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Fluid Kinematics

Fluid Kinematics, tailored for competitive exams like SSC JE, HPCL, and other PSUs—along with relevant previous year questions (PYQs) and their explanations.

๐Ÿ’ง Fluid Kinematics – 

✅ What is Fluid Kinematics?

Fluid kinematics is the study of fluid motion without considering the forces or energy that cause the motion. It focuses only on velocity, acceleration, and flow description using streamlines, pathlines, etc.

๐Ÿ“˜ Key Concepts in Fluid Kinematics

1. Types of Flow

Flow Type Description
Steady Flow Flow properties (velocity, pressure) do not change with time
Unsteady Flow Flow properties vary with time
Uniform Flow Properties are the same at every point in space
Non-Uniform Flow Properties vary from point to point
Laminar Flow Streamlined, orderly layers (Re < 2000)
Turbulent Flow Random, chaotic flow (Re > 4000)
Compressible Flow Density changes (gases)
Incompressible Flow Density constant (liquids)

2. Flow Descriptors

Term Meaning
Streamline A line tangent to the velocity vector at every point
Pathline Actual path followed by a fluid particle
Streakline Locus of particles that have passed through a common point
Stream Function (ฯˆ) 2D representation; constant along streamlines
Velocity Potential (ฯ•) Scalar function; flow is irrotational if it exists

3. Continuity Equation

For incompressible and steady flow:

A1V1=A2V2A_1 V_1 = A_2 V_2

For general flow:

∂ฯ∂t+∇⋅(ฯV⃗)=0\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \vec{V}) = 0

4. Acceleration in a Fluid Particle

a⃗=Dv⃗Dt=∂v⃗∂t+(v⃗⋅∇)v⃗\vec{a} = \frac{D\vec{v}}{Dt} = \frac{\partial \vec{v}}{\partial t} + (\vec{v} \cdot \nabla)\vec{v}

5. Flow Visualization Tools

  • Flow net: Combination of streamlines and equipotential lines

  • Streamlines are useful in steady incompressible flow

  • Streaklines are observed in smoke or dye experiments

๐Ÿง  Common PYQs (SSC JE / HPCL / PSU Level)

๐Ÿ”ธ Q1. In steady flow of a fluid, which property remains constant at a point?

A. Pressure
B. Velocity
C. Density
D. Flow Rate
๐Ÿ‘‰ Answer: B

✅ Explanation: In steady flow, fluid velocity at a point does not change with time.

๐Ÿ”ธ Q2. Which of the following represents the continuity equation for incompressible fluid?

A. ∂u/∂x + ∂v/∂y = 0
B. ∂u/∂x + ∂v/∂x = 0
C. u + v = 0
D. ∂u/∂t + ∂v/∂t = 0
๐Ÿ‘‰ Answer: A

✅ Explanation: For 2D incompressible steady flow, the divergence of velocity is zero.

๐Ÿ”ธ Q3. A streamline is a line which is everywhere _______ to the velocity vector.

A. Parallel
B. Perpendicular
C. Tangent
D. Orthogonal
๐Ÿ‘‰ Answer: C

✅ Explanation: By definition, streamlines are always tangent to local fluid velocity vectors.

๐Ÿ”ธ Q4. In a steady flow, the pathline and streamline are:

A. Always different
B. Always same
C. Sometimes same
D. Never same
๐Ÿ‘‰ Answer: B

✅ Explanation: In steady flow, all types of flow lines (streamline, pathline, streakline) are identical.

๐Ÿ”ธ Q5. In which flow, the flow parameters change with time?

A. Steady
B. Uniform
C. Unsteady
D. Compressible
๐Ÿ‘‰ Answer: C

✅ Explanation: In unsteady flow, parameters like velocity and pressure vary with time.

๐Ÿ”ธ Q6. Flow is said to be rotational when:

A. Vorticity is zero
B. Stream function exists
C. Curl of velocity vector is non-zero
D. Continuity equation is not satisfied
๐Ÿ‘‰ Answer: C

✅ Explanation: A flow is rotational if the curl of velocity ≠ 0 (vorticity exists).

๐Ÿ“ Quick Revision Table

Term Meaning
Steady Flow ∂/∂t = 0
Incompressible ฯ = constant
Streamline Tangent to velocity
Continuity Eq. Mass conservation
Velocity Potential Irrotational flow
Stream Function 2D incompressible flow



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