manningc | R Documentation |
This function solves the Manning equation for water flow in a circular pipe at less than full. Uniform flow conditions are assumed, so that the pipe slope is equal to the slope of the water surface and the energy grade line. This is a modification of the code prepared by Irucka Embry in his iemisc package. The iemisc::manningcirc function was adapted here for more limited cases commonly used in classroom exercises, additional checks were included to ensure the pipe is flowing less than full, and a cross-section figure is also available. The iemisc::manningcirc and iemisc::manningcircy functions were combined into a single function.
manningc( Q = NULL, n = NULL, Sf = NULL, y = NULL, d = NULL, y_d = NULL, units = c("SI", "Eng"), ret_units = FALSE )
Q |
numeric vector that contains the flow rate [m^3/s or ft^3/s] |
n |
numeric vector that contains the Manning roughness coefficient. |
Sf |
numeric vector that contains the slope of the pipe [unitless] |
y |
numeric vector that contains the water depth [m or ft] |
d |
numeric vector that contains the pipe diameter [m or ft] |
y_d |
numeric vector that contains the ratio of depth to diameter [unitless] |
units |
character vector that contains the system of units [options are
|
ret_units |
If set to TRUE the value(s) returned are of class |
The possible applications of this function for solving the Manning equation for circular pipes are:
Given | Solve for |
y_d, Q, Sf, n | d |
d, Sf, Q, n | y |
y, d, Q, n | Sf |
y, d, Sf, n | Q |
d, Q, Sf, y | n |
The Manning equation (also known as the Strickler equation) describes flow conditions in an open channel under uniform flow conditions. It is often expressed as:
Q = A\frac{C}{n}{R}^{\frac{2}{3}}{S_f}^{\frac{1}{2}}
where C is 1.0 for SI units and 1.49 for Eng (U.S. Customary) units. Critical depth is defined by the relation (at critical conditions):
Q^2B/gA^3=1
where B is the top width of the water surface. Since B equals zero for a full pipe, critical depth is set to the pipe diameter d if the flow Q exceeds a value that would produce a critical flow at y/d=0.99.
Returns a list including the missing parameter:
Q - flow rate
V - flow velocity
A - cross-sectional area of flow
P - wetted perimeter
R - hydraulic radius (A/P)
y - flow depth
d - pipe diameter
Sf - slope
n - Manning's roughness
yc - critical depth
Fr - Froude number
Re - Reynolds number
Qf - Full pipe flow rate
Ed Maurer, Irucka Embry
xc_circle
for a cross-section diagram of the circular channel
#Solving for flow rate, Q: SI Units manningc(d = 0.6, n = 0.013, Sf = 1./400., y = 0.24, units = "SI") #returns 0.1 m3/s #Solving for Sf, if d=600 mm and pipe is to flow half full manningc(d = 0.6, Q = 0.17, n = 0.013, y = 0.3, units = "SI") #returns required slope of 0.003 #Solving for diameter, d when given y_d): Eng (US) units manningc(Q = 83.5, n = 0.015, Sf = 0.0002, y_d = 0.9, units = "Eng") #returns 7.0 ft required diameter #Solving for depth, d when given Q: SI units manningc(Q=0.01, n=0.0013, Sf=0.001, d = 0.2, units="SI") #returns depth y = 0.042 m, critical depth, yc = 0.085 m
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