1. ES 202 Fluid and Thermal Systems Lecture 8: Application of Bernoulli’s Equation (12/17/2002)

2. Assignments Reading: Homework: Cengel & Turner Section 12-1, 12-2, 9-4
11-43, 11-45, 11-63, in Cengel & Turner

3. Road Map of Lecture 8 Quiz Review on Lecture 7
Some insights into Bernoulli’s equation
Examples and applications
Pitot-static tube
Lift on airfoil, tennis ball
Modified Bernoulli’s equation

4. Quiz
True/False When a fluid is in static equilibrium, the only force acting on the fluid is pressure. Explain your answer.
Explain with clarity the cause of buoyancy force on an object immersed in a fluid

5. Review on Lecture 7
Energy carried by a fluid element can be classified into:
mechanical energy
thermal energy
List the difference(s) between mechanical and thermal energy:
mechanical energy can freely change its form among various components
mechanical energy can be converted to work completely
thermal energy cannot be converted to work completely
In what form(s) can mechanical energy exist?
flow work ( P / r )
kinetic energy ( V2 / 2 )
potential energy ( g z )
Mechanical
Energy
Mechanical
Work
Thermal
Energy

6. Review on Lecture 7 (cont’d)
Write down the (steady) Bernoulli’s equation. Describe your interpretation of the equation.
mechanical energy can be freely interchanged among its various forms as the fluid element moves along its path
Name some assumption(s) behind the Bernoulli’s equation.
steady
no shaft work or friction
small change in thermal energy
constant density
along flow direction

7. Some Insights From statics to dynamics
Similarity and difference between solid and fluid
in addition to K.E. and P.E.,
there is a flow work component
in a fluid system
In compressible flow, there is interchange between thermal and mechanical energy (appreciable temperature change)

8. Different Forms of Bernoulli’s Equation
Pressure form
definition of stagnation pressure
“Head” form (dimension of length)

9. Pressure Variation Along Flow Direction
Consider the following convergent flow device:
air
air d1 d2 d1 d2 Dh Dh
Picture (a)
Picture (b)
Which configuration represents the correct physics? Explain your choice.
If d1 = 10 cm, d2 = 5 cm and air is going at 0.1 m3/sec, determine the value of Dh.
What kind of flow device is it?
If the flow direction is reversed, what do you expect to be the difference?

10. Pitot-Static Tube Principle behind a Pitot-Static tube: V d Dh A B
fluid column A measures the stagnation pressure (why?)
fluid column B measures the static pressure (why?)
according to the Bernoulli’s equation, their difference equals the dynamic pressure:
Pass out hardware of Pitot-static tube and describe position of holes

11. Lift on Airfoil and Tennis Ball
destroy the flow symmetry between the lower and upper surfaces
show visualization
Spin on a tennis ball
what does the spin do to the tennis ball?
Show visualization of flow over airfoil from MMFM. Slowly increase angle of attack. Point out regions governed by Bernoulli’s and regions violating Bernoulli’s

12. “Modified” Bernoulli’s Equation
What if fluid friction causes some losses in the system, can I still apply the Bernoulli’s equation?
Recall the “conservation of energy” concept from which we approach the Bernoulli’s equation
Remedy: introduce a “head loss” factor