Fluid Mechanics 2: Linear Momentum Applications

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Questions and Answers

What is the purpose of analyzing linear momentum in a flow system?

  • To find the forces associated with a steady fluid flow (correct)
  • To calculate the pressure drop across a component
  • To determine the velocity distribution of a fluid
  • To minimize energy loss in fluid transport

In the context of flow through a reducing pipe bend, what does the control volume represent?

  • A specified region in the flow path (correct)
  • The area of energy loss in the pipes
  • The entire fluid system
  • The fluid entering the pipe

What does the linear momentum equation focus on while analyzing pipe flow?

  • Net force acting on the control volume (correct)
  • The viscosity of the fluid involved in the flow
  • The mass flow rate of the fluid
  • The temperature changes within the fluid

Which factor is primarily considered when calculating the forces in a reducing pipe bend?

<p>The change in velocity of the fluid (C)</p> Signup and view all the answers

How does a reducing pipe bend affect the fluid flow inside?

<p>It can induce turbulence and velocity changes (D)</p> Signup and view all the answers

What is the general form of the linear momentum balance equation?

<p>Net force = Change in momentum over time (B)</p> Signup and view all the answers

In a fluid flow analysis, which term is likely NOT included in the momentum balance?

<p>Heat transfer (A)</p> Signup and view all the answers

What should be analyzed to assess force exerted on a pipe with steady fluid flow?

<p>Velocity at inlet and outlet (B)</p> Signup and view all the answers

What is the expression for the net force in the direction of pipe flow?

<p>$C%,( *% - C&amp;,( *&amp; cos 1 + E($ (B)</p> Signup and view all the answers

In the expression for net momentum outflow, which term represents the gravitational component?

<p>$0(−!̇$ (C)</p> Signup and view all the answers

Which of the following represents the shear stress applied by the pipe wall?

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

How is the weight of the fluid represented in the context of forces in a pipe?

<p>$m g$ (A)</p> Signup and view all the answers

What force component is indicated by the term $E$ in the net force equations?

<p>Outlet pressure adjustment (C)</p> Signup and view all the answers

What assumption is made about the fluid's flow characteristics in this scenario?

<p>The fluid has incompressible properties. (A)</p> Signup and view all the answers

Which of the following statements about the momentum within the control volume is true?

<p>The rate of accumulation of momentum is steady. (C)</p> Signup and view all the answers

In the context of flow within a reducing pipe bend, what describes the direction of the flow characteristics?

<p>There is no flow in the y-direction. (D)</p> Signup and view all the answers

What does the condition of 'steady state' imply in this context?

<p>All fluid properties are constant over time. (C)</p> Signup and view all the answers

What can be inferred if the fluid flow is described as having uniform velocities at the inlet and outlet?

<p>The velocity does not change from inlet to outlet. (C)</p> Signup and view all the answers

What is the primary method used to analyze flow in a reducing pipe bend?

<p>Separating velocities into their respective components (C)</p> Signup and view all the answers

Which component is NOT considered when writing momentum expressions at the inlet and outlet?

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

What expression represents the momentum at the inlet?

<p>0̇ = &amp;*%!% (C)</p> Signup and view all the answers

In the outlet momentum expression, which factor contributes to the force calculation?

<p>Cosine of the angle at outlet (A)</p> Signup and view all the answers

Which term is used in the momentum expression related to flow direction at the outlet?

<p>X and Y components combined (D)</p> Signup and view all the answers

What is the equation representing linear momentum balance in the context of the fluid flow problem?

<p>$Wa- (6 − )YX_U-YW[$ (B)</p> Signup and view all the answers

In the fluid flow problem, how does the atmospheric pressure affect force balance?

<p>It cancels out, having no net effect on force balance. (D)</p> Signup and view all the answers

What happens when the force acts to the left according to the fluid flow problem?

<p>It works against the direction of #7. (A)</p> Signup and view all the answers

Which equation represents the total force in relation to the mass flow rates in the fluid system?

<p>$#782,( = 0!̇ 012 − 0!̇/$ (D)</p> Signup and view all the answers

In the context of force balance, what is the role of $0!̇./$?

<p>It is the exit mass flow rate of the fluid. (B)</p> Signup and view all the answers

What is the condition given for the control volume in relation to forces?

<p>It is exposed to atmospheric pressure. (A)</p> Signup and view all the answers

Which statement regarding mass flow rates $0!̇ 012$ and $0!̇./$ is correct?

<p>They are part of the linear momentum equation. (A)</p> Signup and view all the answers

What does the equation $#782,( = -0!̇ 782$ imply about the system?

<p>The net force is directly proportional to the mass flow rate. (A)</p> Signup and view all the answers

What is the main purpose of defining a control volume in the described fluid system?

<p>To identify the forces acting on the plane (B)</p> Signup and view all the answers

Which of the following is an assumption made in the fluid flow problem?

<p>Steady state flow (C)</p> Signup and view all the answers

What does the notation *782 = 0.005 0& represent in the context of the problem?

<p>Mass flow rate through the jet (A)</p> Signup and view all the answers

Which fluid's properties must be taken into account to calculate the force on the plate?

<p>Both water and air (B)</p> Signup and view all the answers

In the equation provided, what significance does the assumption of uniform/constant velocities have?

