 Assistant Professor, Department of Civil Engineering, Wolchen Institute of Technology, Solapur. Topic for today's session, design of Siphon. At the end of this session, student will be able to design Siphon for given discharge of a sewer line. Siphon, it is a pipe carrying in generally liquid from one container to another container. Here, Siphon, sometime called as depressed sewer, used to flow wastewater through a pipe under low laying areas or obstructions such as river, utility, stream, etc. In the diagram, Siphon shown here, from one container to another container, it is transferring the sewer. It is crossing the stream here or river. Take one example for the design of Siphon. A sewer line carrying an average discharge, 200 litre per second, has to cross a stream. Design a three-barrel Siphon for this purpose. If the length of the Siphon measure along the center line include the slope is 90 meter. The river level at the inlet and the outlet ends of the sewer are 152.50 and 151.78 respectively. The maximum and minimum flow are 250% and 40% of the average respectively. Assume the minor losses as 0.07 meter, self-pinsing velocity 1 meter per second. You list out the given data and calculate average flow, maximum flow and the minimum flow. In the numerical, it is given average flow is 200 litre per second. So, average flow is 0.2 in meter cube per second. Maximum flow is given 250% of average flow. So, 250% of 0.2 is 0.5 meter cube per second. Minimum flow, 40% of average flow. So, 40% of 0.2 is 0.08 meter cube per second. Design of Siphon for the flow at minimum discharge. So, minimum discharge is given 0.08 meter cube per second and the formula of discharge is area into velocity. So, 0.08 is equal to area is pi D square by 4 into take self-cleansing velocity 1 meter per second. Calculate diameter, it is 0.319 meter. Use diameter less than 0.319 meter. Say 300 mm diameter. And take material for the sewer, cast and pipe. So, velocity is equal to discharge upon area. Discharge, it use minimum discharge 0.08 and put diameter 300 mm that is 0.3 meter and find out the velocity. That velocity should be greater than self-cleansing velocity and here self-cleansing velocity is 1 and calculated velocity is 1.132. Hence, it is okay. Use Manning's formula of velocity. Manning's formula is velocity is equal to 1 upon N into R to the power 2 by 3 into S to the power 1 by 2. Here R is the hydraulic mean radius. It is area upon perimeter. So, it is D by 4. We assume a diameter 0.3 meter. So, hydraulic mean radius is 0.3 by 4 is 0.075. Assume Manning's constant 0.03 for the sewer material, cast and pipe. It is given in the Manning's chart. Put calculated velocity, Manning's constant and hydraulic mean radius in the Manning's formula and find out the slope. So, slope will get 0.00685. And we will check first what is the available head. The inlet and outlet of the river is given. It is 152.50 and 151.78. So, the available head is 0.72 meter. We will check first frictional head loss plus some minor head loss. It should be less than 0.75. So, first calculate frictional head loss. So, frictional head loss is equal to slope into the length of the siphon. Slope we have calculated 0.00685 into length of siphon is given 90. So, frictional head loss is 0.615 meter. Therefore, total head loss is frictional head loss plus some minor losses. Minor losses is given 0.07. Therefore, total head loss is 0.685 and it is less than the available head 0.72 meter. Hence, the diameter we use 300 mm it is satisfactory. Now, you pause video here and answer the question. What will be your action if the head loss, total head loss is greater than available head loss? Answer, if the head loss is greater than available head loss, then we need to reduce head loss. And the formula of head loss is slope into length. So, we have to reduce the slope. So, from the Manning's formula derive the formula for the slope. So, slope formula is s to the power 1 by 2 is equal to v into n divided by r to the power 2 by 3. From the formula, it is clearly seen that slope and the velocity are directly proportional. So, to reduce slope, reduce velocity also. And velocity formula is discharge upon area. And from this formula, it is seen that velocity and the diameter of the pipe are inversely proportional. So, to reduce velocity, increase the diameter of the pipe. We have to increase the diameter of the pipe if the head loss is greater than the available head loss. Here, if that 300 diameter, suppose not satisfactory, we have to increase the diameter. But do not increase more than 319 meter, remember. We will continue the design. Now, design siphon for the flow at average discharge. So, average discharge is given 0.2 meter cube per second and minimum discharge is 0.08. So, discharge for the second pipe is 0.12 meter cube per second. So, design the second barrel for the discharge 0.12 meter cube per second. So, find out the diameter for the discharge 0.12 meter cube per second. It is 0.39 meter. So, consider a diameter less than 390 mm, say 380 mm diameter. So, recalculate the velocity. Velocity for the discharge 0.12 and the diameter 380 mm is 1.058 meter per second. So, it is greater than 1 meter per second. Hence, it is okay. Now, by using Manning's formula, find out the slope. Calculated velocity, Manning's constant and the hydraulic mean radius put in a formula and find out the slope. Slope will come 0.00436. We will check the head loss should be less than the available head. So, for the frictional head loss, use a formula slope into length of the siphon. Slope we have calculated 0.00436 length of the siphon 90. So, frictional head loss is 0.392. Plus, minor head loss is 0.07. So, total head loss is 0.436. And that head loss is less than 0.72. Hence, the pipe diameter 380 mm is satisfactory for the barrel tool. Now, we will design the siphon for the flow rate maximum discharge. So, average discharge is 0.2 meter cube per second and maximum discharge is 0.5 meter cube per second. So, design third pipe for the discharge 0.3 meter cube per second. Put discharge 0.3 and velocity, it is self-cleansing velocity. It is given 1 meter per second and find out the diameter. So, diameter will get 0.618 meter. We will consider less than 618 mm, say 600 mm diameter and keep same material that is cast and pipe. And calculate velocity. So, velocity for the 600 mm diameter and the discharge 0.3 is 1.061. It is also greater than self-cleansing velocity. Hence, it is okay. Again, by using Manning's formula, calculate slope. So, it is 0.00238. Again, we will check for the head loss. So, find out the frictional head loss. It is slope into length of the siphon. It is 0.214 plus minor losses. It is 0.07. So, total head loss is 0.284. It is less than 0.72 meter. Hence, the pipe diameter 600 mm is satisfactory for the third barrel. Hence, the size of the three barrels are barrel 1 of diameter 300 mm, barrel 2 of diameter 380 mm and barrel 3 of diameter 600 mm. For this video, these are my references. Thank you very much.