Question

To function properly, a water outflow pipe must drop 1 inch for every 22 inches of horizontal distance.

a. Calculate the slope for this drain pipe.
b. A rainwater pipe 30 feet long must run under the edge of a roof. What is the minimum vertical distance the pipe must drop between its ends?
c. A design calls for a drainage pipe to cross a building 45 feet wide as it drops 25 inches. Is this pip steep enough to function properly? Explain.

Answer 1

a. Calculate the slope for this drain pipe.
1/22
b. A rainwater pipe 30 feet long must run under the edge of a roof. What is the minimum vertical distance the pipe must drop between its ends?

Turn 30 feet to inches so 30 * 12 = 360 inches
Now times 1/22 x 360 = 16.32 inches . If they want it in feet just change 16.32 to feet by dividing 16.32 / 12

c. A design calls for a drainage pipe to cross a building 45 feet wide as it drops 25 inches. Is this pip steep enough to function properly? Explain.
Change 45 feet to inches so 45 * 12 = 540

Now times 540 * 1/22 = 24.54 inches so 25 inches would be steep enough since it droops 25 inches.

Answer 2

(a) 1/22; (b) 1.36'; (c) yes

Explanation:

(a)

The slope m is calculated the following way:

m = Δy/Δx

where Δy is the y variation and Δx is the x variation. In the first figure attached we can see that Δy = 1'' and Δx = 22'', therefore m = 1/22 = 0.045

(b)

Rearranging slope definition:

Δy = m * Δx

Here Δx is 30' (see 2nd figure). Replacing:

Δy = 1/12 * 30' = 1.36'

Note: m is an adimensional number, so it doesn't matter if Δx is in feet or inches as long as Δx is in the same units.

(c)

First we need to transform 25'' to feet before we can use the data in the equation (see 3rd figure).

25'' * 1'/12'' = 2.083'

From slope definition:

m = Δy/Δx = 2.083'/45' = 0.046 > 0.045

Every slope bigger than 1/22 will be satisfactory