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Fluid Flow - General Physics I - Lecture Slides, Slides of Physics

Aliah UniversityPhysics

The fundamental aspects of these Lecture Slides are : Fluid Flow, Steady Flow, Ideal Fluid, incompressible,, Streamline Flow, Turbulent Flow, Streamlines, Equation of Continuity, Simple Harmonic Motion, Hooke’S Law

Typology: Slides

2012/2013

Uploaded on 07/26/2013

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5
Fluid Flow
A moving fluid will exert forces parallel to the surface over which it
moves, unlike a static fluid. This gives rise to a viscous force that
impedes the forward motion of the fluid.
A steady flow is one where the velocity at a given point in a fluid is
constant. Steady flow is laminar; the fluid flows in layers.
V1 =
constant
V2 =
constant
v1≠v2
An ideal fluid is incompressible, undergoes laminar flow, and has no viscosity.
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5

Fluid Flow

A moving fluid will exert forces parallel to the surface over which it moves, unlike a static fluid. This gives rise to a viscous force that impedes the forward motion of the fluid. A steady flow is one where the velocity at a given point in a fluid is constant. Steady flow is laminar; the fluid flows in layers. V 1 = constant V 2 = constant v 1 ≠v 2 An ideal fluid is incompressible, undergoes laminar flow, and has no viscosity.

Fluids in Motion: Streamline Flow

  • Streamline flow
    • every particle that passes a particular point moves exactly along the smooth path followed by particles that passed the point earlier
    • also called laminar flow
  • Streamline is the path
    • different streamlines cannot cross each other
    • the streamline at any point coincides with the direction of fluid velocity at that point

Fluids in Motion: Turbulent Flow

  • The flow becomes irregular
    • exceeds a certain velocity
    • any condition that causes abrupt changes in velocity

8 is the mass flow rate (units kg/s)

Av

t

m

= ρ

1 1 1 2 2 2 The continuity equation is ρ Av = ρ A v If the fluid is incompressible, then ρ 1 = ρ2.

9 Example: A garden hose of inner radius 1.0 cm carries water at 2.0 m/s. The nozzle at the end has radius 0.20 cm. How fast does the water move through the constriction? ( 2. 0 m/s) 50 m/s 0.20 cm

  1. 0 cm 2 2 1 2 2 1 1 2 1 2 1 1 2 2 ⎟^ = ⎠ ⎞ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = = v r r v A A v Av A v π π

Recall: Hooke’s Law

• F

s = - k x

  • F s is the spring force
  • k is the spring constant
    • It is a measure of the stiffness of the spring
      • A large k indicates a stiff spring and a small k indicates a soft spring
  • x is the displacement of the object from its equilibrium position
  • The negative sign indicates that the force is always directed opposite to the displacement
  • The force always acts toward the equilibrium position
    • It is called the restoring force

Hooke’s Law Applied to a

Spring – Mass System

  • When x is positive (to the right), F is negative (to the left)
  • When x = 0 (at equilibrium), F is 0
  • When x is negative (to the left), F is positive (to the right)

Motion of the Spring-Mass System

  • Assume the object is initially pulled to x = A and released from rest
  • As the object moves toward the equilibrium position, F and a decrease, but v increases
  • At x = 0, F and a are zero, but v is a maximum
  • The object’s momentum causes it to overshoot the equilibrium position
  • The force and acceleration start to increase in the opposite direction and velocity decreases
  • The motion continues indefinitely

Simple Harmonic Motion

  • Motion that occurs when the net force along the direction of motion is a Hooke’s Law type of force - The force is proportional to the displacement and in the opposite direction
  • The motion of a spring mass system is an example of Simple Harmonic Motion
  • Not all periodic motion over the same path can be considered Simple Harmonic motion
  • To be Simple Harmonic motion, the force needs to obey Hooke’s Law

Acceleration of an Object in Simple

Harmonic Motion

  • Newton’s second law will relate force and acceleration
  • The force is given by Hooke’s Law F = - k x = m a or a = -kx / m
  • The acceleration is a function of position
    • Acceleration is not constant and therefore the uniformly accelerated motion equation cannot be applied

Elastic Potential Energy

  • The energy stored in a stretched or compressed spring or other elastic material is called elastic potential energy PE s = ½kx 2
  • The energy is stored only when the spring is stretched or compressed
  • Elastic potential energy can be added to the statements of Conservation of Energy and Work- Energy

Energy Transformations

  • The block is moving on a frictionless surface
  • The total mechanical energy of the system is the kinetic energy of the block

Energy Transformations, 2

  • The spring is partially compressed
  • The energy is shared between kinetic energy and elastic potential energy
  • The total mechanical energy is the sum of the kinetic energy and the elastic potential energy

Energy Transformations, 4

  • When the block leaves the spring, the total mechanical energy is in the kinetic energy of the block
  • The spring force is conservative and the total energy of the system remains constant

Velocity as a Function of Position

  • Conservation of Energy allows a calculation of the velocity of the object at any position in its motion - Speed is a maximum at x = 0 - Speed is zero at x = ±A - The ± indicates the object can be traveling in either direction

2 2

A x

m

k

v = ± −