Roughness length, calculate z0

paulthomasrowland

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Joined
Sep 24, 2015
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2
I have wind speeds at two heights, h1 and h2, and wind speed measurements at each height. I want to calculate z0, the roughness length. The formula is given as:

v2 = v1 (ln(h2/z0)/ln(h1/z0))

I cannot figure out for to solve for z0 correctly.

Can you help?
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,149
I have wind speeds at two heights, h1 and h2, and wind speed measurements at each height. I want to calculate z0, the roughness length. The formula is given as:

v2 = v1 (ln(h2/z0)/ln(h1/z0))

I cannot figure out for to solve for z0 correctly.

Can you help?
\(\displaystyle \displaystyle{\frac{v_2}{v_1} \ = \dfrac{ln(h_2)-ln(z_0)}{ln(h_1)-ln(z_0)}}\)

\(\displaystyle \displaystyle{\frac{v_2}{v_1} \ - \ 1\ = \dfrac{ln(h_2)-ln(z_0)}{ln(h_1)-ln(z_0)} \ - \ 1}\)

Now continue....
 

Ishuda

Elite Member
Joined
Jul 30, 2014
Messages
3,345
I have wind speeds at two heights, h1 and h2, and wind speed measurements at each height. I want to calculate z0, the roughness length. The formula is given as:

v2 = v1 (ln(h2/z0)/ln(h1/z0))

I cannot figure out for to solve for z0 correctly.

Can you help?
I would do it a slightly different way: Multiply though by ln(h1/z0)=ln(h1)-ln(z0) to get
v2 [ln(h1) - ln(z0)] = v1 [ln(h2) - ln(z0)]
or
v1 ln(z0) - v2 ln(z0) = v1 ln(h2) - v2 ln(h1)
and continue
 

paulthomasrowland

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Joined
Sep 24, 2015
Messages
2
Solved

Very many thanks to you both :)
 
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