<p>It leads to a steady force balance on the plate (C)</p> Signup and view all the answers

How is the force required to hold the plate stationary primarily determined?

<p>By performing force balance on the jet action (A)</p> Signup and view all the answers

What role does the density of the fluids play in this fluid dynamics problem?

<p>It affects the mass flow rate calculations (A)</p> Signup and view all the answers

Which component of the system must be balanced for the plate to remain stationary?

<p>The forces exerted by the jet on the plate (A)</p> Signup and view all the answers

Flashcards

Linear Momentum Balance

The principle that the rate of change of linear momentum of a system is equal to the net force acting on it.

Control Volume

A defined region in space used for analysis, often used to analyze fluid flow.

Mass Flow Rate

The amount of mass flowing through a given area per unit time. It's essentially how much fluid passes through a point.

Momentum Force

The force exerted by a fluid on a surface due to the change in momentum of the fluid as it flows over the surface.

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Reducing Pipe Bend

A pipe bend that reduces the cross-sectional area of the flow path.

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Steady Flow

The flow regime where the properties of the fluid at a given point in space do not change with time.

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Net Momentum Flux

The difference between the momentum flux (mass flow rate x velocity) at the inlet and outlet of the control volume.

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Pressure Force

The force caused by the pressure difference between the inlet and outlet of the control volume.

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What causes momentum force?

The change in momentum of the fluid as it flows over the surface, leading to a force acting on the surface.

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State the Linear Momentum Balance principle.

The rate of change of linear momentum of a system is equal to the net force acting on it.

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Rate of Accumulation of Momentum

The rate at which momentum accumulates within a control volume.

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Net Momentum Outflow

The total momentum leaving the control volume minus the total momentum entering the control volume.

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What is net momentum flux?

The difference in momentum flux between the inlet and outlet of a control volume.

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What is a control volume?

A defined region in space used for analysis, often used to analyze fluid flow.

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Steady State

The assumption that the flow properties at a specific point in space remain constant over time.

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What is mass flow rate?

The mass of fluid flowing through a given cross-sectional area per unit time.

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Incompressible Flow

The assumption that the density of the fluid remains constant throughout the flow.

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Net Force

The sum of all forces acting on a control volume. It's like balancing the forces pushing and pulling on the system.

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Gravity Force

A force that acts perpendicular to the flow direction, caused by the weight of the fluid in the pipe. It's essentially the pull of gravity on the fluid.

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Stationary Force (Equilibrium)

The force required to keep an object, like a stationary plate, from moving due to the impact of a fluid jet. It's akin to balancing a seesaw.

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Force Balance

The force balance principle states that for an object to stay stationary, the sum of all the forces acting on it must be zero. It's like balancing a seesaw.

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Steady State Flow

A fluid flow where the properties at a given point in space remain constant over time, like a steady river.

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What is Net Momentum Outflow?

It's the difference between the total momentum leaving a control volume and the total momentum entering the control volume. It essentially tells us how much momentum has been lost or gained within the control volume.

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What is Steady State?

It's a simplification of the 'Linear Momentum Balance' equation. The assumption states that the properties of the flow at a specific point in space remain constant over time. It doesn't mean nothing changes; It means changes are negligible over time.

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Study Notes

Fluid Mechanics 2 - KIL 3002

  • Course code: KIL 3002
  • Course title: Fluid Mechanics 2
  • Department: Department of Chemical Engineering
  • University: Universiti Malaya

Chapter 3: Applications of Linear Momentum Balance

  • Focuses on the application of linear momentum balance in simple flow analysis for flow problems
  • Aims to determine forces associated with flow systems and maintain balance.

Flow in a Reducing Pipe Bend - Problem 1

  • Problem Statement: Determine force exerted by steady fluid flow in a reducing bend pipe
  • Assumptions:
    • Steady state flow
    • Incompressible fluid
    • Uniform/constant velocities at inlet and outlet
  • Control Volume: A defined region surrounding the flow system.
  • Linear Momentum Equation: A crucial equation used for analysis, with summation of forces equal to rate of accumulation of momentum.

Flow in a Reducing Pipe Bend - Problem 1 (cont.)

  • Forces involved:
    • Pressure difference (Fp)
    • Gravitational force (Fw)
    • Shear stress by the pipe wall (pressure difference)
    • Unknown force (B)
  • Analysis of components: velocity components in x and y-directions, cross section areas, and mass flow rates for inlet and outlet.

Flow in a Reducing Pipe Bend - Problem 1 (Momentum Balance)

  • Solving the problem: Separate x and y directions for analysis
  • x-direction: Sum forces = Net momentum outflow in x direction
  • y-direction: Sum forces = Net momentum outflow in y direction
  • Linear Momentum Balance Equations: Formulas for the x and y-directions to calculate forces and momentum change

Fluid Flow on a Stationary Vertical Plane (Problem 2)

  • Problem Statement: Determine force required to keep a vertical plane stationary when struck by a jet of fluid exiting a nozzle.
  • Assumptions: Steady state, incompressible flow, constant velocity
  • Control Volume: Region surrounding the jet/plate interaction
  • Force Calculation (x-direction): Linear momentum balance will involve mass flow rates and velocities in the x-direction
  • Force Calculation Methods: Applying the force balance in the relevant component, will include calculating force from jet hitting control volume

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