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hi everybody welcome to hydraulic engineering for the 24th of April this is class 38 our last class of the semester a couple of announcements here before we begin homework number 11 which is your last homework assignment it includes a big range of material it's got hydraulic jumps it's got under flow gates it has water surface profiles remember that that assignment needs to be uploaded to blackboard before 11:50 p.m. on Friday the 24th so please submit that on time and if you have questions you can send me an email regarding the final exam we're scheduled to have that on the 1st of may Friday the 1st of May from 12:45 p.m. until 2:45 p.m. and I've previously described what the procedure is going to be for that test it's gonna be similar to our second midterm exam where you'll be able to print it out or you can just solve it on a blank piece of paper and then you're gonna submit with camScanner and a PDF file to blackboard and then you know if it's an excel file that you're using Excel to solve obviously you upload your excel solution as well the parameters that the exams going to be that you can use your previous homework assignments you can use the textbook but you can't collaborate in any way with another person so of course the instructions with the exam will be on the exam itself so that test is on Friday the 1st of May today we're gonna continue talking about the standard step method and this is a technique that we begin began on Wednesday in Wednesday's class we work the first example so today we're going to continue with another illustration another example and you can use that same template file that I provided earlier because if you look at the bottom there's a tab for this second example so let's get into it we've got triangular going to a going to a half circle downstream we know that there are a hundred meters apart the roughness point zero four five and we're putting 1.5 cubic meters per second through there so I've already calculated the critical depth and the normal depth alright that confirms it that this is subcritical conditions because if the critical depth is 0.65 and the normal depth is 0.98 then that means we've got a mild slope and here at location 1 the depth is 1.5 so the question is what is going to be the depth here where it goes to triangular so in the template file that I've provided you we've got basically the same setup but note here that it's cubic meters per second Z's and meters length is in meters and so when you do the G then be sure that you use 9.81 this time and just to make things a little bit simpler let's add that water surface column in again it was next to the y1 between the Y and the a so if we add a column here in B we'll call that the water surface at 1 and heck while we're adding things we might as well even add a velocity head term because we'll use that later so now it's not what would we even call it all right so at 1 where we know we know the conditions we know the depth we know the elevation of the channel bottom so the datum is right at the bottom of the channel there at 1 I'm gonna pause and let you work through this one independently without me narrating and interrupting you but I'll be circulating around with the solution to see if you're on the right track and then when we've maybe got five minutes left I'll start doing the solution on the screen so you can double check to see if you got it if you if you haven't already started with something else try a depth of 1.5 just choose the same depth at that upstream location and see what are all the calculations that arise from that for our triangular [Music] all right so the answer to this second one is that the depth should be one point two six meters and I think the tricky thing here is maybe the geometry of the quarter sir of the half circle and of the triangle but if you figure that out it's really the same process as it was before where I added again a column for the water surface at one in the water surface at two just to simplify the calculations so we see that the percent difference is rapidly declining and it's eventually converging on one point two six