Fluid Mechanics
What is Fluid Mechanics?
A curve that is everywhere tangent to the instantaneous velocity vector of the flow.
Key formula / rule: Continuity Equation (Incompressible Flow)
Key points
- Understand the difference between Eulerian and Lagrangian descriptions.
- Define and calculate fluid velocity and acceleration.
- Apply the continuity equation to solve flow problems.
- Understand the concepts of vorticity and strain rate.
Common exam trap
Confusing streamlines with pathlines.
Definitions
- Term
Streamline
- Meaning
A curve that is everywhere tangent to the instantaneous velocity vector of the flow.
- Term
Pathline
- Meaning
The actual path traced by a fluid particle over a period of time.
- Term
Streakline
- Meaning
The locus of fluid particles that have passed through a particular point in space at different ×.
- Term
Vorticity
- Meaning
A vector quantity representing the local rotation of a fluid element. It is twice the local angular velocity.
Learning objectives
Understand the difference between Eulerian and Lagrangian descriptions.
Define and calculate fluid velocity and acceleration.
Apply the continuity equation to solve flow problems.
Understand the concepts of vorticity and strain rate.
Differentiate between streamlines, pathlines, and streaklines.
Formulae
- Name
Continuity Equation (Incompressible Flow)
- Note
Relates the cross-sectional area (A) and average velocity (V) at two points in a steady, incompressible flow. Assumes uniform velocity across the section.
- Expression
A₁V₁ = A₂V₂
- Name
Material Derivative
- Note
Represents the total rate of change of a property following a fluid particle.
- Expression
D/Dt = ∂/∂t + u ∂/∂x + v ∂/∂y + w ∂/∂z
- Name
Vorticity Vector
- Note
Measures the local angular velocity or rotation of a fluid element. For 2D flow in xy-plane, ω = (∂v/∂x - ∂u/∂y) k.
- Expression
ω = ∇ × V
Prerequisites
Basic understanding of calculus (differentiation and integration).
Familiarity with vectors and vector calculus.
Concepts of density and pressure.
Common mistakes
Confusing streamlines with pathlines.
Incorrectly applying the continuity equation to compressible flows without accounting for density changes.
Misinterpreting vorticity as overall flow rotation rather than local angular velocity.
Assuming steady flow conditions when they are not applicable.
Keywords
Fluid Kinematics
Eulerian
Lagrangian
Velocity
Acceleration
Continuity Equation
Vorticity
Streamline
Pathline
Streakline
Material Derivative
Practice preview
Which of the following statements is INCORRECT regarding viscosity?…
easy
Which of the following statements about the boundary layer is INCORRECT?…
medium
What is the absolute pressure at a depth of 5 meters in water, if the atmospheric pressure is 101.3 kPa and the specific weight of water is 9.81 kN/m^3?…
easy