 Myself, Mr. Deshmukh Sachin, I am working as an assistant professor in department of civil engineering of wall chain stop technology. Today, we are going to learn about different water surface profiles. At the end of this topic, the students will be able to classify water surface profiles and also can find out different slopes for the given channel on the field. Water surface profile is a measure of how the flow depth changes longitudinally, that is, with the length. The profiles are classified on the basis or on the relationship between the actual water depth. Why? Now, whenever we are going on the site, we are seeing the depth of the water which is flowing, that is, y, then the normal depth which is denoted by yn and the critical depth denoted by yc. Normal depth is the depth of the flow that would occur if the flow was uniform and steady and is usually predicted using Manning's equation. Now what is Manning's equation? Manning's equation which gives us the velocity v is equal to 1 upon n, rs to 2 third and s rest to half, r is hydraulic mean depth, s is the slope which is most important and n is Manning's constant and critical depth is defined as the depth of the flow where energy is at minimum for a particular discharge. Now relating these two, yn and yc, different water surface profiles are classified. Now see there are five slopes, mild, critical, steep, horizontal and adverse. All these slopes, these five slopes are defined on the basis of yn and yc. Let us see this table. See for the mild slope, the symbol is m and the criteria is yn, that is, normal depth is more than critical depth and it is a sustaining slope that is falling in the direction of flow which goes in the direction of flow. Again critical slope denoted as c and the criteria is yn and yc. This is also sustaining type, again in falling in the direction of flow. Steep slope, yc here, it is totally opposite of the mild slope that is critical depth is more than normal depth and it is also sustaining and that is we can say it is a falling in the direction of flow. But remaining these two that is horizontal as well as adverse slope, if you can see here as 0 is 0 for horizontal that is channel bottom is totally horizontal. So it is non-sustaining that is we can say here the prediction of normal depth is very difficult or it is impossible. So many times the zones, now we are going to study about the zones. These five slopes are there, how the depth of water is coming from zone 1 to zone 2 to zone 3. Like this when yn is not predicted, we cannot get the relationship between these, yn is in the second zone, y is in the second zone, we can relate. So the first zone is which is not giving the total depth from the channel bottom. So we can say it is non-sustaining and yn does not exist also. Similar case for adverse also as 0 is less than 0, now it is totally opposite and it is also non-sustaining and yn is not exist so that we cannot predict the water surface profiles in the zone 1 of horizontal slope as well as for adverse slope. I would like to mention one more thing in the critical slope. In the critical slope if you can see here, see here if the criteria is yn is equal to yc. So in the zone 1, if in the zone 1 y is there, we can say y is greater than yn and yc but in the second zone as yn and yc both are on the same line, both are on the same line y is not there in between these two. So zone number 2 is not appear that's why the C2 what we can say the water surface profile in the second zone is not appear. Now let us see in details every water surface profile, the entire region of the channel bottom is divided into three as I just mentioned, zone 1 which is refers to the region laying above the uppermost line, zone 2 is in between uppermost line and line near to it and zone 3 refers to the region between the middle line and the channel bottom line. Let us see this first slope, mild slope. Now here this line that means y is here. So y is greater than yn, this uppermost is yn and this line is yc line that is critical depth line. Now here is y, so we can say y is greater than yn which is greater than yc is a m1 type of profile. Similarly when y comes in the second zone, see whenever water flows from the starting point to the through the longitudinal direction, the depth of water is reducing. Here the y level comes in the second zone, we can say here it is a m2 type of profile. Here the criteria is yn is greater than y which is greater than yc, it is m2 type of profile and in third condition we can see the y is here, so yn is greater than yc is greater than y, this is m3 type of profile. Similarly we can go for critical slope, here y is above this line, so y is greater than normal depth level or critical depth level but c2 is not in existence as zone 2 is not in existence. Similarly we can say here yn or yc is greater than y, this is c3 type of profile. Then go for steep slope as I told you it is totally opposite to the mild, critical depth is more than normal depth level, see here it is y in the first zone, y is in the second zone, y is in the third zone, so y is greater than c, this is yc which is greater than yn, similarly yc is greater than y which is greater than you can say yn, so it is a s1, s2 and s3 type of profile. Here in the horizontal slope yn does not exist, so above this line one line must be there and above that y should be there but it is not seen over here, we only know the serial we are not knowing ndl, so whenever y is seen, here y is not seen, here y is seen which is in the second zone, so y is greater than yc, so we can say h2 is there and here yc is greater than h3, we can say this is h3 profile, here y is in the third zone and we can say yc is greater than y which is a h3 type of profile, similarly here yn is not in existence, here we can say y is seen, here y is seen, so y is greater than yc, here yc is greater than y, so it is a2 and this is a3 type of profile, so 5 slopes and 3 zones, so 5 multiplied by 3 must be 15 but c2, a1 and h2 are not in existence, so total profiles are only 12, these are the figures you can see clearly mentioned, m1, m2, m3, normal depth, critical depth is a y, this total water y is here, then y is here, then y goes down like this for critical also, for steep also, s1, s2, s3, then you can say for c1, c2, c1 and c3, sorry c2 is not there, then h1 is not there, h2 and h3 and a2 and a3, so these are the 12 water surface profiles shown clearly over here again, now take a pause and see the questions and answer these questions, these are objective type, so objective options are given to you, now these are the answers, check it clearly, if you find any difficulty just refer these books, go through these books, along with this you can use some text also or some waves or you can find some information from Google also, thank you.