 Assistant Professor, Department of Civil Engineering, W.A.T. Solapur. Topic for today's session, Determination of Velocity of Flow through Sewer Line. Learning outcome of this session, student will be able to determine the velocity of flow through Sewer Line. Following are the empirical formula, which are used to determine the velocity of flow. Chages formula, cutters formula, basins formula, manning formula, crimp and brugs formula, hazen and willions formula. See first, Chages formula. Chages gave a formula, velocity is equal to C under root of R s, where V is the velocity of flow in meter per second. S is the slope of Sewer or hydraulic gradient. R is a hydraulic mean radius. It is in meter. Compute R by formula, area upon perimeter, keep area in meter square and where C is the Chages constant. Cutters formula, cutters give the empirical formula for Chages constant. This is a formula for Chages constant and in this formula, there is S and R. S as usual, it is a gradient of Sewer line and R is the hydraulic mean radius. And the new term is N. Here, N is the rugosity coefficient. The table 1 gives us the rugosity coefficient. It is also called as Manning's coefficient. The N is depend on the roughness or smoothness of the inner surface. In the table, there is a list of various material and the condition of that material, whether it is in good condition or fair condition. Accordingly, there is a value of N. So, for value of N, you refer table number 1. Number 3, Besin's formula. C is equal to 157.6 divided by 1 plus 81 plus K upon under root of R. This is Besin's formula. Besin's also gave us Chages constant C, where K is the Besin's constant and in table 2, a chart for K. Here, again, there is a type of surface, various type of surface and this is a guideline for the value of K. Number 4, Manning's formula. It is Manning's gave us formula for velocity. Velocity is equal to 1 by N, R to the power 2 by 3 into S to the power 1 by 2, where R is the hydraulic mean radius and S is the slope of the sewer, same as Chages formula. And N is the rugosity coefficient that is nothing but the, we have seen in table number 1. You refer table 1 for this value. Number 5, empirical formula is Crimp and Brog's formula. V is equal to 83.47 into R to the power 2 by 3 into S to the power 1 by 3. It is similar to Manning's formula if the value of 1 by N is equal to 83.47. It is similar to Manning's formula. There's a little difference in formula given by Hussins and Williams formula is V is equal to 0.85 into C, R to the power 0.63 into S to the power 0.54. Here, there's a new parameter C. C is the Hussins and Williams coefficient and in table 3, the value of Hussins and Williams coefficient C is given. You refer the formula. There are various types of material with respect to that material, there's a value of C. Take one example. In this example, a siever of 0.6 meter diameter laid at a gradient of 1 in 400 runs full using Crimp and Brog's formula, determine velocity of flow and the discharge. So, Crimp's and Brog's formula is 83.47 into R to the power 2 by 3 into S to the power 1 by 2. So, let us find first R. R is the hydraulic mean radius and it is calculated by area by perimeter. So, what area we have to consider? It is given that that siever having diameter means it is circular in section and it runs full. So, area of the siever is pi D square by 4 and perimeter is 2 pi R that is pi D. So as it is area and perimeter we consider because it runs full. So, R is equal to A by P put A and P in the formula, it will come D by 4. So, R is D by 4. So, calculate it, D by 4 comes 0.15 meter, put R and S in the formula of velocity, V is equal to 1.178 meter per second. Now calculate discharge. Discharge is equal to area into velocity. Here the siever runs full. So, consider whole area that is pi D square by 4 and into velocity that we have 1.178. So, discharge is equal to 0.333 meter cube per second. Also, you can calculate it in liter per second that is 333 liter per second. Now, you pause video here for minute and write answer of the question. What is the hydraulic mean radius of circular section siever running half full? Here is the answer. Formula for hydraulic mean radius is area upon perimeter. It is running half full, so consider half of area that is half of pi D square by 4 and also consider perimeter half of the total section that is pi D by 2. Put the values of area and perimeter in the formula of R, it come again D by 4. So, when siever run full, hydraulic radius is D by 4 and when siever run half full then also R is equal to D by 4. Take one example, determine the velocity of flow and discharge in a siever of circular section having diameter 1 meter laid at a gradient of 1 in 500. Use Manning's formula, take N is equal to 0.012. Assume that siever is running half full. Manning's formula is velocity is equal to 1 by N R to the power 2 by 3 and into S to the power 1 by 2. We have seen when siever run half full hydraulic mean radius is D by 4. So diameter by 4 it is 1 by 4 is equal to 0.25. N is given to you, if it is not given you can refer the chart N is equal to 0.012 and the gradient of siever line is given 1 in 500. Put all the values in our formula V is equal to 1 by N into R to the power 2 by 3 into S to the power 1 by 2. After putting all the values in formula we get velocity is equal to 1.479 meter per second. Find out discharge as we know discharge is equal to area into velocity but here siever is running half full so consider half of the area so pi D square by 8 it is the half of the area into velocity, velocity we have 1.479 so discharge will get 0.581 meter cube per second or 881 liter per second these are my references thank you.