The formulas to calculate the dimensions of a floating-type cylindrical gas chamber are:

1. Inner Diameter (\(D_g\)):

\[ D_g = \frac{45 \cdot D_d - w}{50} \]

2. Height of Pyramidal Roof (\(h\)):

\[ h = D_g \cdot \tan\left(\frac{9.5}{2}\right) \]

3. Height of Gas Chamber (\(H_s\)):

\[ H_s = 1.15 \left[ \left( \frac{4 \cdot V_s}{\pi \cdot D_s} \right) + H_p \right] \]

Where:

• \(D_g\) is the inner diameter of the gas chamber in meters (m).
• \(D_d\) is the inner diameter of the digester in meters (m).
• \(V_s\) is the effective gas chamber volume in cubic meters (m³).
• \(w\) is the gas chamber wall thickness in centimeters (cm).
• \(h\) is the height of the pyramidal roof in meters (m).
• \(H_s\) is the height of the gas chamber in meters (m).
• \(H_p\) is the desired pressure head in meters (m).