Note: The soluitions to this problem set were provided by Dr. Shelplak.
Problem 1 Given: Find: A jet of water issuing into a moving cart, declined at an angle as shown. 1. 2. 3. 4. 5. 6. Schematic: Draw the appropriate control volume, explicity stating un
EGM6812/FluidMechanicsI Homework#6
Fall2009
1.
(Bernoulli equation in axisymmetric flows) For steady axisymmetric flows of an inviscidfluidofconstantdensity,showthat + +F()=constant whereisthepotentialforthebodyforce,istheStokesstreamfunction. Hint:younee
EGM 6812 Fluid Mechanics 1 Fall 2010
3rd Homework
Problem 1: A jet of water that is declined at an angle is filling a moving water car. The water car is moving away from the jet at a constant velocity U and possesses a diameter D . The liquid level in the
EGM 6812 Fluid Mechanics 1 - Fall 2010
5th Homework
Problem 1 Given: For high-speed, oscillatory, compressible flow past a finite length cylinder, the drag force, FD , is known to be a function of cylinder diameter, D , cylinder length, L ,
Find: a)
cyli
EGM 6812 Fluid Mechanics 1 - Fall 2010
10/4/10, 6th Homework
1.
2.
3.
4.
Consider the flow in an annulus generated by a solid cylinder of radius b rotating at a speed in a larger cylindrical tube of inner radius a . The space between the cylinders is fill
EGM 6812 Fluid Mechanics 1 - Fall 2010
10/25/10, 8th Homework 1. Starting with the Cartesian form of the N-S equation, derive Bernoulli's equation for incompressible, inviscid, and irrotational flow. Please state all assumptions and show all steps. Starti
1 Introduction1
1.1 Definitions:2
Solid: Substance in which the molecules tend to retain a fixed position If a shear force is applied the substance will deform
Figure 1 Shear load on a solid (Shames 2003).
When the force is released the material is retu
7 Dimensional Analysis and Similarity
Why? 1. 2. 3. 4. 5. Reduced number of experiments Compact data representation Solve problem fewer times Lab prototype to full scale If we non-dimensionalize the governing equations, we can "simplify" the equations by
EGN 6812 - Fluid Mechanics I Fall 2004
12/17/04, Final Exam Name: _ _
Questions: (40 points total, 3 points each, unless otherwise marked)
1.
State the 5 conditions for incompressibility discussed in class (5 equations and/or sentences describing each con
EGM 6812 - Fluid Mechanics I - Fall 2015
Homework 5 is due October 16, 2015 at the beginning of class.
1. A two-dimensional ow eld has the following velocity components:
u = x(1 + t),
v = 1,
w=0
Determine the following:
(a) The equation of the streamline
EGN 6812 - Fluid Mechanics I Fall 2003
12/18/03, Final Exam Name: _
Questions: (50 points total, 4 points each, unless otherwise marked)
1.
According to Morton's vorticity paper, describe the generation, transport and decay of vorticity in a fully develop
EGN 6812 - Fluid Mechanics I Fall 2005
10/11/05, Exam 1 Name: _
Questions: (20 points total, 4 points each, unless otherwise marked)
1.
Provide a physical explanation of Stokes' hypothesis (i.e., not an equation) and describe when it is and is not valid f
EGN 6812 - Fluid Mechanics I Fall 2003
10/23/03, Mid Term Exam Name: _
Questions: (40 points total, 4 points each)
xi
1.
( u ) is the surface work term due to viscous forces in the energy equation.
ij j
Mathematically decompose this term into components
EGM 6812 Fluid Mechanics 1 - Fall 2010
10/27/10, Exam 2 Information Announcements: 1. 2. 3. Exam 2 will be given at night on Wednesday, 11/3/10 in 100 NEB from 8:20 pm 10:10 pm. It will cover material through section 9.2 (up to Bernoulli's equation) and H
EGM 6812 Fluid Mechanics 1 - Fall 2010
9/22/10, Exam 1 Information Announcements: 1. Format: 1. 2. Bring a pencil, eraser, etc. DO NOT bring your notes, textbook, calculator, crib sheet, etc. I anticipate that we will have 2-4 problems and several short-a
EGN 6812 - Fluid Mechanics I Fall 2005
12/16/05, Final Exam Name: _ _
Questions: (40 points total, 4 points each, unless otherwise marked)
1.
What are the conditions under which both the streamfunction and the velocity potential can be defined for a spher
EGM 6812 Fluid Mechanics 1 - Fall 2010
9/17/10, 4th Homework
1. 2.
Problem 5.1 from Panton. Using the differential conservation of momentum equation as a starting point, derive the differential kinetic energy equation,
V 2 V 2 V V f b V p V . Hint: start
EGM 6812 Fluid Mechanics 1 - Fall 2010
12/8/10, 10th Homework
Problem 1 Given: Consider a uniform, ideal flow over an ellipse with major and minor axes of A and B , respectively. The freestream velocity is U and the angle of attack is . The complex potent
2 Vector Calculus and Indicial Notation1
To analyze fluid dynamics, we need to formally define and discuss some properties of scalar, vectors, and tensors. The goal is to gain familiarity and comfort indicial notation and vector calculus.
2.1 Definitions
3 Thermodynamics 3.1 Perfect gas
Intermolecular forces between gas particles is dependent upon distance strong for small intermolecular spacing weak for large intermolecular spacing Intermolecular forces determine motion of particles => thermodynamic prop
EGM 6812 Fluid Mechanics I Fall 2015
HW 7 is due November 16, 2015
For each problem, obtain the leading order composite solution, state the boundary
layer thickness, and plot the composite solution for two small values of (be sure
to label the figure and
EGM 6812 Fluid Mechanics I Fall 2015
HW 3 is due September 25, 2015
Solve Problems: 6.1; 6.3; 4.2; 4.7; 4.9; 4.11
Relations for vorticity, strain rate tensor, and viscous stress tensor in several coordinate systems
can be found in the Appendices of Panton
1.3
PropertiesofFluids
i)
Transport properties :
mass diffusivity,
viscosity,
thermal conductivity,
- all related to the molecular collisions.
Transport phenomena always bring the system towards equilibrium.
Mass Diffusion:
Place species A next to specie
ii.
IndicialNotation
Free Index
Consider:
Dui
p
f i ji , i=1, 2, 3
Dt
xi
x j
o
Any index that appears only once in an additive term
o
for i 1,2,3 is implied for a free index
o
free indices must balance for each additive term in an
equation except for con
EGM 6812 - Fluid Mechanics 1 Fall 2012
.
Instructor: Dr. Mark Sheplak, Room 215 Larsen Hall, 2-3983, [email protected],
Lecture Times: MWF 3rd period (9:35-10:40 am) in NEB 201
Office Hours: W & F 10:30 11:30 am, other times by appointment.
Teaching Assista