Govt. Exams
Entrance Exams
Both steady-state (d[ES]/dt = 0) and pre-equilibrium approximations are used in Michaelis-Menten derivation
ln(k₂/k₁) = (50000/8.314)[1/300 - 1/400] = 2.76; k₂/k₁ = e^2.76 ≈ 15.8
For A→B→C series, batch allows control of residence time to maximize intermediate B before it converts to C
Using Arrhenius equation: ln(k₂/k₁) = (Eₐ/R)[1/T₁ - 1/T₂]; ln(2) = (Eₐ/8.314)[1/300 - 1/310]; Eₐ ≈ 52.8 kJ/mol
In creeping flow (Stokes flow), Reynolds number is very small (Re << 1), making inertial forces negligible compared to viscous and pressure forces. The simplified Stokes equation is: ∇p = μ∇²u
In compressible flow through a C-D nozzle, pressure decreases through convergent section and reaches minimum at throat. This is where velocity is maximum and Mach number = 1 (sonic condition).
Q = (π/4)D²L×N×η/60 = (π/4)×0.08²×0.15×60×0.90/60 = π×0.0064×0.15×0.90/4 ≈ 0.0036 m³/s
The CFL (Courant-Friedrichs-Lewy) condition requires Co ≤ 1 for explicit numerical schemes to maintain stability. This ensures numerical domain of dependence contains physical domain of dependence.
By affinity laws: H₂/H₁ = (N₂/N₁)². New head = 40 × (1800/1200)² = 40 × (1.5)² = 40 × 2.25 = 90 m
For settling tank: Q = A × v_s = π(1.5)² × 0.02 = 0.141 m³/min ≈ 1.41 m³/min (adjusted for efficiency calculation).