Govt. Exams
Entrance Exams
Lowering inlet pressure decreases (P - Pv), reducing σ. Raising temperature increases Pv, also reducing σ. Both conditions increase cavitation risk in turbomachinery. This is critical in high-speed pump operations.
The √x dependence comes from solving the Navier-Stokes equations with boundary layer approximations (Blasius solution). This is fundamental to aerodynamic design in Indian aircraft industries.
Specific speed Ns < 50 indicates Pelton turbines, 50-250 indicates Francis turbines, and >250 indicates Kaplan turbines. This classification is essential in hydroelectric projects across Indian dams.
At very high Reynolds numbers in rough pipes, friction factor depends only on relative roughness, not Re. This region is called the 'fully turbulent' or 'zone of complete turbulence' region in the Moody diagram.
In a converging nozzle with subsonic inlet flow, velocity increases and Mach number increases as flow approaches throat. This principle is critical in rocket propulsion and aerospace applications in India.
From Bernoulli: P₁/ρg + V₁²/2g = P₂/ρg + V₂²/2g. Using continuity A₁V₁ = A₂V₂, and solving: V₁ = √(2(P₁-P₂)/(ρ(A₂²/A₁²-1))) ≈ 10.5 m/s. Venturi tubes are standard in flow measurement systems.
The perpendicular force component = ρQV²sin(θ), where Q is discharge and V is velocity. This principle is used in water turbines and industrial jet applications.
Force = ρAV²(1 - cos60°) = 1000 × 0.02 × 64 × 0.5 = 6.4 kN. The deflection angle affects the force component.
From Bernoulli and continuity: V₂ = √(2ΔP/(ρ(A₁²/A₂² - 1))) = √(16000/(1000 × 15)) = 4.12 m/s
Using momentum equation with 45° deflection, the resultant force = ρAV² × √2 = 1000 × 0.000707 × 225 × 1.414 = 2648 N