( v n ) dA
Evaluating
( v n ) dA
for Conservation of Mass Problems
This is our general expression for mass flowrate. We will use it a
lot for conservation of mass problems. How we determine its valu
Conservation of mass
Rate of accumulation
Of mass
v
dA
n
Arbitrary Control Volume
=
Rate of
inflow

Rate of
efflux
Look at efflux or flow of
Matter out of CV
For a CV, the normal unit
vector points o
Fluid of specific gravity 0.9 flows into a horizontal Yjoint at a velocity of 5 in/s j
and splits equally into two streams. If the diameter D 1 is 6 in. and diameter D2 is
3 in., determine the force
In the figure below, the xdirection velocity profiles are shown for a control volume surrounding
a cylinder. If the flow is incompressible, what must the rate of flow be across the horizontal
control
While on summer vacation, a chemical engineering student visits a park with a high
waterfall. The student considers stepping from behind the waterfall into the stream of
water as shown in the figure.
A pair of gates at one end of a
X
river lock retains water within the
enclosure. Find the torque, which
acts to open one gate (i.e., the y
L
z
g
H2O
y
component of torque on the gate).
W
Hint: What i
Conservation of Momentum ExampleUtube Bend
Given:
3
ft
s
Q
3
D
p1
p2
H2O
4 in
.33 ft
21 psia
lbm
62.4
ft
3
1.0 cp
6.3 psig
4.3 psig
Find: Force to hold the Ubend
in place Rx
Basic equation:
i
Fx
Crowd Control
A Study In Forced
Submission
Brant Bennett, Mariana Dionisio, Sami Karam, Amy Robertson,
Michael Steele
Rioting and Anarchy
Order = Safety
Coercion May Be
Necessary to Maintain
Order
P
This is a conservation of mass problem. We reasonably assume the sprayer functions in a steady
mode, so there should be no accumulation. Water going in to the sprayer from the left must equal
that ex
CASO: GRUAS PARA LA INDUSTRIA
Gras para la industria S.A. (GISA) es una empresa lder dedicada al diseo,
manufactura, instalacin y mantenimiento de puentegras para la industria en general.
Su manufact
Dv g P 2v
Dt
Earlier we solve for velocity profile in a tube using a shell balance approach. This was long and
tedious. Now we will use the NavierStokes equation.
For Flow in Cylindrical Conduit:
r
Calculate the required torque in lbfft and heat loss (power
consumption) in horsepower to turn the shaft on the friction
bearing shown. You may assume the length of the bearing surface
on the shaft i
Differential Equation: Conservation of Momentum
cfw_
cfw_
Sum of the
External Forces =
z
+cfw_
Accumulation of Linear
Momentum within C.V.
Net Rate of Linear
Momentum Efflux
(x+x, y+y, z+z)
y
z
.
F
Conservation of Mass  Equation of Continuity
z
(x+x, y+y, z+z)
y
z
.
y
(x,y,z)
[Accumulation] = [Input]  [Output]
Or
[Rate of
[Rate of Accumulation] = Influx]
[Rate of
Efflux]
x
Mass is neither crea
.
Components of in Rectangular and Cylindrical Coordinates
The rate of deformation is important in characterizing flows. As described earlier,
material properties like viscosity can depend on the rate
Basic Steps for Solution of Flow with the NavierStokes Equation
1. Examine the flow situation. Select an appropriate coordinate system that is compatible
with the geometry.
2. Identify key features f
SHOW ALL WORK ON THIS EXAM. STATE ANY ASSUMPTIONS MADE. YOU MUST
SHOW INTERMEDIATE STEPS FOR CREDIT. Please write legibly.
Chemical Engineering 3113 / 29
Spring2016 2/ N
First Exam 7, IQ;
a, M
W
OPE
Fluid of specific gravity 0.9 flows into a horizontal Yjoint at a velocity of 5 in/s j
and splits equally into two streams. If the diameter D 1 is 6 in. and diameter D2 is
3 in., determine the force
Group 2
Volumetric Flowrate and Average
Velocity
Sage Ross
Randy Goll
Lisa Gourley
Marci Wyatt
Jennifer Oberlag
April 21, 2001
Problem Statement
Fluid flows through a conduit with a quarter circle cro
Fluid Flow Across a Vertical
Surface
Group #10
Andrea Watson
Rena Armstrong
Oluseyi Harris
Crystal Casey
Fluid flows across a surface with uniform velocity v.
The surface has height H and width W as s
Water polo is an olympic sport played in a swimming pool of specified dimensions.
The ball has a circumference of about 70 cm. If the rubber shell of a ball is about 0.3
cm thick with a density of 1.0
In the figure below, the xdirection velocity profiles are shown for a control volume surrounding
a cylinder. If the flow is incompressible, what must the rate of flow be across the horizontal
control
Mass Flow
Into a Separator
Problem Presented by Group 15:
Brandy Nolan
Kameelah Wesley
Andrew Carswell
Juste Tchandja
Problem Statement
Coal is delivered to a power plant as a water slurry and
seperat
A stationary jet engne is shown. Air with a density of 0.0805 lb m /ft 3 enters with velocity v1 while
the exhaust exits with velocity v2 as indicated. The inlet and outlet crosssectional areas are
b
Chemical engineers are interested in the mass transfer of gas molecules to a liquid
phase such as occurs with the sparging of oxygen in a fermenter. Shape of bubbles
has been studied experimentally us