 I am Assistant Professor in WIT, Swalapur. Today, we are going to learn about dissolved oxygen in the streams and its analysis. At the end of this session, students will be able to understand the analysis of DO in the streams. We are taking one example to understand the analysis of DO. Here, a stream is given, which is saturated with DO, having its flow of 1.2 meter cube per second. It is also having a DOD of 4 mg per liter and a rate constant of 0.3 per day. It receives an effluent discharge of 0.25 meter cube per second, having its DOD of 20 mg per liter and DO of 5 mg per liter and also having a rate constant of 0.13 per day. OK, average velocity of flow of a stream is 0.18 meter per second. Now, it has been asked that to calculate the DO deficit at a point 20 kilometer and 40 kilometer downstream. Assume that the temperature is 20 degrees Celsius throughout and a BOD is measured at 5 days. And it is also given a saturation DO at 20 degrees as 9.17 mg per liter. So, let us dissolute that question in a simplified way. Fine? It is a stream which is flowing and an effluent discharge is added in that stream. What will happen? The DO will be taken down to the stream and it will be dissolved and it will be decreased with respect to the distance and time. And while the adding, all its parameters are given. That is effluent parameters are given. That is our discharge, that is QE, which is equal to 0.25 meter cube per second, BOD, YE, 20 mg per liter, DOE, 5 mg per liter and rate constant of 0.13 per day. Stream parameters are also given. That is our QS, which is equal to 1.2 meter cube per second, BOD, that is YS, which is equal to 4 mg per liter, saturation DO, that is 9.17 mg per liter and rate constant. That is our re-aeration rate constant. That's why it is written as R, capital R, which is given as 0.3 per day. And here also, here it is written as K, that is deoxygenation constant. So, the DO is going to decrease. Here the DO is going to increase. So, both these constants are very much different. Fine? And it has been asked to calculate what is the DO difference at 20 kilometer and 40 kilometer. Fine? After the analysis, we are arising for few questions. Okay? So, let us have few questions on it. With the increase in temperature, DO will increase as in the question 20 degree Celsius is given. Then why it is given? And what will happen if we increase that temperature or decrease that temperature? Or what is the relation between temperature and DO for that? And the second question is DO deficit. That is our oxygen deficit will be maximum when? So, what are its answers? When we increase the temperature, the DO will decrease. So, this sentence becomes false. And the rate at which the oxygen deficit is maximum, it will happen when R is always equal to K. Fine? At that point only, the DO difference will be maximum. So, let us analyze by taking few steps to solve that question. So, what is our first step? First, we will calculate the ultimate BOD of mixture in the downstream. What does it mean? When we add the stream, which is having the higher BOD and the lesser DO to the stream, which is having the lesser BOD and higher DO, what will happen at that point? What will happen to the BOD at that point? Okay? So, it is calculated as QS into YS plus QE plus YE divided by QS plus QE. So, what are these? These are discharge multiplied by BOD of the stream plus discharge of effluent into BOD of effluent of the stream divided by the summation of the discharge of stream plus discharge of effluent. So, by putting these values, we will be getting a value as 6.759 mg per liter. Now, it is the BOD which is calculated after five days as in the question, they have been given that the BOD, which these quantities are these YE and YS are representing, they are BOD five. Okay? They are not ultimate BOD. So, how we can calculate the ultimate BOD? First, find the BOD five of the mixture, then the ultimate BOD of mixture, which is having the formula of Y5 is equal to L naught in bracket one minus 10 raise to minus KD. Here K is deoxygenation constant, fine? So, the BOD five, that is, which we had calculated here is 6.759 is equal to L naught, which that is our ultimate BOD in bracket one minus 10 raise to minus 0.13 multiplied by five. Why here we are taking five because we had calculated the BOD for the days of five. So, that's why we are taking five. So, by these calculations, we will be getting L naught is equal to 8.71 mg per liter. So, that is our ultimate BOD. What is the second step? Second step is, find the initial DO deficit of the mixture. We are calculating the initial DO deficit at the point where the stream is getting added by the effluent. So, how it is calculated? The formula will be remaining the same, but instead of BOD, we are taking DO, fine? Putting these values into these formulas, we will be getting the value of 8.45 mg per liter, fine? Now, we will calculate the initial DO deficit of mixture, fine? As we have the formula, initial DO deficit as saturation DO of stream minus initial DO of mix. By putting these values, that is saturation DO, which is given to us, that is 9.17 minus 8.45, which we are calculated here. By putting this into here, we will be getting the initial DO deficit and it is coming to be 0.72 mg per liter. Now, what is the third step? We will be calculating the DO difference at a point 20 kilometer downstream. Here, we have to first calculate the time as we know the distance and the velocity of stream is also given to us, okay? By this, we can calculate the time. We will be first converting this 20 kilometer into the meters by multiplying thousand and the velocity into days, okay? It is given in mg per second. We will be converting this second into days, okay? How we can do that? By multiplying 360 into 24, okay? It is hours and it is in one hour, okay? But that we can convert this second into day, fine? By these calculations, we will be getting the time in days, fine? Now, we will calculate the DO deficit at a point 20 kilometer downstream. How we can do that? We can use the Streeter-Felps equation. So, this is the equation, okay? Here, dt is the DO deficit at that particular point after that time, okay? What is min by t? Here, t is our time. After that time, what is the DO difference? What is the formula? It is the deoxygenation coefficient multiplied by ultimate BOD, which we had calculated earlier in the first step, divided by R, that is reoxygenation constant, minus K, that is deoxygenation constant, multiplied by in the box, 10 raise to minus KT, minus 10 raise to minus RT. Here, small t is representing our time, fine? Plus D naught, that is initial DO difference, okay? Of the mix, multiplied by 10 raise to minus RT. By putting all this formula here, we will be getting the DO deficit at that particular time. Ultimately, it is indirectly representing the DO deficit at that distance, fine? So, we are getting 2.089 mg per liter, okay? Fine? So, this is the DO difference at the 20 kilometer downstream. Now, what is the fourth step? We had also told to calculate the DO difference at 40 kilometer. Same steps will be there. First, we will calculate time. Here, what will change? The velocity will not change because stream velocity from the start to end is constant. Okay, the stream is flowing at the same velocity. So, the velocity is not going to change, but the distance will change. Fine? And again, by calculating this part, we will be getting the time as 2.572 days. And again, using the Streeter-Felps equation, thus, we will be getting the value of DO deficit. Here, what is going to change? Only the small t is going to change because reoxygenation constant is the same, okay? And deoxygenation constant is also going to be the same. And ultimate BOD is not going to change because it is never going to be changing, fine? By that, we can calculate the DO deficit at that time. What is here? The time is 2.572 days. By putting these values, we will be getting the DO deficit as 2.079. What you are going to analyze that the DO deficit is not too much varying. Here, the DO deficit is coming to be 2.079 mg per liter. And in the earlier step, the DO deficit is coming to be 0.089 mg per liter. So the difference is very much less. So what it is showing to us, how we can understand these values, okay? We can understand by taking few questions by that. Here, with the increase in the distance, the DO deficit is going to increase, decrease, or remains constant or none of the above. By analyzing the third and fourth step, we can say with the increase in the distance, the DO deficit is not too much varying. It is not too much changing. So it is becoming constant. It is not going to change. That's why the C is the answer. That is, it will remain constant. So these are the reference I have used. Thank you.