Fluid Mechanics II Examl
Name: Score
1 A particle moves along the horizontal centerline of a converging channel. The velocity at the
centerline of the channel is given by 17 = V1(1 +f)t, where VI and L are constant. Find an
expression for the accelerat
Practice Problems on Fluid Statics
manometry_01
Compartments A and B of the tank shown in the figure below are closed and filled with air and a liquid with a
specific gravity equal to 0.6. If atmospheric pressure is 101 kPa (abs) and the pressure gage rea
Practice Problems on the Navier-Stokes Equations
ns_02
A viscous, incompressible, Newtonian liquid flows in steady, laminar, planar flow down a vertical wall. The
thickness, , of the liquid film remains constant. Since the liquid free surface is exposed t
Practice Problems on the Linear Momentum Equations
COLM_01
A frequently used hydraulic brake consists of a movable ram that displaces water from a slightly larger cylinder, as
shown in the figure. The cross-sectional area of the cylinder is Ac and the cro
Chapter 6
SOLUTION OF VISCOUS-FLOW PROBLEMS
6.1 Introduction
T
HE previous chapter contained derivations of the relationships for the conservation of mass and momentumthe equations of motion in rectangular,
cylindrical, and spherical coordinates. All the
Practice Problems on Conservation of Mass
COM_01
Construct from first principles an equation for the conservation of mass governing the planar flow (in the xy plane)
of a compressible liquid lying on a flat horizontal plane. The depth, h(x,t), is a functi
Practice Problems on Pipe Flows
pipe_02
A homeowner plans to pump water from a stream in their backyard to water their lawn. A schematic of the pipe
system is shown in the figure.
sprinkler
inlet pipe-to-pump
3 m coupling
1 m stream
hose-to-hose coupling
Notes on Fluid Mechanics and Gas Dynamics
Carl Wassgren, Ph.D.
School of Mechanical Engineering
Purdue University
wassgren@purdue.edu
16 Aug 2010
Chapter 01:
Chapter 02:
Chapter 03:
Chapter 04:
Chapter 05:
Chapter 06:
Chapter 07:
Chapter 08:
Chapter 09:
C
Fluids Basics
Definition of Fluid:
A fluid is a substance that deforms
continuously under the application of a shear
(tangential) stress no matter how small the
shear stress may be.
Liquids and gases
Liquids and gases are very different
Liquids become les
Agenda
Basic Terminology
Steady:
Next few classes review of
undergrad fluids
Integral or control volume
approach
chapter 4 in Fox and McDonald
Incompressible:
Perfect fluid:
Todays lecture
Reynolds Transport Theorem
Integral approaches to governi
COM Problem
8/31/2006
ME509: Fluid Mechanics
1
Conservation of Linear Momentum
inertial reference frame
8/31/2006
ME509: Fluid Mechanics
2
Conservation of Linear Momentum
rectilinearly accelerating reference frame
8/31/2006
ME509: Fluid Mechanics
3
COLM E
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1SQIRXYQ )UYEXMSRW JSV (MJJIVIRXMEP ': '301 GSRXH
Navier-Stokes Solutions
Plane Couette Flow
Consider two infinite parallel plates, the top one
moving at fixed speed U in its own plane and the
bottom one f
172
Chapter 3 Integral Relations for a Control Volume
EXAMPLE 3.19
A hydroelectric power plant (Fig. E3.19) takes in 30 m3/s of water through its turbine and discharges it to the atmosphere at V2 2 m/s. The head loss in the turbine and penstock system is
1. In fluid mechanics, it is the ratio of the area of the vena contracta to the area of the smaller pipe.
Answer: A. Contraction coefficient
2. When the Reynolds number of a fluid flow is 3500, the flow is
Answer: C. Intermediate between turbulent or lami
CHAPTER 3
FLOW PAST A SPHERE II: STOKES LAW, THE
BERNOULLI EQUATION, TURBULENCE, BOUNDARY
LAYERS, FLOW SEPARATION
INTRODUCTION
1 So far we have been able to cover a lot of ground with a minimum of
material on fluid flow. At this point I need to present to
Ch. IV Differential Relations for a Fluid Particle
This chapter presents the development and application of the basic differential
equations of fluid motion. Simplifications in the general equations and common
boundary conditions are presented that allow
Appendix A
VECTORS, TENSORS AND
MATRIX NOTATION
The objective of this section is to review some of the vector operations that you have already covered
in your MATH and ENGR courses. For more details and examples you should refer to your calculus
text unde
Home > Notes > Equations > Substantial Derivative of scalar field - also known as Total derivative @Wolfram
D = + V Dt t
In rectangular coordinates D = +u +v +w Dt t x y z where V is the fluid velocity field, u is the component of V in the x direction, v
Fluids Lecture 10 Notes
1. Substantial Derivative
2. Recast Governing Equations
Reading: Anderson 2.9, 2.10
Substantial Derivative
Sensed rates of change
The rate of change reported by a ow sensor clearly depends on the motion of the sensor.
For example,
Fluid Dynamics IB
Dr Natalia Berlo
1.3 Material derivative
Consider a eld F (x, t).
Rate of change with time seen by an observer moving with uid, DF , is found by using
Dt
the chain rule for dierentiation (Remember: the value of x for a given uid particle