Fluid Dynamics This section explores how fluids behave when they’re on the move — from Bernoulli’s principle to venturi meters and head losses in pipes.Test your understanding of real-world flow applications and see how pressure, velocity, and energy balance together in motion.Perfect for learners who want to connect equations with real engineering insights! 1 / 20 The total energy line lies Coinciding with the pipe axis At atmospheric level Above the hydraulic gradient line Below the hydraulic gradient line The total energy line includes both pressure and velocity heads, so it’s always above the hydraulic gradient. 2 / 20 In a horizontal pipe, the total energy line and hydraulic gradient line are Perpendicular Parallel Intersecting Coinciding For steady flow in a horizontal pipe, energy losses are uniform, keeping lines parallel. 3 / 20 The discharge through a venturi meter increases when Pipe diameter decreases Fluid density decreases Flow becomes turbulent Pressure difference increases Higher pressure difference means higher velocity and hence greater flow rate. 4 / 20 In laminar flow, the head loss is proportional to Velocity Velocity squared Pressure Area In laminar regime, head loss ∝ velocity, while in turbulent regime it ∝ velocity². 5 / 20 The Hagen–Poiseuille equation applies to Laminar flow through circular pipes Turbulent flow Flow over flat plate Flow through nozzles It defines relation between pressure drop and flow rate for viscous, laminar flow in pipes. 6 / 20 The discharge through an orifice is given by a × h Cd × √(2gh) a × √(2gh) Cd × a × √(2gh) The actual discharge depends on the orifice area, head, and coefficient of discharge. 7 / 20 The flow in a pipe is turbulent if Reynolds number is Greater than 4000 Less than 2000 Equal to 2000 Between 0 and 1000 At high Reynolds numbers, inertial forces dominate viscous forces, creating turbulence. 8 / 20 Flow separation occurs when Viscosity becomes zero Adverse pressure gradient causes reversal of flow Velocity increases suddenly Pressure is constant Flow separates when the fluid decelerates against an increasing pressure region, leading to turbulence. 9 / 20 In a nozzle, the velocity of fluid Decreases as pressure decreases Remains constant Becomes zero Increases as pressure decreases According to Bernoulli’s principle, as pressure energy drops, velocity energy rises 10 / 20 The value of coefficient of discharge for a venturi meter generally lies between 0.7 to 0.8 1.0 to 1.2 0.95 to 0.99 0.5 to 0.6 Venturi meters have high efficiency with minimal losses, giving Cd values close to 1.0. 11 / 20 The coefficient of discharge is the ratio of Actual discharge to theoretical discharge Theoretical discharge to actual discharge Velocity head to total head Measured head to velocity head It corrects for energy losses and gives the real discharge from theoretical calculations. 12 / 20 The head loss due to friction in pipes is given by Archimedes’ principle Darcy–Weisbach equation Bernoulli’s equation Pascal’s law Darcy–Weisbach equation relates head loss to pipe length, diameter, flow velocity, and friction factor. 13 / 20 The loss of energy due to fluid friction in a pipe is called Energy drop Pressure head Head loss Velocity loss When fluid flows through a pipe, friction converts part of mechanical energy into heat, causing head loss. 14 / 20 The flow through a nozzle is an example of Rotational flow Uniform flow Steady flow Unsteady flow The velocity and flow rate remain constant with time — hence steady flow. 15 / 20 In a horizontal venturi meter, pressure is Maximum at inlet and minimum at throat Minimum at inlet and maximum at throat Constant throughout Zero at throat As velocity increases at the throat, pressure decreases — a direct result of Bernoulli’s principle. 16 / 20 The device based on Bernoulli’s principle used to measure flow rate is Orifice plate Barometer Venturimeter Manometer Venturimeter uses pressure difference between two points in a pipe to measure discharge. 17 / 20 Bernoulli’s equation holds good for Turbulent flow Viscous flow Compressible flow Inviscid, incompressible, steady flow along a streamline It assumes fluid is non-viscous, incompressible, and flowing steadily without energy losses. 18 / 20 The total head in a flowing fluid is equal to Pressure head + Velocity head + Potential head Pressure head + Density head Velocity head + Energy head Pressure head only Total head is the sum of pressure energy, kinetic energy, and potential energy per unit weight. 19 / 20 In Bernoulli’s equation, head due to pressure is represented as V²/2g z pV p/ρg The term p/ρg represents the pressure head or energy per unit weight due to pressure. 20 / 20 Bernoulli’s equation is based on the principle of Conservation of energy Conservation of mass Conservation of momentum Conservation of volume Bernoulli’s theorem states that the total energy (pressure + kinetic + potential) of a fluid remains constant along a streamline. 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