00:01
In this problem, we're asked to repeat a previous problem if the upstream depth is 0 .4 meters.
00:07
Okay.
00:08
So let me get started.
00:10
I'm going to start with the following equations.
00:24
That will equal 2 squared over 2g.
00:36
And the first two velocities have to be evaluated.
00:41
We can do this from the continuity equation.
00:48
And we'll get v1.
00:54
That'll be 4 over 0 .4 meters per second.
00:59
Equals 10 meters per second.
01:03
And at v2 at our midstream, we have 4 over y, m over s.
01:13
So then we can substitute the rest of the known terms into the bernoulli equation.
01:19
So we'll get 10 squared over 2 times 9 .81 meters plus 0 .4 meters, and that will equal 4 squared.
01:38
Over y squared times 2 9 .81m plus ym plus 0 .2 e to the negative x squared.
01:59
I need to go to my next page here.
02:02
This will get me 5 .49 equals 0 .82 over y squared plus plus y plus 0 .2 e to the negative x squared.
02:30
Oops that'll be equals 0 .82 plus y cubed plus 0 .2 e to the negative x squared.
02:50
So this will end up as y cubed plus negative 5 .49 plus 0 .2 e to the negative x squared.
03:06
Y squared plus 0 .82 equals 0.
03:14
It's a cubic equation.
03:16
We'll get three possible solutions for every x value, and which one is right? well, you use the type of flow using frode's number.
03:32
So frode's number will be v1 over the square root of y1 times g.
03:39
So this will be 10 times 0 .0 .0 .2.
03:46
0 .4 times 9 .81.
03:50
This equals 5 .05.
03:54
So the flow, thus the flow is super critical, and the smallest solution will be correct one.
04:27
Okay, so we're going to, given an interval of x, we're going to substitute several different values, and we'll use software for, appropriate software for solving this, my first one.
04:42
I'm going to start with x equals zero.
04:45
So we'll get y squared or y cubed plus 0 .5, negative 5 .49 plus 0 .2, e to the 0...