CIVL2103_ch4 - Kinematics Quiz

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Questions and Answers

What is a key characteristic of the Lagrangian description of fluid motion?

  • It describes properties as functions of space only.
  • It focuses on the forces acting on the fluid.
  • It tracks individual fluid particles over time. (correct)
  • It observes properties at fixed points in space.

In the context of fluid mechanics, what defines the Eulerian approach?

  • Analyzing the individual motion of fluid particles.
  • Calculating the forces acting on the fluid.
  • Tracking fluid particles based on their initial position.
  • Observing the flow at specific locations and times. (correct)

Which statement best describes fluid kinematics?

  • It calculates the rates of energy transfer in fluids.
  • It describes pressure changes within a fluid.
  • It involves analyzing the forces acting on fluid motion.
  • It focuses only on the motion of fluids without considering forces. (correct)

What does the Reynolds Transport Theorem help to calculate?

<p>The changing rate of properties in a control volume. (B)</p> Signup and view all the answers

Which of the following best describes streaklines in fluid flow?

<p>They are imaginary lines that connect points of fluid motion recorded over time. (D)</p> Signup and view all the answers

What characterizes steady flow in fluid dynamics?

<p>Velocity is only a function of position. (A), Flow properties do not change with time. (D)</p> Signup and view all the answers

Which type of flow is characterized by fluid properties that are functions of time?

<p>Unsteady flow (A)</p> Signup and view all the answers

How can unsteady flows be categorized?

<p>Periodic, non-periodic, and random (A)</p> Signup and view all the answers

Which of the following best describes a streamline?

<p>Curves that are tangent to the velocity vector at every point. (A)</p> Signup and view all the answers

What visualization technique joins all present locations of fluid particles that have passed through a specific point?

<p>Streakline (D)</p> Signup and view all the answers

In which dimensional flow does velocity not change with one or two of the space coordinates?

<p>One-dimensional flow (A), Two-dimensional flow (D)</p> Signup and view all the answers

Which of the following statements is true regarding flow visualization?

<p>It utilizes particles like smoke or dyes to represent fluid movement. (D)</p> Signup and view all the answers

In steady flow, streaklines, pathlines, and streamlines will:

<p>Have the same pattern. (B)</p> Signup and view all the answers

What is the net rate of increase of the algae population per minute?

<p>0.2% (B)</p> Signup and view all the answers

In the Eulerian description, what does the velocity at a point represent?

<p>The velocities of different fluid particles passing that point (B)</p> Signup and view all the answers

How is the acceleration vector field of the flow expressed using Newton’s second law?

<p>a = dU/dt = (du/dt) + (dv/dt) + (dw/dt) (C)</p> Signup and view all the answers

What is the 'total acceleration' at a point derived from in the Eulerian framework?

<p>Both local and convective acceleration (C)</p> Signup and view all the answers

Which mathematical principle is used to obtain the scalar time derivatives in the Eulerian description?

<p>Chain rule (C)</p> Signup and view all the answers

What principle does flow continuity express regarding mass in a flow section?

<p>Mass inflow equals mass outflow. (D)</p> Signup and view all the answers

Which equation is used to describe the relationship between fluid density, cross-sectional area, and fluid velocity at two points?

<p>$\rho_1A_1v_1 = \rho_2A_2v_2$ (A)</p> Signup and view all the answers

How is the flux of a scalar concentration, such as sediment, calculated?

<p>$B_m = \int a \rho (U \cdot n) dA$ (D)</p> Signup and view all the answers

What does a control volume focus on in fluid mechanics?

<p>A region of space surrounded by a control surface. (D)</p> Signup and view all the answers

What does the Reynolds Transport Theorem primarily deal with?

<p>The use of conservation laws to analyze material volume changes. (A)</p> Signup and view all the answers

In the conservation of mass, what is true about a closed system over time?

<p>Mass remains constant. (B)</p> Signup and view all the answers

Which of the following represents an example of a scalar concentration carried by fluid flow?

<p>Temperature of the fluid (D)</p> Signup and view all the answers

What defines the rate of change of momentum in a system according to fluid mechanics?

<p>It equals the sum of external forces acting on the mass. (B)</p> Signup and view all the answers

What does dBsys/dt represent in the context provided?

<p>The rate of change of an extensive property (B)</p> Signup and view all the answers

In the context of Reynolds Transport Theorem, what happens to the first term on the right-hand side during steady flow problems?

<p>It becomes zero. (B)</p> Signup and view all the answers

When analyzing a fixed control volume with multiple boundary sections, what determines the change in a property of the system?

<p>The fluxes through the control surface (C)</p> Signup and view all the answers

For a system at time t = 1:30 pm with 50,000 m³ of water, which property is primarily being analyzed?

<p>The energy of the system (B)</p> Signup and view all the answers

In the expression given, what does the variable β represent?

