Question: A wooden flume (n=0.012) with a rectangular cross section is 2' wide. the flume carries
3 cfs of water down a 1% slope. What is the depth of flow?


I'm having trouble figuring out where the 5/2 comes from in the answer here. I though you were supposed to add fractional exponents. For some reason I think it should be 8/3.

No the answer is correct:
if you simply you will get
d (1)xd (2/3)= d (1+2/3) = d (5/3) = d (5/2x2/3)
all values in brackets is power
Please correct me if I am wrong

You raise the left side of the equation to the 3/2 power, to clear the exponents.

Yep, that does it. Thanks, I was having trouble seeing that albeit its simplicity.

wait how does it become [(d^5/2)/(d+1)]^(2/3). Can someone help clarify? But I think I would probably just plug in numbers d to equate 0.1208 to find the depth.

Hey guys,
I ask my husbend for the explanation of this "simple question" (of cause he is professional mathematic and I haven't path exam at my first attempt), and that what he said.

6th grade (Middle School level in Russia)– need to repeat expressions with rational exponents:

Da x Db = Da+b

D1 x D2/3 = D 1 + 2/3 = D5/3

The solution wants to maintain the denominator of (d+1) for ease of solving by trial and error.

Look at it this way:

d x d^(2/3) = x^(2/3)

Solving for x:

[x^(2/3)]^(3/2) = [d x d^(2/3)]^(3/2)

x^1 = d^5/3^3/2

x = d^5/2

It's not very intuitive, but this problem is a good example of the analytical skills you need to demonstrate when taking the exam.

Good luck!

Or... this problem is a good example of knowing how to best approach the question. This does *NOT* need a trial-and-error solution. It is a simple process to try each of the four choices in the equation as soon as you get it reduced to one variable. Sure, a quick simplification will save you some keystrokes, but only if you don't make an algebra mistake.

My advice: don't sweat the simplifications and just plug-and-chug!