The theoretical aerobic oxidation of biomass (C₅H₇O₂N) is given below:

C₅H₇O₂N + 5O₂ → 5CO₂ + NH₃ + 2H₂O

The biochemical oxidation of biomass is assumed as a first-order reaction with a rate constant of 0.23/d at 20ºC (logarithm to base e). Neglecting the second-stage oxygen demand from its biochemical oxidation, the ratio of BOD₅ at 20ºC to total organic carbon (TOC) of biomass is _______ (round off to two decimal places).

[Consider the atomic weights of C, H, O and N as 12 g/mol, 1 g/mol, 16 g/mol and 14 g/mol, respectively

A system of seven river segments is shown in the schematic diagram. The R_i’s, Q_i’s, and C_i’s (i = 1 to 7) are the river segments, their corresponding flow rates, and concentrations of a conservative pollutant, respectively. Assume complete mixing at the intersections, no additional water loss or gain in the system, and steady state condition. Given: Q₁ = 5 m³/s ; Q₂ = 15 m³/s ; Q₄ = 3 m³/s ; Q₆ = 8 m³/s ; C₁ = 8 kg/m³; C₂ = 12 kg/m³; C₆ = 10 kg/m³. What is the steady state concentration (in kg/m³, rounded off to two decimal place) of the pollutant in the river segment 7 ? ______

The pressure in a pipe at X is to be measured by an open manometer as shown in figure. Fluid A is oil with a specific gravity of 0.8 and Fluid B is mercury with a specific gravity of 13.6. The absolute pressure at X is ________ kN/m2 (round off to one decimal place).

[Assume density of water as 1000 kg/m3 and acceleration due to gravity as 9.81 m/s2 and atmospheric pressure as 101.3 kN/m2]

A compound symmetrical open channel section as shown in the figure has a maximum of _______ critical depth(s).

B_m – Bottom width of main channel

B_f – Bottom width of flood channel

y_m – Depth of main channel

y – Total depth of the channel

n_m – Manning’s roughness of the main channel

n_f – Manning’s roughness of the flood channel