The Manningcirc function solves for one missing variable in the Gauckler-
Manning equation for a circular cross-section and uniform flow. The
possible inputs are Q, n, Sf, y, and d. If y or d are not initially known,
then Manningcircy can solve for y or d to use as input in the Manningcirc
function.The Manningcircy function solves for one missing variable in the Gauckler-
Manning equation for a circular cross-section and uniform flow. The possible
inputs are y, d, y_d (ratio of y/d), and theta.
Gauckler-Manning-Strickler equation is expressed as
$$V = \frac{K_n}{n}R^\frac{2}{3}\sqrt{S}$$
[object Object],[object Object],[object Object],[object Object],[object Object]
This equation is also expressed as
$$Q = \frac{K_n}{n}\frac{A^\frac{5}{3}}{P^\frac{2}{3}}\sqrt{S}$$
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Other important equations regarding the circular cross-section follow:
$$R = \frac{A}{P}$$
[object Object],[object Object],[object Object]
$$A = \left(\theta - \sin \theta\right) \frac{d^2}{8}$$
[object Object],[object Object],[object Object]
$$\theta = 2 \arcsin\left[1 - 2\left(\frac{y}{d}\right)\right]$$
[object Object],[object Object],[object Object]
$$d = 1.56 \left[\frac{nQ}{K_n\sqrt{S}}\right]^\frac{3}{8}$$
[object Object],[object Object],[object Object],[object Object],[object Object]
Note: This will only provide the initial conduit diameter, check the design
considerations to determine your next steps.
$$P = \frac{\theta d}{2}$$
[object Object],[object Object],[object Object]
$$B = d \sin\left(\frac{\theta}{2}\right)$$
[object Object],[object Object],[object Object]
Assumptions: uniform flow and prismatic channel
Note: Units must be consistent