Chapter 23 Fluid Dynamics
page 23-1 The Current State of Fluid Dynamics A fluid is a substance that can flow. Liquids and gases are fluids. What could make the study of liquids and gases complicated?
page 23-2 The Velocity Field We will skip this section.
page 23-4 The Vector Field
A vector has magnitude and direction. Is the acceleration due to gravity a vector field?
What advantage results if the gravitational field is known?
Which is the easier calculation: F = G m1 m2 / r2 or F = mg ?
A field is a device that can be used to solve problems. This is similar to the device labeled "energy."
page 23-4 Streamlines
Does material from one streamline mix with material from another streamline?
What is the direction of the velocity vector of the material compared to the direction of the streamline?
Do streamlines exist in a region where there is significant turbulence in the fluid?
page 23-5 The Continuity Equation
Imagine that it is August. Imagine that you are going to wash a car with a garden hose. There are no attachments to put on the end of the hose. How can you increase the speed of the water as it leaves the end of the hose?
Many fluids are nearly incompressible. This means that the density of the fluid is approximately constant.
Suppose that 0.4 liters of water leave the outside faucet and enter the hose every second. How many liters of water leave the end of the hose every second?
Suppose that ¾ of the area of the opening at the end of the hose is covered by your thumb. Describe the speed of the water as it leaves the hose compared to when the end of the hose is not covered. How many liters of water leave the hose every second when your thumb covers ¾ of the exit area?
Equation of Continuity
A1 V1 = A2 V2 V is the magnitude of the velocity, the speed
Suppose that the water leaves the hose at a speed of 8 cm/sec when the end of the hose is not covered. Calculate the speed of the water when ¾ of the area of the end of the hose is covered.
page 23-6 Velocity Field of a Point Source We will skip this section.
page 23-7 Velocity Field of a Line Source We will skip this section
page 23-8 Flux
Continuing with the water analogy, flux can be defined as the volume of water that leaves a volume every second. In electricity and magnetism it is more useful to define flux as the measure of the fluid speed times the area (perpendicular to the velocity) the fluid passes through. As the fluid exits the volume it passes through the area that bounds the volume.
What is the value of the total flux for the case of water flowing through a garden hose?
Is the value of the flux of people leaving our classroom at the end of a class positive or negative or zero?
page 23-9 Bernoulli’s Equation
Bernoulli’s Equation is a statement of Conservation of Energy for a fluid. You will see terms in the equation that remind you of kinetic energy, potential energy and work.
This equation can only be used for the case of streamline flow. We will also assume that the fluid is incompressible.
page 23-11 The result of the discussion is Bernoulli’s Equation:
P + (1/2) ρ V2 + ρ g h = a constant (along one streamline)
Which terms in this equation are similar to KE, PE, and work?
What common factor has been removed from all three terms?
We will use this equation to solve problems with the methods similar to conservation of energy and conservation of momentum. There will be two locations in many problems. The sum of the three terms at each location will be set equal to each other.
page 23-12 Applications of Bernoulli’s Equation We will examples concerning:
A leak in a large tank
Airplane wing
Throwing a curve in baseball
page 23-14 You should read about sailboats.
page 23-15 You should read about the Venturi Meter pages 23-16 to 23-23 We will skip these sections.
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