Govt. Exams
Entrance Exams
F_D ∝ V². When V doubles (V₂ = 2V₁), F_D increases by factor of (2)² = 4
ΔP = ρ_Hg × g × h = 13,600 × 9.81 × 0.05 = 6,667 Pa
For laminar flow in circular pipes, the Hagen-Poiseuille solution gives f = 64/Re. This is independent of roughness and applies for Re < 2300.
By continuity equation: A₁V₁ = A₂V₂. π(0.1)²/4 × 3 = π(0.05)²/4 × V₂. V₂ = (0.01/0.0025) × 3 = 12 m/s
In laminar flow through circular pipes, the velocity distribution follows Hagen-Poiseuille flow with parabolic profile. Maximum velocity is at the centerline (V_max = 2×V_avg), and velocity is zero at the wall (no-slip condition).
Re = (V×D)/ν = (2×0.05)/(1.0×10⁻⁶) = 0.1/(1.0×10⁻⁶) = 100,000
Bernoulli equation in head form: P/ρg + V²/2g + Z = constant. Option A is energy form, C is Darcy-Weisbach, D is modified form.
Critical or sonic conditions occur at Mach number = 1.0, where velocity equals the speed of sound in the fluid.
The H-Q (head vs flow rate) curve is the primary pump characteristic curve that shows how head decreases as flow rate increases.
Cavitation occurs when NPSH available < NPSH required. Here 4.5 > 3.2, so cavitation is prevented and pump operates safely.
