Example Problem Exact Solution for Couette Flow
Given: Steady, incompressible, laminar flow in the x-y plane between two infinite parallel plates.
V Moving plate h Fluid: , Fixed plate y x
Assumptions and approximations: 1. The flow is steady [/t
Name(s) (up to three students per homework set): Due: In class, Friday September 16, 2005 1. 2. 3.
ME 33 Fall Semester, 2005
Homework Set # 2
Professor J. M. Cimbala
For instructor or TA use only: Problem Score Points 1 15 2 15 3 20 4 15 5 10 6 10
Stability of a Boat (Figure 3-46, engel and Cimbala)
Line of action of the buoyancy force before rotation Line of action of the buoyancy force after rotation
Point M is above point G
Point M is below point G
M = the metacenter = the point where th
Example of Grade Lines in a Fluid Flow
At point 0, HGL = EGL inside the tank, since the fluid is at rest (V = 0). Neither EGL or HGL can rise above this value unless work is added to the flow (e.g., with a pump). At any location in the duct, the diff
Laminar Versus Turbulent Flow A Comparison (Section 8-2, engel and Cimbala) Laminar Flow Can be steady or unsteady. (Steady means that the flow field at any instant in time is the same as at any other instant in time.) Turbulent Flow Is always unste
Example Drag on a Bicycle Rolling Down a Hill
Given: A person coasts a bicycle down a long hill with a slope of 5o in order to measure the drag area of the bike and rider. The mass of the bike is 7.0 kg, the mass of the rider is 70.0 kg, and the rol
ME 33
Fall 2005
Lecture 41
12-09-2005
Example Drag on a Bicycle Rolling Down a Hill
Given: A person coasts a bicycle down a long hill with a slope of 5o in order to measure the drag area of the bike and rider. The mass of the bike is 7.0 kg, the
Example Problem Diffuser
Given: Water ( = 1000 kg/m , = 1.00 10-3 kg/ms) flows through a horizontal diffuser, as sketched. The flow is fully developed at both locations 1 and 2. The inner diameter changes from d to D through the diffuser. The outl
Comparison of two cars with identical engines, transmissions, etc., but different aerodynamics
Scion XA
EPA Mileage estimate with manual transmission: 32 City, 37 Highway. Scion XB
EPA Mileage estimate with manual transmission: 30 City, 33 Highway.
Fully Developed Pipe Flow Equations (Section 8-5, engel and Cimbala) There are several empirical equations available to use in place of the Moody chart. The most important one (in fact, the equation with which the turbulent portion of the Moody chart
Guidelines for Manipulating the Parameters
There are several guidelines for manipulating the parameters. These guidelines are listed concisely in Table 7-4 in the text, as repeated below:
The goal is to get each into a form that looks like one of
The Power of Dimensional Analysis
In some cases of dimensional analysis, particularly when there is only one nondimensional parameter, you can predict the trend of one variable as a function of the other variables often to within a single constant.
Rules for Exam 1 Closed-book, closed notes, no calculators allowed. Equation sheet from the website not permitted you will get a fresh new one. Put answers in the space provided on the exam. Restroom one person out of the room at a time. Show
Pumps
(Most material from Fluid Mechanics, engel and Cimbala, Chapter 14) Introduction and Terminology: "Pump" is a general term for any device that adds mechanical energy to a fluid. For liquids, we usually call them "pumps". For gases, we usuall
Turbines
(Most material from Fluid Mechanics, engel and Cimbala, Chapter 14) Introduction and Terminology: "Turbine" is a general term for any device that extracts mechanical energy from a fluid generally converting it to rotating energy of a turbi
Examples of Cavitation and Cavitation Damage
Photographs supplied by David R. Stinebring, Eric G. Paterson, and William A. Straka
Penn State Applied Research Laboratory
Cavitation occurs in regions of the flow where the local pressure is low enough
The Taxonomy of Fluid Dynamics
The Cauchy Equation
Valid for any fluid r V r rr r r + VV = g + ij t
( )
(
)
The Navier-Stokes Equation
Approximations of the Navier-Stokes equation:
Valid for Newtonian fluid only r r r DV r = -P + g +
Steps in the Method of Repeating Variables
There are 6 steps that comprise the method of repeating variables. These are listed concisely in Fig. 7-22 in the text, as repeated below:
Step 4 is often the most difficult or mysterious step. There are gu
Name(s) (up to three students per homework set): Due: In class, Friday November 18, 2005 1. 2. 3.
ME 33 Fall Semester, 2005
Homework Set # 9
Professor J. M. Cimbala
For instructor or TA use only: Problem Score Points 1 15 2 10 3 15 4 30 5 10 6 10 7