The formulas to calculate the dimensions of a floating-type square/rectangular gas chamber are:

1. Inner Length (\(L_g\)):

\[ L_g = \frac{45 \cdot L_d - w}{50} \]

2. Inner Width (\(W_g\)):

\[ W_g = \frac{45 \cdot L_d - w}{50} \]

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

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

4. Height of Gas Chamber (\(H_g\)):

\[ H_g = 1.15 \left[ \left( \frac{V_g}{L_g \cdot W_g} \right) + H_p \right] \]

Where:

• \(L_g\) is the inner length of the gas chamber in meters (m).
• \(W_g\) is the inner width of the gas chamber in meters (m).
• \(L_d\) is the inner length of the digester in meters (m).
• \(V_g\) 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).
• \(H_g\) is the height of the gas chamber in meters (m).
• \(H_p\) is the desired pressure head in meters (m).