Calculating surface roughness correlating with Manning’s n in shallow water model?

max0014 · December 4, 2012, 01:48

I have difficulty calculating appropriate surface roughness that correlates with Manning’s n of my model,
I used Eq (3) given in Chapter 12 of v10 of FLOW-3D manual, to calculate parameter called ROUGH that correlates with Manning’s n. Manning’s n is known for my simulation. But if I use this ROUGH value in drag coefficient for bottom shear stress in Shallow Water physics of FLOW-3D, the simulation does not yield good match. It seems that for good match, the ROUGH value has to be increased more than 100 times the magnitude given by the above equation. The result with default value of 0.0026 is slightly better but still no way close to measured data. Am I using appropriate equation to calculate roughness which correlates Manning’s n into flow model? I used ROUGH as equal to “btmshr” in shallow water physics of FLOW-3D. Is this correct? Is there a direct way of inputting Manning’s n value into the FLOW-3D model?
Any suggestion is highly appreciated.
Thank you.

JBurnham · December 5, 2012, 12:16

ROUGH is the physical roughness length for 3-D solutions and laminar shallow water solutions ONLY. When you convert Manning's n to get ROUGH, and use it in shallow water physics, it under-predicts the drag, as you have observed, and must be adjusted to give an equivalent drag, as you have also observed. in v10.0 and later, you can use a turbulent shallow water model, in which case ROUGH is not applied: instead, a drag coefficient BTMSHR is specified, default value 0.0026. This is not a physical roughness length.

BTMSHR = fDARCY/8 ≈ nMANNING^2 g (Sf/Sb) / (Rh^(1/3) αMANNING^2)

fDARCY = D'Arcy friction factor [dimless]
nMANNING = Manning's n [ALWAYS s/m^(1/3)]
g = constant magnitude of gravitational acceleration [m/s^2 or ft/s^2]
Sf = energy gradient (free surface slope) of water [m/m or ft/ft]
Sb = bed gradient (bed slope) of water [m/m or ft/ft]
Sf/Sb = 1.0 (assumed by Manning's equation)
Rh = hydraulic radius (= depth for wide channels, wetted area/wetted perimeter for narrow channels) [m or ft]
αMANNING = 1.0 m^(1/3)/m^(1/3) when Rh & g are in m OR
αMANNING = 1.486 ft^(1/3)/m^(1/3) when Rh & g are in ft.

As you can see, there are different n values for different depths of flow, so the n value and Rh value you use to get BTMSHR must be appropriate for each other AND the flow being modeled.

December 4, 2012, 01:48	Calculating surface roughness correlating with Manning’s n in shallow water model?	#1
max0014 New Member max Join Date: Oct 2011 Posts: 10 Rep Power: 15	I have difficulty calculating appropriate surface roughness that correlates with Manning’s n of my model, I used Eq (3) given in Chapter 12 of v10 of FLOW-3D manual, to calculate parameter called ROUGH that correlates with Manning’s n. Manning’s n is known for my simulation. But if I use this ROUGH value in drag coefficient for bottom shear stress in Shallow Water physics of FLOW-3D, the simulation does not yield good match. It seems that for good match, the ROUGH value has to be increased more than 100 times the magnitude given by the above equation. The result with default value of 0.0026 is slightly better but still no way close to measured data. Am I using appropriate equation to calculate roughness which correlates Manning’s n into flow model? I used ROUGH as equal to “btmshr” in shallow water physics of FLOW-3D. Is this correct? Is there a direct way of inputting Manning’s n value into the FLOW-3D model? Any suggestion is highly appreciated. Thank you.

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December 5, 2012, 12:16		#2
JBurnham Senior Member Jeff Burnham Join Date: Apr 2010 Posts: 204 Rep Power: 17	ROUGH is the physical roughness length for 3-D solutions and laminar shallow water solutions ONLY. When you convert Manning's n to get ROUGH, and use it in shallow water physics, it under-predicts the drag, as you have observed, and must be adjusted to give an equivalent drag, as you have also observed. in v10.0 and later, you can use a turbulent shallow water model, in which case ROUGH is not applied: instead, a drag coefficient BTMSHR is specified, default value 0.0026. This is not a physical roughness length. BTMSHR = fDARCY/8 ≈ nMANNING^2 g (Sf/Sb) / (Rh^(1/3) αMANNING^2) fDARCY = D'Arcy friction factor [dimless] nMANNING = Manning's n [ALWAYS s/m^(1/3)] g = constant magnitude of gravitational acceleration [m/s^2 or ft/s^2] Sf = energy gradient (free surface slope) of water [m/m or ft/ft] Sb = bed gradient (bed slope) of water [m/m or ft/ft] Sf/Sb = 1.0 (assumed by Manning's equation) Rh = hydraulic radius (= depth for wide channels, wetted area/wetted perimeter for narrow channels) [m or ft] αMANNING = 1.0 m^(1/3)/m^(1/3) when Rh & g are in m OR αMANNING = 1.486 ft^(1/3)/m^(1/3) when Rh & g are in ft. As you can see, there are different n values for different depths of flow, so the n value and Rh value you use to get BTMSHR must be appropriate for each other AND the flow being modeled.