Dynamics of fluidca Introduction to Fluid Flow .pptx

What is Fluid Flow?
The movement of a fluid (liquid or gas) due to forces like pressure, gravity, or external influence.

Why is Fluid Flow Important?
Essential in engineering (pipelines, aerodynamics, hydraulics).

Natural phenomena (weather patterns, ocean currents, blood circulation).

Industrial applications (aircraft design, oil and gas transport).

Types of Fluids:
Liquids
Gases

1. Dynamics of luid NAME: SOUMIK BHAR UNIVERSITY ROLL NO.: 14200723005 DEPARTMENT: MECHANICAL ENGINEERING SUBJECT NAME: SUBJECT CODE: SEMISTER: 4 th

2. Introduction to Fluid Flow What is Fluid Flow? The movement of a fluid (liquid or gas) due to forces like pressure, gravity, or external influence. Why is Fluid Flow Important? Essential in engineering (pipelines, aerodynamics, hydraulics). Natural phenomena (weather patterns, ocean currents, blood circulation). Industrial applications (aircraft design, oil and gas transport). Types of Fluids: Liquids Gases

3. Types of Fluid Flow Based on Flow Characteristics: Laminar Flow: [ Re < 2000] Smooth, orderly, and parallel layers. Low velocity, minimal mixing. Turbulent Flow: [ Re > 4000 ] Chaotic, irregular motion, eddies, and vortices. High velocity, significant mixing. Transitional Flow: [2000 < Re < 4000] A mix of laminar and turbulent flow. Based on Compressibility: Incompressible Flow Compressible Flow Based on Time Dependence: Steady Flow Unsteady Flow

4. Euler’s Equation What is Euler’s Equation? Euler's equations for fluid mechanics describe the motion of an inviscid (zero viscosity) fluid. They are derived from the Navier-Stokes equations by neglecting the viscosity terms. Assumes inviscid (frictionless) flow  

5. Navier-Stokes Equations General Form of the Navier-Stokes Equations For an incompressible, Newtonian fluid, the Navier-Stokes equation in vector form is:

6. Bernoulli’s Equation – Energy Conservation in Fluids What is Bernoulli’s Theorem? Bernoulli’s theorem states that the total energy in a steady, incompressible, and frictionless fluid remains constant along a streamline. It is derived from Euler’s equation and is a form of the conservation of energy for fluid motion. 🔹 2. Bernoulli’s Equation:  

7. Derivation of Bernoulli’s Equation from Euler’s Equation Integration Along a Streamline Euler’s equation in the direction of fluid flow is: For steady flow ( ), the equation simplifies to: Rearrange the equation: Now, integrate each term   Multiplying by ρ to express in terms of energy per unit volume:  

8. Viscosity – The Resistance to Flow What is Viscosity? Viscosity (μ) is the property of a fluid that resists motion due to internal friction between its layers. It determines how easily a fluid flows. Higher viscosity → Fluid flows slowly Lower viscosity → Fluid flows quickly Types of Viscosity: Dynamic Viscosity ( ) Measures a fluid’s internal resistance to flow. Units: Pa·s (Pascal-second) or N·s/m² . Kinematic Viscosity ( ) Ratio of dynamic viscosity to fluid density: ​ Units: m²/s . Types of Fluids Based on Viscosity: Newtonian Fluids – Constant viscosity, e.g., water, air. Non-Newtonian Fluids – Viscosity changes with shear stress, e.g., blood, ketchup.  

9. Reynolds Number What is Reynolds Number? Reynolds Number (Re) is a dimensionless number used to predict whether a fluid flow is laminar, turbulent, or transitional . It represents the ratio of inertial forces (momentum) to viscous forces (friction) in a fluid. Reynolds Number Formula: ​ Where: = Reynolds Number = Fluid density (kg/m³) = Flow velocity (m/s) = Characteristic length (m) (e.g., pipe diameter, wing length) = Dynamic viscosity ( Pa·s ) =Kinematic viscosity (m²/s)  

10. Reynolds Number Reynolds Number (𝑅𝑒) Flow Type Characteristics Re<2000 Laminar Flow Smooth, orderly layers (low turbulence) 2000<Re<4000 Transitional Flow Mix of laminar & turbulent regions Re>4000 Turbulent Flow Irregular, chaotic motion with eddies Factors Affecting Reynolds Number: Velocity (v) – Higher velocity increases Re. Fluid Viscosity ( μ) – Higher viscosity decreases Re (resists flow). Characteristic Length (L) – Larger pipes or objects increase Re.

11. Real-World Applications of Fluid Flow

12. Conclusion Euler’s & Bernoulli’s Equations – Describe ideal, inviscid flow based on energy conservation. Navier-Stokes Equations – Govern real-world fluid flow by including viscosity effects. Viscosity & Reynolds Number – Determine whether flow is laminar or turbulent. Real-World Applications – Fluid dynamics is crucial in engineering, medicine, weather prediction, and transportation. Helps optimize designs in aerospace, automotive, and industrial systems. Improves healthcare through better understanding of blood flow and respiration. Aids in environmental studies like weather forecasting and ocean circulation.

13. References https://www.geeksforgeeks.org/applications-of-fluid-dynamics/ https://byjus.com/physics/reynolds-number/ https://en.wikipedia.org/wiki/Reynolds_number https://www.engineeringtoolbox.com/laminar-transitional-turbulent-flow-d_577.html https://en.wikipedia.org/wiki/Viscosity https://byjus.com/physics/fluid-flow/ https://www.thermal-engineering.org/what-is-navier-stokes-equation-definition/ https://en.wikipedia.org/wiki/Euler_equations_(fluid_dynamics)