Govt. Exams
Entrance Exams
For smooth pipes at high Re, Blasius correlation (f = 0.316/Re^0.25) is used with Darcy-Weisbach equation
From Darcy-Weisbach: h_f = f(L/D)(V²/2g). Friction loss is proportional to length and approximately proportional to V² (in turbulent flow, f decreases slightly with V).
From Bernoulli's equation: P_stagnation - P_static = ½ρV². This dynamic pressure difference is measured by pitot tubes to determine local flow velocity.
Venturimeter uses Bernoulli's equation principle. The pressure difference between throat and upstream is related to flow velocity and can be used to calculate the volumetric flow rate.
The maximum height is approximately 10.3 m (or one atmosphere height), determined by h = P_atm/(ρg) = 101325/(1000 × 9.81) = 10.33 m. Friction losses reduce this in practice.
Drag force F_d = 0.5 × ρ × V² × A × Cd. The V² dependence comes from dynamic pressure (½ρV²). This applies to both skin friction and pressure drag.
For turbulent flow in smooth pipes, the Blasius equation is explicit and simpler, while Colebrook-White is implicit but more accurate. Both are used depending on applications.
Stokes law (Cd = 24/Re) applies for creeping flow where Re < 1. For low Reynolds numbers, viscous forces dominate over inertial forces.
Hagen-Poiseuille equation: Q = (πΔPd⁴)/(128μL), showing Q ∝ d⁴. This is why small diameter pipes are very sensitive to pressure drops.
The coefficient of contraction for sharp-edged orifices is typically 0.60-0.65 due to the vena contracta effect where the jet contracts after leaving the orifice.
