 Vati Ghadge, Assistant Professor, Department of Civil Engineering, Volchin Institute of Technology, Solapur. Topic for today's session, determination of self-cleansing velocity of sewage flow through sewer line. At the end of this session, student will be able to determine the self-cleansing velocity of sewage flow through sewer line. Why the self-cleansing velocity is required? Why it is important? As we know that sewage content in organic and organic solid material in a suspended form when the sewer flow. If it is not flowing, what will happen that solid material will settle down in a sewer and maybe it is resulting in its clocking. That required minimum velocity is called as the self-cleansing velocity and it is not necessary that throughout the day, velocity is equal to self-cleansing velocity. It may be sometime less than self-cleansing velocity, sometime more than it. It depends on the fluctuation in the sewage flow, but at least once in a day, the self-cleansing velocity should achieve. We will see the shield expression for self-cleansing velocity. Despite the slope of the sewer line B alpha, consider a sediment of sewage of unit length, unit width and the thickness T. The self-weight of the sediment acting vertically downward W. R is the frictional force acting against in the direction of the flow and the tractive force offering by the water on the sewer, the tractive force is indicated by the symbol tau. Tau is density of water into R into S, where gamma W is the density of water, R is the hydraulic main radius and S is the slope of the sewer. Slope of the sewer can be calculated by head fall per unit length of the sewer. But our sediment is not only pure water, it is having some solid material in that. So, submersive weight of the sediment is gamma W into specific gravity minus 1 divided by 1 plus E, where E is the void ratio and G s is the specific gravity. In the form of porosity, the equation is submerged density is equal to water density into G s minus 1 into 1 minus N. Here N is the porosity. In this same diagram shown here, W is acting vertically downward and the frictional resistance force is acting against the direction of motion. Here in the red colour shown the component of W perpendicular to sewer is W cos alpha and parallel to sewer line it is W sin alpha. Weight of the sediment is density into volume. So, density is takes submerged density and volume is as we consider unit length and unit width and the thickness T. So, volume is 1 into 1 into T. So, this is the weight of the sediment. In the form of density of water, if W is equal to density of water into G s minus 1 into 1 minus N into T. Here apply the equilibrium condition here R and W sin alpha are in same direction. So, they must be same. So, R is equal to W into sin alpha. Put W in the equation. So, R is gamma W into G s minus 1 into 1 minus N into T into sin alpha. So, here we calculated W put in the equation you will get the R. When the sediment is just about to flow that tractive force will be equal to the frictional resistance. Tractive force is gamma W into R into s and put R that we just now calculated put that R in the equation to simplify it put 1 minus N into sin alpha is equal to K where K is this very special characteristic of sewage and it can be determined by the experiment. So, equation of S from this relation tau is equal to R from the relation determine the equation for the slope it is K upon R into G s minus 1 into T. If we consider 1 single solid particle then T become the function of the diameter of that solid particle. So, S is equal to K upon R into G minus 1 into D s. D s is the diameter of single solid particle instead of thickness we consider here 1 single solid particle. Now, derive velocity. So, use Chages equation here is equal to C under root of R s it is the Chages equation. For self cleansing velocity take V is equal to V s and calculate self cleansing velocity. So, we have calculated slope equation the value of slope in this equation will get C under root of R into under root of K upon R into G s minus 1 into D s. So, V s is equal to that under root of R will get cancelled. So, we will get the equation for self cleansing velocity C under root of K into G s minus 1 into D s. Here in this equation C is the Chages constant. So, we have to determine this Chages constant. So, to determine the Chages constant use Darcy Wiesbach head loss formula f L V square upon 2 G D. Now, you pause video here think and write the answer of this question find the values of Chages constant determine slope by the formula s is equal to H L upon L you remember that slope of siever we consider that is the head loss per unit length. So, by H L upon L it is slope you determine the slope from that equation then find R of circular siever running full and that calculated S and R put in the Chages formula and determine the Chages constant C. Here is the answer. So, as the slope is head loss divided by the length of the siever is f L V square upon 2 G D and this is the L. So, S will get f V square upon 2 G D and R as the siever running full and it is circular in section. So, R is equal to we know that it is area upon perimeter put area and perimeter and that equation. So, after calculation we will get area is equal to D by 4. So, put R and S in this equation in this Chages equation and find C it will 8 under root of 8 G upon f. Now, we will continue the continue our derivation. So, you put C in the equation of self cleansing velocity it is V s is equal to under root of 8 into beta upon f into G s minus 1 into G D G D s. So, this is the equation for the self cleansing velocity where B is the B or we can say K B is the characteristic of solid flowing in the sewage and it is range here in bracket I have shown 0.04 it is initiating score of clean grit and 0.8 for full removal of sticky grit. So, the value of B will vary in this range 0.04 to 0.8 f is the Darcy Wiesbach friction factor and its value it approximately 0.03 for the sewage and specific gravity of sediment it is ranges from 2.65 for the inorganic sediment and 1.2 for the organic sediment and specific gravity is indicated by the G s. Take one example find the minimum velocity is nothing but the self cleansing velocity and gradient required to transport coarse sand through sewer of 60 centimeter diameter with sand particle of 1 mm diameter and take a specific gravity 2.66 assume beta 0.06 friction factor 0.02 and the sewer run half full take n is equal to 0.012 and we have derived self cleansing velocity equation that in that formula put the given values B f and G s find out V s. So, B is 0.06 f is 0.02 G s is 2.66 it is given and diameter of solid particle is given 1 mm. So, put in a meter 0.001 meter. So, put everything in a formula and calculate V s it is 0.625 meter per second. Now, we have it is given that rugosity coefficient. So, we have to use Manning's formula for that r as the sewer run half full r is equal to d by 4 and diameter of it is given that 6 centimeter. So, it is 0.6 meter divided by 4. So, r is 0.125 no n is given that is 0.012. So, put r n and self cleansing velocity in the equation only the slope is unknown find out slope from the equation. So, slope you will get 1 upon 1111 hence the required gradient it 1 in 1111. These are my references. Thank you.