Fluid Mechanics and Fluid Machinery
This domain checks whether you can move between the energy equation, friction losses and pump or fan behaviour. Typical Nezam items give a pipe run, a flow rate and a roughness or friction factor and ask for head loss, pump head, or the effect of a speed change.
Core rules
- Continuity: Q = A₁V₁ = A₂V₂. Reynolds number Re = ρVD/μ; Re < 2300 laminar, > 4000 turbulent.
- Darcy–Weisbach: h_f = f(L/D)(V²/2g). For laminar flow f = 64/Re, independent of roughness.
- Minor losses: h_m = K(V²/2g), applied to the downstream velocity unless stated otherwise.
- Pump affinity laws: Q ∝ n, H ∝ n², P ∝ n³. A modest speed rise means a large power rise.
- NPSH available must exceed NPSH required; throttling the suction or raising the pump above the tank lowers NPSH_a.
Worked example
Water flows at Q = 10 L/s through a 100 mm diameter pipe, L = 50 m, f = 0.02. A = π(0.05)² = 0.007854 m², V = 0.010/0.007854 = 1.273 m/s, V²/2g = 1.621/19.62 = 0.0826 m. h_f = f(L/D)(V²/2g) = 0.02 × (50/0.1) × 0.0826 = 0.02 × 500 × 0.0826 = 0.83 m. Check Re = 1000 × 1.273 × 0.1/0.001 ≈ 127,000 - turbulent, so f = 0.02 is consistent.
Traps
- Using diameter where the formula needs radius, or mixing mm and m inside Q = AV.
- Applying affinity laws to power as n² instead of n³.
- Forgetting that velocity head and minor losses still count when the pump raises pressure only.