CBE 6333, R. Levicky
Homework Set 5
1). One method of producing vacuum is to discharge water through a venturi tube, and connect
the system to be evacuated with the throat of the venturi tube as shown in the below figure. How
much water must discharge thr

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Transport I 2015, Exam 1 explanation of points
1. This question was a lot like #2 on HW 4
a) (40 pts) This was broken down into:
define postulates (10 pts)
Navier-Stokes equation and boundary conditions (10 pts)
cancel the Nav-Stokes equation correctly (1

Transport Phenomena I Professor Joshua Gallaway
Transport Phenomena Required Reading 4
The purpose of this reading is to introduce:
1. Use of the Navier-Stokes equation.
2. Plotting a velocity profile.
3. Mathematically manipulating a velocity profile.
1.

Transport Phenomena I Professor Joshua Gallaway
Transport Phenomena Required Reading 3
The purpose of this reading is to introduce:
1. Stress tensors in curvilinear coordinates.
2. The substantial derivative.
1. Stress Tensors in Curvilinear Coordinates
A

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CBE 6333, R. Levicky
Homework Set 2
1). In all the expressions below:
A and B are 2nd rank tensors.
c and d are vectors (1st rank tensors).
is the del operator.
r is the result of the indicated operation.
Determine the rank of r. Also, using Cartesian no

CBE 6333, R. Levicky
Homework Set 3
1). The velocity field for a flow is given by:
v2 = -C(x22) / 2t ft/sec
v1 = Cx1 x2 / t ft/sec
v3 = 0
Consider a differential fluid element, like we did in handout #7. C is a constant equal to 1 ft -1.
a). Is the fluid

CBE 6333, R. Levicky
Homework Set 4
1). How would you set up the problem of an accelerating plate, discussed on pages 3-5 of Handout 10,
at short and long times? "Long times" means sufficiently long for a velocity perturbation, imposed at
the plate, to pr

R. Levicky, CBE 6333
1
Review of Vector Analysis in Cartesian Coordinates
Scalar: A quantity that has magnitude, but no direction. Examples are mass, temperature, pressure,
time, distance, and real numbers. Scalars are usually represented by italic letter

CBE 6333, R. Levicky
1
Review of Fluid Mechanics Terminology
The Continuum Hypothesis: We will regard macroscopic behavior of fluids as if the fluids
are perfectly continuous in structure. In reality, the matter of a fluid is divided into fluid
molecules,

CBE 6333, R. Levicky
1
Fluid Statics
Fluid statics deals with situations of "static equilibrium."
In static equilibrium:
- no part of a fluid is in motion relative to another part of the fluid
- no shear stress is present in the fluid
- only normal isotro

CBE 6333, R. Levicky
1
Integral (Macroscopic) Balance Equations
The Basic Laws. A body (here, of a fluid) consisting of a given set of fluid particles with a total mass
m, total momentum p, and total energy E (E = internal + kinetic + potential) obeys the

CBE 6333, R. Levicky
1
Differential Balance Equations
We have previously derived integral balances for mass, momentum, and energy for a control volume.
The control volume was assumed to be some large object, such as a pipe. What if the balance equations
w

CBE 6333, R. Levicky
1
Fluid Kinematics and Constitutive Laws
In using the differential balance equations derived previously, it will be insightful to better understand
the basic types of motion that a fluid element may experience. This is the area of "fl

CBE 6333, Levicky
1
Differential Balances - Alternate Forms
To recall, differential balance equations express the basic laws of conservation of mass, momentum,
and energy:
D
Dt
Dv
Dt
De
Dt
= v
(conservation of mass)
(1)
= B +
(momentum balance)
(2)
= q +

Othmer Department of Chemical and Biological Engineering
CBE 6333 Transport Phenomena
Instructor:
Rastislav Levicky (rlevicky@poly.edu)
Rogers Hall 816 A
(718) 260-3682
Class Times and Location
Lecture:
Office hours:
Mon 6:00 - 8:25 PM
Room RH 702
Mon 5:0

CBE 6333, R. Levicky
1
Introduction to Turbulent Flow
Turbulent Flow. In turbulent flow, the velocity components and other variables (e.g. pressure, density
- if the fluid is compressible, temperature - if the temperature is not uniform) at a point fluctu

CBE 6333, R. Levicky
1
Orthogonal Curvilinear Coordinates
Introduction. Rectangular Cartesian coordinates are convenient when solving problems in which the
geometry of a problem is well described by the coordinates x1, x2, and x3. For example, in Fig. 1,

CBE 6333, R. Levicky
1
The Bernoulli Equation
Useful Definitions
Streamline: a line that is tangent to velocity v at each point at a given instant in time.
Path Lines: lines traced out by fluid particles moving with the flow. At steady state, streamlines