<p>The specific energy (A)</p> Signup and view all the answers

What does the differential form of the control volume equation provide regarding the extensive property B?

<p>It relates changes in B to fluid flow across boundaries. (C)</p> Signup and view all the answers

Which equation describes the rate of change of the extensive property B across the control volume?

<p>$\frac{dB_{sys}}{dt} = \int_C^{V} \beta \rho dV + \int_C^{S} \beta \rho (U \cdot n) dA$ (A)</p> Signup and view all the answers

How can the rate of change of energy of the system in a fixed control volume be calculated?

<p>By applying the control-volume equation using energy as the property (B)</p> Signup and view all the answers

What does the volume flow rate (Q) measure?

<p>The volume of fluid passing through a flow area per time (A)</p> Signup and view all the answers

If the fluid flow area (A) is increased while keeping the velocity (U) constant, what happens to the volumetric flow rate (Q)?

<p>It increases proportionally (B)</p> Signup and view all the answers

Which equation correctly represents the mass flow rate (ṁ) in terms of fluid density (ρ), flow area (A), and velocity (U)?

<p>ṁ = ρAU (D)</p> Signup and view all the answers

What happens to the volumetric flow rate (Q) when the net is placed at a vertical angle of 45 degrees to the fluid flow?

<p>Q is calculated using the net's inclined area (D)</p> Signup and view all the answers

In a flow scenario where the velocities vary across the area, how is the volumetric flow rate (Q) determined?

<p>Through surface integration of the velocity across the flow area (A)</p> Signup and view all the answers

What would be the volume flow rate (Q) if U = 0.3 m/s and A = 0.04 m²?

<p>0.012 m³/s (B)</p> Signup and view all the answers

Why must flow rate (Q) be connected with a flow area (A)?

<p>To quantify the amount of fluid flowing per unit time (C)</p> Signup and view all the answers

What characteristic of the fluid must be assumed to apply the equation ṁ = ρAU uniformly over a flow area?

<p>Fluid density must be consistent (B)</p> Signup and view all the answers

Flashcards

Lagrangian description

Describes fluid flow by tracking individual fluid particles over time, specifying their properties based on initial location and time.

Eulerian description

Describes fluid flow by observing properties at fixed points in space and time, recording velocities, densities, etc. as functions of location and time.

Fluid kinematics

Study of fluid flow motion without considering forces and moments.

Fluid kinetics

Study of fluid flow motion, considering the forces and moments.

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Flow rate

The rate at which mass or volume of fluid passes a given point.

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Velocity Field

Velocity as a function of space and time in fluid flow (Eulerian view).

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Steady Flow

Fluid flow where properties (velocity, temperature, etc.) don't change with time.

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Unsteady Flow

Fluid flow where properties change with time.

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3-D Flow

Fluid flow where velocity or other properties alter across all three spatial directions.

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2-D/1-D Flow

Fluid flow where velocity doesn't change along certain spatial dimensions.

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Flow Visualization

Using techniques like tracers and dye to observe and understand fluid flow patterns.

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Streamlines

Lines that are tangent to the velocity vector, showing the direction of flow.

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Steady vs. Unsteady Flow Differences

In steady flow, properties do not change with time; in unsteady flow, they do.

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Flow Rate (Q)

The volume of fluid passing through a specific area per unit of time.

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Mass Flow Rate (ṁ)

The mass of fluid flowing through a specific area per unit of time.

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Uniform Flow

Fluid velocity is the same everywhere across the flow area.

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Volumetric Flow Rate Formula (simple case)

Q = A * U, where A is the flow area and U is the uniform velocity.

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Mass Flow Rate (when density is uniform)

ṁ = ρ * A * U, where ρ is the fluid density.

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Flow Area (A)

The cross-sectional area through which the fluid flows.

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Surface Integral

Used to calculate flow when velocities are not uniform across the area.

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Discharge (Q)

Another term for volumetric flow rate.

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Flow Continuity

The principle that in a flow section bounded by solid surfaces, the mass flow rate entering the section must equal the mass flow rate leaving the section.

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Flux of Matter

The rate at which a specific substance, like sediment or energy, is transported by a fluid flow.

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Rate of Flow of Matter

The amount of a specific substance being transported by fluid flow through a given area per unit time.

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Control Volume

A region of space in which fluid properties are analyzed, typically used to study the flow through a device.

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Control Surface

The boundary of the control volume, representing the area through which fluid enters or exits.

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Conservation of Mass

The principle that the total mass within a system remains constant over time.

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Conservation of Momentum

The principle that the rate of change of momentum of a system equals the sum of external forces acting on it.

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Conservation of Energy

The principle that the rate of change of energy within a system is equal to the sum of work and heat transfer.

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Fluid Acceleration

The rate of change of velocity of a fluid particle at a given point in space and time. It's more complex than just the derivative of velocity because fluid particles are constantly moving.

