Question

Estimate the required pipe diameter using manning's equation, where S=0.005, Q = 19.80 cfs, and n = 0.013.

Assume the circular pipe is full but not yet pressurised.Manning's equation gives:

Q = {1.486/n} A Rh^{2/3} S^{1/2}

Answer 1

To estimate the required pipe diameter using Manning's equation, we can rearrange the equation to solve for the cross-sectional area (A) of the pipe.

The equation is:

Q = (1.486/n) * A * Rh^(2/3) * S^(1/2)

Given the values:
Q = 19.80 cfs (cubic feet per second)
n = 0.013
S = 0.005 (slope)
We need to find the pipe diameter (D).

To solve for A, we can substitute the values into the equation and solve for A:

19.80 = (1.486/0.013) * A * Rh^(2/3) * 0.005^(1/2)

Now, since the pipe is assumed to be circular and full, we can substitute the relationship between the pipe diameter (D) and the hydraulic radius (Rh):

Rh = D/4

19.80 = (1.486/0.013) * A * (D/4)^(2/3) * 0.005^(1/2)

Simplifying the equation further, we get:

19.80 = 114.31 * A * (D/4)^(2/3)

Now, we need more information to determine the required pipe diameter. Specifically, we would need either the cross-sectional area (A) or the shape of the pipe (such as a circular pipe with a known diameter). Without that information, we cannot directly estimate the required pipe diameter using Manning's equation.