Govt. Exams
Entrance Exams
U₂ = π × 0.3 × 1500/60 = 23.56 m/s. This velocity is critical in pump design as it affects the Euler's head and pump efficiency in Indian water supply and irrigation projects.
In Bernoulli's equation (P/ρg + V²/2g + Z = constant), when flow is in a horizontal pipe at constant elevation, Z (potential energy head) remains constant and can be neglected in differential form.
Using continuity equation: A₁V₁ = A₂V₂. Area ratio = (D₁/D₂)² = (100/50)² = 4. Therefore V₂/V₁ = 4:1. This is critical for pipe flow analysis in water supply systems.
Pascal's law states that pressure applied to a confined fluid is transmitted undiminished in all directions. This principle is fundamental to hydraulic systems used in Indian industries.
Mach number classification: M < 1 (subsonic), M = 1 (sonic), 1 < M < 5 (supersonic), M > 5 (hypersonic). M = 1.2 is supersonic.
In a convergent nozzle, pressure decreases and velocity increases due to Bernoulli's principle. Temperature may decrease due to pressure drop.
Hagen-Poiseuille equation applies only to laminar flow where Re < 2300. Beyond this critical value, flow becomes transitional or turbulent.
By continuity equation A₁V₁ = A₂V₂. Since diameter ratio is 2:1, area ratio is 4:1, so V₂ = 1.5 × 4 = 6.0 m/s
Ketchup is a pseudoplastic fluid whose viscosity changes with shear rate. Water, air, and mercury are Newtonian fluids with constant viscosity.
Shear stress τ = μ × (du/dy) = 0.8 × 100 = 80 Pa. This is a direct application of Newton's law of viscosity.
