 I am Dr. Satish Kumar Kashi, Professor Department of Civil Engineering, Valshan Institute of Technology presenting a topic, application of finite hydrograph for deriving a direct runoff hydrograph using Vinnit hydrograph. Learning outcome of this session? At end of this session, students will be able to derive direct runoff hydrograph using Vinnit hydrograph of given duration. Before going to this, let us discuss the assumptions of Vinnit hydrograph theory. The Vinnit hydrograph method is based on the assumption of a linear relationship between the rainfall axis and the direct runoff rates. More specifically, the method assumes that, number one, the base time of direct runoff hydrograph resulting from a rainfall axis of a given duration is constant, regardless of the amount of rainfall axis. And second is, the ordinates of direct runoff hydrographs resulting from a rainfall axis of a given duration are directly proportional to the total amount of rainfall axis. Also, in other words, we can say the base of direct runoff hydrograph resulting from a rainfall axis of say 1.5 centimeter rainfall produced over 2 hour duration is same as that of 2 hour Vinnit hydrograph. And also, the ordinates of this direct runoff hydrograph for 1.5 times the ordinates of the Vinnit hydrograph to our duration at respect to times. So, we can simply state that direct runoff hydrograph ordinates will be c times Vinnit hydrograph of 2 hours. So, for example, suppose the 1.5 centimeter is rainfall axis, so this ordinates to be multiplied by 1.5. A small question ordinates of direct runoff hydrograph produced by a 4.5 centimeter rainfall axis will be option 1 equal to ordinates of Vinnit hydrograph equal to 2 times ordinates of Vinnit hydrograph equal to 4.5 times ordinates of Vinnit hydrograph equal to half of the ordinates of Vinnit hydrograph. And answer is obvious, it will be equal to 4.5 times ordinates of Vinnit hydrograph as we have seen in this particular formula, right. Now, here we will see one example, say this is a time 0, 3, 6, 9, 12, 15, 18 hours and we have ordinates of 6 hour unit hydrograph with us. ordinates are in meter cube per second, they are 0, 25 meter cube per second, 50 meter cube per second, 85 meter cube per second and so on. It means we have a certain catchment over which a 6 hour storm takes place with 1 centimeter rainfall axis and in that case this produces the hydrograph with these values. Now, question is if on the same catchment rainfall axis in the same period of 6 hours is 3.5 centimeters, it means it is 3.5 times 1 centimeter rainfall axis. So what will be the ordinates? So obviously every ordinate according to unit hydrograph theory will be multiplied by rainfall axis of 3.5 centimeter, so this will be 0 into 3.5, 0, 25 into 3.5 is 87.5, 50 into 3.5 is 175 and so on. So this particular column gives you the values which are multiplied by 3.5 to the hydrographs ordinates of a Vinnit hydrograph of 6 hours. Now, same thing can be shown graphically, here this is time and this time is shown on the x axis, then the ordinates of Vinnit hydrograph, 6 hour Vinnit hydrograph are shown with reference to this time here. So these are the ordinates of 6 hour Vinnit hydrograph and these ordinates are result of a 6 hour rainfall event with 1 centimeter rainfall axis, this is due to 1 centimeter rainfall axis. But in the same duration of 6 hours if 3.5 centimeter rainfall axis occurs, then according to unit hydrograph theory these ordinates are to be multiplied by 3.5, ordinate at 6 hours multiplied by 3.5, ordinate at 12 hours multiplied by 3.5 and so on which we have done here, every ordinate multiplied by this. So this graphs gives you the idea, this is the period of rainfall, this is the base of the unit hydrograph and this is the direct of hydrograph resulting from 3.5 centimeter rainfall axis. So in this way you need to add those, the example to 2 storms each of 6 hour duration having rainfall axis values 3 centimeter and 2 centimeter respectively occur successively. The 2 centimeter a rain follows 3 centimeter rain, the 6 hour unit hydrograph of the catch point is same as given in previous example calculate resulting direct of hydrograph. Now here this is the first part ordinates of 6 hour unit hydrograph, these are the ordinates due to 3 hour rainfall axis and these are the ordinates due to 2 centimeter direct run of hydrograph lag by 6 hours. So this is the first page and then the time is continued from here that is after 18 hours 24, 60, 36, 42, 48. So this is the contribution from 3 centimeter rainfall axis, third column here and this is contribution from 2 centimeter rainfall axis in this way. These things are added further and ultimately we get the result of these 2 storms in this way. So if you see the things graphically we find a is the direct runoff due to first period of 3 centimeter axis rainfall, b is direct runoff due to 2 centimeter rainfall axis. This is second spell is starting at 6, first spell is starting at 0. So we will be adding these 2 ordinates to get the composite direct runoff hydrograph due to 3 centimeter rainfall axis for 4, 6 hours and 2 centimeter rainfall axis for 12 hours. Now I have developed one Excel tool to understand this. So here you can find this is one some different example just see for hours 0 to 1, 2 centimeter rainfall axis for there for our 1 to 2, 2.5 centimeter rainfall axis for there for our 2 to 3, 3 centimeter rainfall axis was there. So these are recorded here this spell, this spell I have recorded here 2.5 centimeter rainfall axis and this spell I have recorded here. Time in hours we are you dealing with the 1 hour unit hydrograph. So these are the unit hydrograph ordinates. So due to 2 centimeter rainfall axis you will get these ordinates due to 2.5 centimeter rainfall axis we will get these ordinates which are multiplied by 2.5 to the unit hydrograph. This 3 centimeter rainfall axis in third spell starts from here and we get this. So these are the subtotals here and when we add a base blue to this ultimately we get this direct runoff hydrograph. So here I have shown a graph also in Excel. So in Excel all these times are shown in this way. The unit hydrograph and then the first spell, the second spell and the third spell. What are calculations we do in Excel those are giving those are reflected in these graphs and ultimately this is the sum of all the ordinates including the base flows given you the output. So this Excel tool explained development of direct runoff hydrograph using Ginnit hydrograph. These are my references thank you.