1. ES 202 Fluid and Thermal Systems Lecture 10: Pipe Flow (Major Losses) (1/6/2003)

2. ES 202 Fluid & Thermal Systems
Assignments
Reading:
Cengel & Turner Section 12-5, 12-6
Homework:
12-25, 12-35, in Cengel & Turner
Lecture 10
ES 202 Fluid & Thermal Systems

3. ES 202 Fluid & Thermal Systems
Road Map of Lecture 10
Announcements
Comments on Lab 1
Recap from Lecture 9
Modified Bernoulli’s equation
Concept of viscosity
Pipe friction
friction factor
significance of Reynolds number
laminar versus turbulent
Moody diagram
flow chart to determine friction factor
Lecture 10
ES 202 Fluid & Thermal Systems

4. ES 202 Fluid & Thermal Systems
Announcements
Lab 2 this week
dress casually
you may get wet
formation of lab group of 2-3 students (need to split into 2 groups, 1.5 periods per group)
report your lab group to me by the end of today via , otherwise I will assign you
Extra evening office hours this week (8 pm to 10 pm)
(From tutor) Review package for Exam 1 available at the Learning Center and the new residence hall
Review session for Exam 1 on Saturday evening 8 pm to 10 pm
Lecture 10
ES 202 Fluid & Thermal Systems

5. ES 202 Fluid & Thermal Systems
Comments on Lab 1
Write your memorandum as if your project manager will not read your attachments:
list your p groups
state the functional relationship between p groups
Fundamental rules of plotting
always label your axes clearly
always plot the dependent variable against the independent variable!
Unit conversion is a good practice but NOT necessary in forming p groups (one of the many advantages of p group)
What is a log-log plot for? (Not necessary if a linear functional relationship exists!)
Invariance of p term does NOT imply invariance of dependent variable
Marking scheme (total 10 points):
correct p group formulation: 4 points
correct plotting of data: 4 points
correct conclusion of data: 2 points
coherence (adjustment up to 2 points)
Lecture 10
ES 202 Fluid & Thermal Systems

6. Summary of Lab 1 Write-up
Upon dimensional analysis, the relevant p terms are found to be
Part a: Part b:
Data analysis reveals
Part a: Part b:
Lecture 10
ES 202 Fluid & Thermal Systems

7. ES 202 Fluid & Thermal Systems
Recap from Lecture 9
The Torricelli experiment (A2<< A1)
The “Bent” Torricelli experiment V H
Area = A1
Area = A2 V H
Lecture 10
ES 202 Fluid & Thermal Systems

8. “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
Lecture 10
ES 202 Fluid & Thermal Systems

9. One Major Reason for the Losses
Fluid friction
also termed “Viscosity”
basketball-tennis-ball demonstration
exchange of momentum at the molecular scales (nature prefers “average”)
no-slip conditions at the solid surface (imagine thin layers of fluid moving relative to one another) generates velocity gradients
the two-train analogy
stress-strain relation in a Newtonian fluid
Lecture 10
ES 202 Fluid & Thermal Systems

10. Frictional Pipe Flow Analysis
Recall Modified Bernoulli’s equation
How does the head loss manifest itself?
flow velocity is constant along the pipe (which physical principle concludes this point?)
pressure is the “sacrificial lamb” in frictional pipe flow analysis
Lecture 10
ES 202 Fluid & Thermal Systems

11. Pressure Drop in Pipe Flow
Recall supplementary problem on dimensional analysis of pipe flow
In dimensional representation (7 variables)
In dimensionless representation (4 p groups)
Lecture 10
ES 202 Fluid & Thermal Systems

12. Significance of Reynolds Number
Definition of Reynolds number:
The Reynolds number can be interpreted as the ratio of inertial to viscous effects (one of many interpretations)
At low Reynolds number,
viscous effect is comparable to inertial effect
flow behaves in orderly manner (laminar flow)
At high Reynolds number,
viscous effect is insignificant compared with inertial effect.
flow pattern is irregular, unsteady and random (turbulent flow)
Lecture 10
ES 202 Fluid & Thermal Systems

13. Introducing the Friction Factor
Recall results from dimensional analysis of pipe flow
From hindsight, cast the above equation as
The friction factor (as defined) only depends
Reynolds number
relative roughness
Lecture 10
ES 202 Fluid & Thermal Systems

14. How to find the friction factor?
Since the friction factor only depends on two independent p groups, it is simple to represent its variation with multiple contour lines on a 2D plane
Show the Moody diagram
representation of two p groups
partition of different flow regimes
The whole problem of finding the pressure drop across piping system is reduced to finding the friction factor on the Moody diagram
Lecture 10
ES 202 Fluid & Thermal Systems

15. Flow Chart Find Reynolds number fluid properties (r, m) geometry (D)
flow speed (V)
Turbulent (Re > 2300)
Laminar
(Re < 2300)
Find relative roughness
Look up Moody diagram
Lecture 10
ES 202 Fluid & Thermal Systems