Fluid Dynamics and Viscosity

topicmedium8 MCQ

Equation of continuity, Bernoulli's theorem, Stokes' law and terminal velocity. (Physics › Properties of Bulk Matter, NEET UG syllabus.)

What is Fluid Dynamics and Viscosity?

The branch of fluid mechanics that studies the motion of fluids and the forces acting on them.

Key formula / rule: Equation of Continuity

Define and explain key terms such as fluid dynamics, viscosity, streamline flow, and turbulent flow.
State and apply the Equation of Continuity to solve problems involving fluid flow through varying cross-sections.
State and apply Bernoulli's Theorem to analyze fluid flow in different scenarios, understanding its energy conservation aspect.
Explain Stokes' Law and calculate the viscous drag force on a spherical object moving through a fluid.

Forgetting the ideal fluid assumptions (incompressible, non-viscous, steady, irrotational) when applying Bernoulli's theorem.

Term: Fluid Dynamics
Meaning: The branch of fluid mechanics that studies the motion of fluids and the forces acting on them.

Term: Viscosity
Meaning: A measure of a fluid's resistance to flow, arising from internal friction between its layers.

Term: Streamline Flow (Laminar Flow)
Meaning: Fluid flow where every particle passing a given point follows the same path as particles that passed it previously, with no abrupt changes in velocity.

Term: Turbulent Flow
Meaning: Irregular, chaotic fluid flow characterized by unpredictable changes in pressure and velocity, often involving eddies and swirls.

Term: Coefficient of Viscosity (η)
Meaning: A proportionality constant that quantifies a fluid's resistance to shear flow, representing the internal friction.

Term: Terminal Velocity
Meaning: The constant maximum velocity attained by an object falling through a fluid when the net force acting on it (gravitational, buoyant, and viscous drag) becomes zero.

Define and explain key terms such as fluid dynamics, viscosity, streamline flow, and turbulent flow.
State and apply the Equation of Continuity to solve problems involving fluid flow through varying cross-sections.
State and apply Bernoulli's Theorem to analyze fluid flow in different scenarios, understanding its energy conservation aspect.
Explain Stokes' Law and calculate the viscous drag force on a spherical object moving through a fluid.
Derive and apply the formula for terminal velocity of a spherical object, considering gravitational, buoyant, and viscous forces.
Identify and explain real-world applications of fluid dynamics and viscosity principles.

Name: Equation of Continuity
Note: For an incompressible fluid in steady flow, A is the cross-sectional area and v is the fluid speed. This represents the conservation of mass.
Expression: A₁v₁ = A₂v₂

Name: Bernoulli's Equation
Note: P is pressure, ρ is fluid density, v is fluid speed, g is acceleration due to gravity, h is height. Applies to ideal fluid (incompressible, non-viscous) in streamline flow, representing conservation of energy.
Expression: P + ½ρv² + ρgh = constant

Name: Viscous Force (Stokes' Law)
Note: F_v is the viscous drag force, η is the coefficient of viscosity, r is the radius of the spherical object, and v is its speed relative to the fluid. Valid for laminar flow around the sphere.
Expression: F_v = 6πηrv

Name: Terminal Velocity of a Sphere
Note: v_t is the terminal velocity, r is the sphere radius, ρ_object is the sphere's density, ρ_fluid is the fluid's density, g is acceleration due to gravity, and η is the fluid's viscosity.
Expression: v_t = [2r²(ρ_object - ρ_fluid)g] / (9η)

Forgetting the ideal fluid assumptions (incompressible, non-viscous, steady, irrotational) when applying Bernoulli's theorem.
Incorrectly applying Stokes' law to non-spherical objects or in turbulent flow conditions.
Confusing the density of the object and the fluid in the terminal velocity formula.
Misinterpreting the relationship between pressure and velocity in Bernoulli's principle (higher velocity means lower pressure).
Not accounting for buoyant force when calculating net force for terminal velocity.

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Which of the following factors does NOT directly influence the viscous force acting on a small spherical body falling through a fluid according to Stokes' law?…
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