This is given by the two gentlemen Green and Ampt in 1911 very old literature.This particular equations this is for the horizontal flow the x by the square root of time is = square root of 2 ks times h o - hi by Θ o - Θ s. Here Θ o or Θ s. So, here x is the spatial distance and t is a time and ks is the saturated hydraulic conductivity of the soil h o is thepositive head you maintain it could be 0 or more than 0. And h i is initial head and Θ s is saturated volumetric water content and Θ i is initial volumetric water content. Similarly, for the vertical flows, we have this expression instead of x you will have the independent variables z here this expression is implicit and you can obtain for a giventime what is wetting front location in the vertical direction can be obtained using this particular equation. Here the z is assumed to be positive upward. So, when there is an infiltration against the gravity that is taking place then we have used positive value for zand this is an expression for this. Again once again I remind you that these expressions are derived in 1911. So, when the computation was nearly a very costly and during that time the analytical expressions for the transient flows were derived. This expressions can be used for the coarse-grained soils, but not applicable for fine-grained soils because sharp wetting front generally you do not find for most of the soils, but that approximation is can be born for coarse-grained soils; for some coarse-grained soils. Interestingly capillary rise in soils has been studied slight little earlier by Buckingham in his classical work on studies on the movement of soil moisture which is published in 1907 very old work which is a classical work in soil science literature. In this particular work here done to establish the rate of capillary rise, he found the capillary rise data with time for several soils. The experiment involves somewhat like this; this figure is not from this work this is setup from our lab at IITG. And you will have a soil column it could be a sand column in this case and you have a reservoir, water reservoir these two are connected through these pipes.So, you have a water table maintain at a particular level. So, this is the water table that is maintained which can be read on the scale. So, when the water table level in the reservoir is this at equilibrium the water table level in the soil also is expected to be here somewhere here. So, this is the water table and z is measured upward positive from here onwards and here you can see the capillary rise that is taking place and capillary fringe you can be seen the fringe the way the water moves in the sand which is called a capillary fringe you can be seen here. So, the rate at which the movement of water takes place within the soil mass wasobtained for different soils where are the porosity values for different and all compassion densities could be different, therefore, the porosity varies or the saturated hydraulic conductivity varies than at equilibrium what is a maximum a capillary height that was achieved, that was found which is indicated with h c capillary height. So, for these three different values, for example, the capillary height values for different soils were correlated this capillary height correlated with different soil pore size distribution parameters by several researchers afterwards also, for example, several works in later on were conducted by lane and wash burn. This is in 1946 he establishedrelationship between h c and detain of soil h c measured in millimetre and here - 990 log d 10 - 1540. This is one im-prickle equation he derived by conducting experiments on several soils and here detain is also substituted in mm. So, h c was predicted using such empirical equations. So, this is one such empirical equation, another empirical equation given by peck et al this is in 1974. So, here the h c is = c by e D 10. Here D 10 is substitute in mm and c s units of mm square and h c has units of mm, e is a void ratio and c generally it varies between 10 to 50 mm square. So, such empirical correlations are available for predicting the capillary rise or capillaryheight for different coarse-grained soils generally, because for fine-grained soils it takes enormous time to reach equilibrium and the height will be very significantly high.
Video 2