Mechanical Engineering
Fluid Mechanics

τ = μ(du/dy) = 0.1 × 50 = 5 Pa

Continuity equation for incompressible flow states Q = constant, so A₁v₁ = A₂v₂

Head H ∝ D²N² at constant N, so head increases by 2² = 4 times

Equivalent length L_e = K × (d/f) ≈ 0.9 × (0.05/0.02) ≈ 2.25 m for typical elbow

Cavitation occurs when local pressure drops below fluid vapor pressure, causing vapor bubbles to form.

M < 0.3 indicates incompressible flow approximation is valid; compressibility effects are negligible.

Force component = ρQv(1 - cos θ) where θ is deflection angle from momentum equation.

Re = vd/ν = (2 × 0.5)/(2 × 10⁻⁴) = 5000 > 4000, so turbulent

Critical depth in open channel flow corresponds to Fr = 1, minimum specific energy condition.

Fr = v/√(gL) compares inertial forces (ρv²) with gravitational forces (ρgL).