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Local Acceleration

The rate of change of velocity at a fixed point in space due to changes in the velocity field over time. Like a wave increasing in height over time at a location.

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Convective Acceleration

The rate of change of velocity at a point due to the fluid particle moving from one velocity field to another. Like a boat moving from a calm river to a faster current.

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Total Acceleration

The sum of local acceleration and convective acceleration, representing the overall change in velocity of a fluid particle.

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Rate of Change of an Extensive Property

The rate at which an extensive property (like mass or energy) of a system changes over time. It's calculated by taking the limit of the change in the property over a very small time interval.

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Reynolds Transport Theorem

A fundamental theorem that links the rate of change of an extensive property of a system to the fluxes of that property across the system's boundaries. It's used to analyze the transport of mass, energy, and momentum in fluid systems.

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Flux

The rate at which a property (like mass, energy, or momentum) flows across a given area or surface.

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One-Dimensional Flux Approximation

A way to simplify the calculation of fluxes by assuming that the property being transported is uniform across the control surface.

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Rate of Change of Energy

The rate at which the total energy of a system changes. Includes changes in kinetic energy, potential energy, and internal energy.

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Study Notes

Fluid Mechanics - Kinematics

  • Fluid flow occurs over space and time, like water flow in a river.
  • Fluid kinematics describes fluid motion without considering forces.
  • Fluid kinetics describes fluid motion with driven forces.

Learning Outcomes

  • Students will understand approaches (Lagrangian vs Eulerian) to describe fluid motion.
  • Students will understand streaklines, pathlines, and streamlines.
  • Students will learn to calculate mass and volumetric flow rates.
  • Students will use control volume approach to calculate changing fluid properties (Reynolds Transport Theorem).
  • Students will describe fluid acceleration using Eulerian description for flow in motion.

Lagrangian vs Eulerian Description

  • Lagrangian: Tracks individual fluid particles in time, considering their initial location and velocity, and their behavior over time.
  • Eulerian: Observes properties (velocity, density, pressure) at fixed points in space and time in a flow. This is generally more straightforward for analyzing fluid flow.

Velocity Field

  • Velocity: A function of space and time (U = U(x, y, z, t)). Usually, there are three components of velocity in 3D space.
  • Steady Flow: Fluid properties do not change with time. In this case, the velocity is a function of only space (U = U(x, y, z)).

Steady vs Unsteady Flow

  • Steady: All flow properties (velocity, temperature, pressure, density) are independent of time.
  • Unsteady: Flow properties change with time.
  • Unsteady flows can be categorized further as periodic, non-periodic, or random flows.

Types of Flow (based on dimensions)

  • 3-Dimensional Flow: Velocity (or other fluid properties) changes with any change in any one spatial coordinate. (e.g., ocean currents, air flow)
  • 2- and 1-Dimensional Flow: Velocity (or other fluid properties) is constant along one or two of the spatial coordinates (e.g. flow of water in a pipe)

Flow Visualization

  • Flow visualization techniques help observe fluid motion. Typical methods include:
    • Wind vanes/threads attached to rods (for wind direction)
    • Tracers such as smoke, dust, bubbles or dyes (for liquid or gas flows)
  • Streaklines: Show the present locations of all particles that have passed through a common point in the past.
  • Pathlines: Show the trajectory of a single fluid particle.
  • Streamlines: Always tangent to the velocity vector. They represent flow lines in Eulerian presentation.

Flow Rate

  • Flow carries matter (mass or volume)
  • Mass flow rate: (Kg/s)
  • Volume flow rate (discharge): (m³/s), the volume of fluid passing through a location and area in a time period.
  • Flow rate is related to a "flow area" or flow section.

Flow Continuity

  • In a flow section bounded by solid surfaces, the amount flowing in must equal the amount flowing out (m1 = m2).
  • ρ<sub>1</sub>A<sub>1</sub>V<sub>1</sub> = ρ<sub>2</sub>A<sub>2</sub>V<sub>2</sub> if velocities and densities are uniform over the two sections

Flow of Matter: Flux

  • Flow carries matter, concentration, turbidity, oxygen, temperature and energy.
  • Flux (ßm): Rate of flow of a different substance contained within a certain amount of fluid mass.
  • Example: sediment or leaked oil

Reynolds Transport Theorem

  • Used for calculating rate of change of properties within a control volume.
  • Based on mass, momentum and energy conservation.
  • Extensive properties (proportional to quantity of matter, e.g. mass, momentum, energy).
  • Intensive properties (independent of quantity of matter, e.g. concentration).
  • d(B<sub>sys</sub>)/dt = ∫(ρβ) dV + ∫(βρ(U·n)) dA

Fluid Acceleration

  • Eulerian description: Acceleration of a fluid particle at a point is not simply the ordinary derivative of velocity.
  • The velocity at a point reflects the velocities of different particles passing that point at different times.
  • a = dU/dt = ∂U/∂t + (U·∇)U

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