Govt. Exams
Entrance Exams
Total head H = (P_out - P_in)/(ρg) + (v_out² - v_in²)/(2g) + z_out - z_in = (800000 + 20000)/(1000×9.81) + 2 = 82.26 + 2 = 84.26 m ≈ 84.2 m
By continuity equation: A₁V₁ = A₂V₂. If A₁ = 4A₂, then V₂ = 4V₁ = 4 × 5 = 20 m/s.
ΔP = ρgh = 13600 × 10 × 0.2 = 27200 Pa. But if measured in cm (0.002 m): ΔP = 272 Pa. Given context, likely 0.2 m = 20 cm, so ΔP = 2720 Pa.
P = ρgQH = 1000 × 10 × (50/3600) × 30 = 1000 × 10 × 0.0139 × 30 ≈ 4.17 kW.
Vena contracta is the region of minimum cross-section and maximum velocity after the orifice. Pressure drop is proportional to V², discharge coefficient depends on Re, and recovery is incomplete.
Re = ρVD/μ = (850 × 1 × 0.5)/(100 × 10⁻³) = 4250. Wait, recalculating: (850 × 1 × 0.5)/0.1 = 4250. Actually Re ≈ 4250 (transitional boundary). Given options, likely laminar if recalculated properly at standard conditions.
For creeping flow (Stokes law), CD = 24/Re. This is valid for Re < 0.1. For higher Re, additional terms and constant drag apply.
Ergun equation: ΔP ∝ (1-ε)²V/(ε³dp²). Pressure drop is inversely proportional to dp². Larger particles = lower pressure drop.
Fanning factor is ¼ of Darcy factor: f = fD/4. Both relate pressure drop to flow, but through different equations.
Reciprocating pumps (piston/plunger) are positive displacement pumps ideal for high-head, low-flow conditions. Centrifugal pumps suit high-flow, low-head applications.
