In[]:=
BaffleSize=3.5
Out[]=
3.5
In[]:=
ActualBaffleWidth:=2rSin
BaffleSize
2r
/.FindRoot
FillHeight
2
==2r
2
Sin
BaffleSize
4r

,{r,1,BaffleSize}
In[]:=
LossFraction:=ActualBaffleWidth/BaffleSize

Actual baffle size vs flat baffle size

In[]:=
Grid[PrependTo[Table[{FillHeight,ActualBaffleWidth,LossFraction},{FillHeight,0.5,2/3*BaffleSize,0.1}],{"FillHeight","ActualBaffleWidth","LossRatio"}]]
Out[]=
FillHeight
ActualBaffleWidth
LossRatio
0.5
3.45192
0.986262
0.6
3.43046
0.980132
0.7
3.40486
0.972816
0.8
3.37497
0.964276
0.9
3.34063
0.954466
1.
3.30165
0.943328
1.1
3.25777
0.930792
1.2
3.20872
0.916777
1.3
3.15412
0.901178
1.4
3.09355
0.883872
1.5
3.02646
0.864703
1.6
2.95217
0.843477
1.7
2.86981
0.819945
1.8
2.77822
0.793778
1.9
2.67588
0.764537
2.
2.56059
0.731597
2.1
2.42911
0.694032
2.2
2.27623
0.65035
2.3
2.09244
0.597841
In[]:=
Plot[LossFraction,{FillHeight,0.5,2/3*BaffleSize},AxesLabel{"Fill Height","Length Loss Frac"}]
Out[]=

Actual baffle area vs. "naive" baffle area

In[]:=
ActualBaffleArea:=2*
2
r
a
2
-
Sin[a]
2
/.a
BaffleSize
r
/.FindRootFillHeight2==2r
2
Sin
BaffleSize
4r

,{r,1,5}
In[]:=
Grid[Table[{​​FillHeight,​​ActualBaffleArea,​​(FillHeight*BaffleSize),​​ActualBaffleArea/(FillHeight*BaffleSize)​​},​​{FillHeight,0.5,2/3*BaffleSize,0.1}]]
Out[]=
0.5
1.15545
1.75
0.660259
0.6
1.38054
2.1
0.657402
0.7
1.60228
2.45
0.653994
0.8
1.82005
2.8
0.650018
0.9
2.03318
3.15
0.645454
1.
2.24097
3.5
0.640277
1.1
2.44265
3.85
0.634455
1.2
2.63741
4.2
0.627954
1.3
2.82431
4.55
0.620728
1.4
3.00234
4.9
0.612722
1.5
3.17032
5.25
0.60387
1.6
3.32688
5.6
0.594087
1.7
3.47042
5.95
0.583265
1.8
3.59896
6.3
0.571263
1.9
3.70999
6.65
0.557893
2.
3.80021
7.
0.542888
2.1
3.86503
7.35
0.525854
2.2
3.89745
7.7
0.506162
2.3
3.88552
8.05
0.482673