Question

Please explain how to set up and find answer. Thank you
To protect cities from flooding during heavy rains, open channels are sometimes constructed to handle runoff. The rate R at which water flows through the channel is modeled by R=k sqrt m, where m= slope of the channel and k is a constant determined by the shape of the channel.
a) suppose that a channel has a slope of m = 0.01 and a runoff rate of R=340 cubic feet per second. Find K.
b) If the slope of the channel increases to m=0.04 what happens to R?

Answer 1

Ok so to sum it up you have the equation: \[R=k\sqrt{m}\] where
R = rate at which water flows through the channel
m = slope of the channel
k = a constant
a). In this part you are given m and R, so just plug them into the equation and solve for k.
b). You can use the same k you found in part a to answer part b, but this time use .04 for m and solve for R. Compare this answer to the one in part a, what happened? Did R increase or decrease?

Answer 2

I think that I just figured out a. 340=[\sqrt{0.01}\]

Answer 3

divide the sqrt on both side and I got 3400

Answer 4

Yep so that gives you k.

Answer 5

for b I got R= 680 cubic feet per second

Answer 6

Okay so what does this tell you about the relationship between R and m?

Answer 7

the slope rised double

Answer 8

Yep so as m increases so does R right? This makes them proportional.

Answer 9

yes

Answer 10

Thank u