I agree with the other comments - we're missing some explanation on what is going on, as soon as step 2. I think I figured out what is going on... please correct me if I'm wrong. This looks to me like a unit hydrograph solution, which does not appear in the PERH, but is in the CERM (page 20-9). It also looks like the problem statement should have read: The following table is historical data. For a 3 hour storm that produced 1.5 inches of runoff over 120 acres, find the peak stream discharge. In other words, use a unit hydrograph to analyze storms of different volumes. Otherwise, why would we calculate the volume of runoff from the stream monitoring station when it can be directly calculated from the runoff x area in the problem statement? Step 2 calculates the volume of runoff for the historical storm, using the stream data. Step 3 calculates the average runoff depth for the historical storm. Step 4 does double duty: it converts the peak historical discharge into a peak unit [hydrograph] discharge (peak/ average depth) and simultaneously calculates the peak runoff for the new storm by multiplying by the 1.5 inch runoff depth. In CERM it's broken into 2 steps, here it is combined. Step 5 just adds back the base flow for this particular stream.
Good thoughts. Here are some thoughts to consider. Calculated from the problem statement? 1.5in x 1ft/12in = 0.125 ft 120 acre x 43560 ft²/ac = 5,227,200 ft² 0.125x5,227,200 = 653,400 ft³ This doesn't work because we don't get our time unit involved, the problem statement is asking for discharge which always has the volume unit divided by the time unit. The unit hydrograph method is not shown in the PERH so this is a method to step through the problem using basic reasoning w/o the unit hydrograph information readily available. Other things to think about: 1 - recognize that a discharge other than 0 at time 0 means baseflow is present and needs to be subtracted out at each discharge interval value. 2 - use proper time step in total runoff volume calculation 3 - review the ability to determine average runoff depth by dividing total volume by total area 4 - remember to add back in the baseflow to get the final answer. Hopefully, that helps. This may be a long one but elements of these problems can always be asked in the exam and frankly, you never know what you get on the depth exam. We hope this helps!
I think I've figured out what's going on because I had the same hang-up in the logic that you did. 1.) We're given the average hourly flows at some point in a stream within this 120-acre watershed area. 2.) We're given the average runoff depth for the entire watershed. 3.) Given these things, we calculate the average runoff depth for the area feeding into the gauge point we have discharges for. 4.) We then extrapolate the peak runoff discharge at the very end of this stream leaving the 120-acre watershed area by assuming it to be proportional to the ratio of average runoff depths (step 4 tipped me off on this multiplying the peak discharge by the ratio of runoff depths), taking care to account for the baseflow. I think technically it's worded correctly but could have been clearer.
@@CivilEngAcademy The problem should have been worded quite differently if this was your intention. First of all, the problem stated that the data in the table was recorded AFTER the 3-hour storm. Your explanation of the discharge at t=0 being the base flow of the stream means the data was recorded DURING and 3 hours AFTER the storm. Second, the problem stated that, "...a 3-hour storm event produced 1.5 in of runoff over 120 acres...". The 3-hour storm produced 1.5 in of runoff over 120 acres. The problem clearly states the volume of runoff by the storm. It doesn't matter if a 12-hour storm produced 1.5 in of runoff over 120 acres, it's still the same volume, so I'm not sure why you felt the need to calculate this from the table. Third, the problem is asking for the peak stream discharge following the storm. If the storm starts at t = 0, the storm will have stopped at t = 3. The "peak stream discharge" was recorded in the table. So, the answer should be 124 cfs.
Here's how the problem should read: "The following table shows recorded discharge at a stream monitoring station following a 3-hour storm event. The tributary watershed area contributing runoff to the stream is 120 acres. The peak discharge (ft3/s) that would be recorded following a storm producing 1.5 inches of runoff (rainfall excess) is most nearly?" Also, don't forget to subtract baseflow and then add it back in at the end!
Interesting & tough problem. Steps 4 and 5 aren't clear still despite good video. Tried to use ncees pe hb 1.1, p. 3, 378, 394 without success despite these eqns being close to what we need for problem. But there were too many unknowns to use them! Perhaps someone succeeded in using the refs above. If so, post here how you did it.
