4-Intro, fluid mech

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Scientific Learning Outcome ...
C H A P T E R
4
Flowing Fluids
and Pressure
Variation
SCIETIFIC LEARIG OUTCOMES
This photograph shows the eye of a hurricane. The motion is the result of pressure
variations.
Conceptual Knowledge
·
Distinguish between steady, unsteady, uniform, and nonuniform flows.
·
Distinguish between convective and local acceleration.
·
Describe the steps to derive the Bernoulli equation from Euler's equation.
·
Explain what is meant by rotation and vorticity of a fluid element.
·
Describe flow separation.
Procedural Knowledge
·
Apply Euler's equation to predict pressure.
·
Predict pressure distributions in rotating flows.
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Scientific Learning Outcome ...
·
Apply the Bernoulli equation to pressure and velocity variations.
·
Evaluate the rotation and vorticity of a fluid element.
Applications (Typical)
·
In variable area ducts, relate pressure and velocity distributions.
·
Measurement of velocity with stagnation tube or a Pitot-static tube.
·
Cyclonic storm pressure distribution.
Many phenomena that affect us in our daily lives are related to pressure in flowing fluids. For
example, one indicator of our health, blood pressure, is related to the flow of blood through veins
and arteries. The atmospheric pressure readings reported in weather forecasts control atmospheric
flow patterns related to local weather conditions. Even the rotary motion generated when we stir a
cup of coffee gives rise to pressure variations and flow patterns that enhance mixing.
The relationship between pressure and flow velocity is also important in many engineering
applications. In the design of tall structures, the pressure forces from the wind may dictate the design
of individual elements, such as windows, as well as the basic structure to withstand wind loads. In
aircraft design, the pressure distribution is primarily responsible for lift and contributes to the drag of
the aircraft. In the design of flow systems, such as heating and air conditioning, the pressure
distribution is responsible for flow in the ducts.
The force balance between pressure and weight in a static fluid was presented in Chapter 3, which
lead to an equation for pressure variation with depth. In this chapter the pressure variation in flowing
fluids will be addressed. The concepts of pathlines and streamlines help visualize and understand
fluid motion. The definition of fluid velocity and acceleration leads to an application of Newton's
second law relating forces on a fluid element to the product of mass and acceleration. These
relationships lead to the Bernoulli equation, which relates local pressure and elevation to fluid
velocity and is fundamental to many fluid mechanic applications. This chapter also introduces the
idea of fluid rotation and the concept of irrotationality.
Copyright ¨ 2009 John Wiley & Sons, Inc. All rights reserved.
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