Hydraulic Radius and Area of Multiple Box Culverts.(Chezy Mannings)

[slange]

For a preliminary sizing I have looked at using the Chezy Manning's Equation for box culverts.
1. can you use Chezy Manning's on CBC that are multiple barrels? If yes do you sum up all the areas of each individual box culvert? Do you sum up the hydraulic radius of each individual barrel for the total hydraulic radius?
Q=(1.49/n)(A)(R)^.67(S)^.5

 

[psmart]

Since your equation is a linear function on area, you can use the combined area, but the hydraulic radius should be for a single barrel. If in doubt, evaluate a singe barrel and multiply by the number of barrels.

Peter Smart
HydroCAD Software

http://www.hydrocad.net

 

[appot]

Unless the barrel inverts are at different elevations, or the barrels are non uniform in shape/size, the hydraulic radius should remain the same regardless of the number of barrels

A = area of flow in one barrel
P = wetted perimeter in one barrel
n = number of barrels

r = n*A/(n*P) = A/P

 

[slange]

So
for example you have a CBC and assume flowing full
IE 5-8x4 CBC assuming flowing full
A=8*4=32 sf
∑A= 32+32+32+32+32= 160 sf
P = 4+4+8+8=24 feet
r=5*32/5*24=1.33
assuming n=.011, S=.0025
Q = (1.49/.011)(160)(1.33)^.67*(.0025)^.5= 1311.79 cfs

 

[cvg]

all fine except I would not expect n=0.011. for conservative sizing design, I would normally use 0.015 which gives you more like 960 cfs

for instance MDOT says 0.013

https://www.michigan.gov/documents/MDOT_MS4_App_91727_7._05_B_Drainage_Manual.pdf

precast.org and INDOT says 0.012 to 0.015

http://precast.org/wp-content/uploads/2014/08/Box_Culvert_Presentation.pdf

http://www.in.gov/indot/design_manual/files/Ch31_2012.pdf

 

[slange]

One other question why wouldn't you use R = 32/5+32/5+32/5+32/5+32/5= 32 hypothetically doesn't each box have a surface? Just curious?

 

[psmart]

slange: As you already stated: r= A/P = 5*32/5*24 which reduces to r=32/24

The hydraulic radius for a single barrel is the same as the hydraulic radius for the entire multi-barrel structure. Check the equation - you cannot add the radius for each barrel.

Again, the easy solution is to evaluate the flow for a single barrel and multiply by the number of barrels. Keep it simple.

Peter Smart
HydroCAD Software

http://www.hydrocad.net