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Quizzes > Science

Fluids and Conservation Laws Quiz

15 questions with instant results - a fluid mechanics practice quiz to sharpen skills.

Editorial: Review CompletedCreated By: Shreyas LenkalaUpdated Aug 27, 2025
Difficulty: Moderate
Questions: 15
Study OutcomesAdditional Reading
3D voxel art representation for the course Fundamentals of Fluid Dynamics

This fluids and conservation laws quiz helps you check core ideas like continuity, momentum, and energy in fluid dynamics. Answer 15 quick questions with instant feedback, then build skills with our mechanical engineering fundamentals quiz, a focused dynamics quiz, and a hands-on convection quiz.

Which mathematical expression represents the continuity equation for an incompressible fluid?
∇·v = 0
∂ϝ/∂t + ∇·(ϝv) = 0
∇-v = 0
∂v/∂t + (v·∇)v = -∇p/ϝ + ν∇²v
For an incompressible fluid, density is constant, which simplifies the continuity equation to ∇·v = 0. This equation ensures conservation of mass within the flow.
What does the Reynolds number quantify in fluid dynamics?
The ratio of gravitational forces to inertial forces
The ratio of viscous forces to inertial forces
The ratio of inertial forces to viscous forces
The ratio of pressure forces to gravitational forces
The Reynolds number is a dimensionless parameter that compares inertial forces with viscous forces in a flow. Its value helps predict whether the flow will be laminar or turbulent.
Which assumption is fundamental in ideal inviscid flow theory?
Heat conduction effects are the primary concern
Viscous effects are neglected
The fluid density varies significantly with pressure
Turbulence is assumed to be dominant
Ideal inviscid flow theory assumes that the fluid has zero viscosity, effectively neglecting frictional forces. This simplifies the governing equations to focus on inertial and pressure forces.
Bernoulli's equation in an ideal fluid flow establishes a relationship between which three quantities?
Acceleration, pressure, and volume
Pressure, velocity, and elevation
Pressure, temperature, and density
Viscous shear, velocity, and density
Bernoulli's equation relates the pressure, kinetic energy per unit volume (through velocity), and potential energy per unit volume (through elevation) along a streamline. It provides a useful energy conservation principle for ideal fluid flows.
In compressible high-speed flows, a high Mach number typically leads to which phenomenon?
Complete suppression of turbulence
Transition to incompressible flow behavior
Formation of shock waves
Elimination of flow separation
At high Mach numbers, compressibility effects become significant and can lead to the formation of shock waves. These shocks are characterized by abrupt changes in pressure, temperature, and density.
When analyzing internal flows in a pipe, which non-dimensional number is most critical for predicting the transition from laminar to turbulent flow?
Euler number
Reynolds number
Mach number
Froude number
The Reynolds number is essential for determining flow regimes in pipes by comparing inertial and viscous forces. Its value reveals whether the flow will remain laminar or transition to turbulence.
In the Navier-Stokes equations, which term is responsible for the viscous diffusion of momentum?
ν∇²v
∇p/ϝ
(v·∇)v
∂v/∂t
The term ν∇²v in the Navier-Stokes equations describes the diffusion of momentum due to viscosity. It becomes particularly significant in flows with high viscous effects or near solid boundaries.
Why is the boundary layer typically much thinner than the characteristic dimensions of a body in fluid flow?
Viscous effects are significant only near the solid surface
The entire flow is dominated by inviscid phenomena
Pressure gradients are substantially larger away from the surface
Thermal conduction dominates far from the surface
In boundary layer theory, viscous effects are confined to a thin layer adjacent to the solid surface where the no-slip condition applies. Beyond this region, the flow is largely inviscid, resulting in a boundary layer much smaller than the overall flow domain.
In high-speed compressible flows, which phenomenon is responsible for the sudden change in flow properties such as pressure and temperature?
Laminar-turbulent transition
Shock waves
Acoustic oscillations
Gradual acceleration
Shock waves are characteristic of high-speed compressible flows and lead to abrupt changes in pressure, temperature, and density. This discontinuity is a direct result of compressibility effects at supersonic speeds.
How does an increase in viscosity affect the flow around an object?
It only affects pressure distribution, not drag
It eliminates the formation of a boundary layer
It decreases the boundary layer thickness and drag
It increases the boundary layer thickness and drag
An increase in viscosity enhances momentum diffusion, thickening the boundary layer and increasing frictional (skin friction) drag. This effect is particularly noticeable in flows over surfaces, where viscous forces play a key role.
For isentropic processes in compressible flows, which relation is used to connect pressure and density?
p/ϝ = constant
p/ϝ^γ = constant
pϝ = constant
pϝ^γ = constant
In isentropic flow, where the process is both adiabatic and reversible, the relation p/ϝ^γ = constant holds. This relation is instrumental in analyzing compressible flows under the assumption of constant entropy.
Which forms of energy are incorporated in the conservation of energy equation for fluid flow?
Internal energy and pressure energy only
Kinetic, potential, and internal energy
Only kinetic energy
Kinetic and potential energy only
The conservation of energy equation in fluid dynamics accounts for kinetic energy, potential energy (typically from gravity), and internal energy. This comprehensive energy balance is essential for accurately modeling the behavior of fluid systems.
When performing a momentum balance on a control volume in fluid dynamics, which fundamental principle is applied?
Bernoulli's principle
Archimedes' principle
Newton's second law applied to fluids
Pascal's law
A momentum balance in fluid dynamics relies on Newton's second law, which relates the rate of change of momentum to the sum of forces acting on the control volume. This principle provides the foundation for analyzing fluid forces and the resulting motion.
In inviscid flow analysis, which assumption simplifies the Navier-Stokes equations into Euler's equations?
Steady state conditions
Constant temperature
Uniform gravitational field
Negligible viscous forces
By assuming that viscous forces are negligible, the viscous diffusion terms in the Navier-Stokes equations drop out. This simplification leads to Euler's equations, which govern inviscid flow dynamics.
In the analysis of incompressible flows, which property is typically assumed to be constant?
Density
Pressure
Velocity
Viscosity
In incompressible flow analysis, the density of the fluid is assumed to remain constant. This assumption greatly simplifies the governing equations by decoupling variations in density from pressure and velocity changes.
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Study Outcomes

  1. Analyze the principles governing both viscous and inviscid fluid flows.
  2. Apply mathematical techniques to solve problems in incompressible flow dynamics.
  3. Evaluate the impacts of compressibility in high speed flow scenarios.
  4. Integrate theoretical concepts with practical applications in fluid mechanics.

Fundamentals Of Fluid Dynamics Additional Reading

Ready to dive into the fascinating world of fluid dynamics? Here are some top-notch resources to guide your journey:

  1. This undergraduate course offers a comprehensive introduction to fluid mechanics, covering topics like pressure, hydrostatics, buoyancy, and flow through pipes. It includes problem sets and exams to test your understanding.
  2. A collection of essays delving into advanced topics such as Lagrangian and Eulerian representations, dimensional analysis, and the Coriolis effect. Ideal for those seeking a deeper understanding of fluid dynamics concepts.
  3. Offered by École Polytechnique, this course explores the interactions between fluids and solid structures, providing insights into real-world applications and challenges in engineering.
  4. Presented by the University of Minnesota, this course delves into the principles and applications of fluid power systems, including hydraulics and pneumatics, essential for various engineering fields.
  5. A comprehensive lecture series covering fundamental concepts of fluid mechanics, including fluid statics, kinematics, and dynamics, suitable for both beginners and those seeking a refresher.
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