 Hi friends, my name is Mahirubali, I am the Assistant Professor of the Department of Civil Engineering, WIT, Saulapur. In the first discussions, we have done the theory of settling of discrete particles. Today, we are going to discuss about the problems on settling of discrete particles. The learning outcome at the end of this session, students will be able to solve the questions on settling velocity of discrete particles in sedimentation time. Let's have a quick revision on the formulas. Now, the terminal settling velocity that is vs can be solved by two laws. The first we have seen is Newton's law. That is, vs is equal to the root of 4G bracket, specific gravity that is as small as minus 1 into D, that is diameter of particle, divided by Cd into 3. The second law we have seen for the discrete particles of spears. Now, its formula is vs is equal to 1 by 18 multiplied by G by nu multiplied by as small as minus 1 D square. We have also seen for the different temperatures, we have different settling velocity formulas. At the standard 10 degree Celsius temperature, we have vs is equal to 418 s small s minus 1 D square. And for the other temperature, different than 10 degree Celsius, we have vs is equal to 418 s small s minus 1 D square multiplied by 3T plus 70 divided by 100. Here, the small t is the temperature. Let's have the first question. The question is, a settling tank is designed for an overflow rate of 4000 liters per meter square per hour. What temperature of diameter 0.05 mm and 0.02 mm will be removed in this tank at 10 degree Celsius? It has been asked that for the discrete particles of diameter 0.05 mm and 0.02 mm can be settled down, or if they can settle down, then what is its percentage? Now, how we can solve it? Now, we know that the overflow rate that is Q by A is given as 4000 liters per hour. That is, small vs is equal to Q by A. Here, the Q that is our overflow rate is given in liters per hour. So, as per the standard format, we have to convert it to meter cube per second. How we can do that? You have to first convert liters to meter cube. That is, by multiplying the 10 raise to minus 3, we can convert the liters to meter cube. Now, the hours can be converted to seconds by multiplying 60 by 60. That is 60 minutes multiplied by 60 seconds. Here, the area that is our surface area has been given indirectly. If you see the overflow rate, overflow rate has been given that 4000 liters per meter square per hour. Here, the per meter square means surface area has been given 1 meter square. So, we have to get that our area is 1 meter square. So, now we know Q and we also know the surface area that is our A. So, from that, we can find the vs that is our terminal settling velocity. By putting Q and A into the formula of settling velocity that is vs is equal to Q by A, we will get 4000 multiplied by 10 raise to minus 3 divided by 1 that is our area. That is 1 meter square multiplied by 3600 seconds. So, now it is in meter minute per second. So, we have to convert it to centimeter per second. So, by multiplying 100, we will get in the form of centimeter per second. So, finally, we will get answer vs is equal to 0.111 centimeter per second. We know the Q and A here has been given in the question only. So, vs is the given vs in another way we can see it. So, this 0.111 centimeter per second is the given vs. Now, let's see the particles of diameter 0.05 mm. Here, the specific gravity of particle is not given. So, we have to assume that specific gravity of particle to be 2.65. It is typically normal at the temperature of 10 degrees Celsius and as per the standards of discrete particles, it is always assumed to be 2.65. So, if in the question specific gravity is not given, you always have to assume a specific gravity of particle to be 2.65. So, here we assume as small as to be 2.65. So, from the Stokes law at 10 degrees Celsius that is our normal formula at 10 degrees Celsius, which is vs is equal to 418 small s minus 1 d square. So, putting the value of ss and the diameter of particle that is 0.05, we will get the answer in mm per second. So, our answer will be 1.72 millimeters per second. But we have to get the answer in cm per second as the given vs is also in cm per second. So, we can write the 1.72 mm per second to be 0.172 cm per second. So, you have to divide by 10 to get convert from mm per second to cm per second. So, in this way we will get 2 vs. One will be the given vs that is 0.111 cm per second and the second will be from the Stokes law that is 0.172 cm per second. So, now the percentage settled particles will be the calculated vs, the calculated settling velocity from Stokes law divided by the given vs multiplied by 100. So, how we can write it? The percentage settled particles will be 172 divided by 0.111 multiplied by 100. So, it will come up to be 154.95 percentage. Here it is greater than 100. It means every particle which is having the diameter of 0.05 mm will get settled fully. For the second diameter that is 0.02 mm particles same with the same equation we can find out the settling velocity. We know the specific gravity of particle which is 2.65 and the given diameter that is 0.02 mm. By putting in the formula we will get a settling velocity to be 0.0276 cm per second. In the similar fashion we will get the percentage settled which is coming up to be 24.86%. So, here it is not greater than 100. It means the only 24.86% of the 0.02 mm particles will get settled down and remaining will flow from the settling tank. Now, let's have another question. The question is, find the diameter of particles with a specific gravity of 1.2 removed in the tank having a surface area of 250 m2 and treating 8 million liters of water per day. Assume temperature to be 26 degrees centigrade. Here you can find overflow rate as we have found out earlier. So, it will come up to be 1.33 m3 per m2 per hour. From which we can also find the settling velocity that is Vs from the previous question. From that, we will get the settling velocity to be 0.037 cm per second. But this settling velocity will be the given settling velocity. We have found out from the overflow rate which has been given to us. We had not calculated by appropriate equations. Now, what they want us is the diameter of particles which will get settled. For that, they have also given temperature different than 10 degree centigrade. So, by applying the formula for the different temperature, we will get Vs. So, by putting the formula of 418Ss-1d2 multiplied by 3t plus 70 by 100. Here, we know SS, we know the temperature, also know the settling velocity which is given to us. So, from that, we will get the diameter of particles. So, in this way, we can find out the diameter of particles which is going to be settled. It also means the diameter which is lesser than 0.019 mm is always going to settle. The diameter which is more than 0.19 mm will not settle 100%. It may settle lesser than 100% but it will not settle fully 100%. Now, we will have some questions. These are the two questions which you have to solve. So, just pause the discussion, solve both the questions. Then you will again unpause that and so that you will get the right answers. So, this is the answer for the first question. The hint is you have to use the formula for different temperature. And this is the solution for the second question. So, just check it if you are not getting it. Please revise the video and think again so that you will get to know how to solve every question. So, this discussion I have used two references. Thank you.