Pressure Variation Along Streamlines
ME332: Fluid Mechanics
Joseph Senechal
Section: 005
8:00 AM 10:50 AM
Aryan Mehboudi
October 9, 2014
1
Abstract
In this lab experiment, pressure and velocity were both determined along various streamlines.
Once pressure
Pressure Variation Along
Streamlines
1. Introduction
The purpose of this lab is to demonstrate the connection between
pressure and velocity variations along streamlines using the Bernoulli equation,
and the utilization of this equation for velocity measur
Conservation of Energy
Lab Session 8
ME 332 Fluid mechanics
Andrew Hildner
Section 8
Tuesday, 7:00 pm
Aryan Mehboudi
March 31, 2015
Abstract
The focus of the experiments in this laboratory session was to reinforce the concepts of
a characteristic curve, a
Name:_
ME 332, Spring 2009
Exam 2
Problem 1 (50 points):
The nozzle assembly on a fire-fighting boat is fixed to the boat deck by several heavy bolts.
The nozzle is directed at an angle of 35 degrees to the horizontal and has an outlet diameter
of d = 3 i
Homework 12 Solutions
P6.1 An engineer claims that flow of SAE 30W oil, at 20C, through a 5-cm-diameter smooth pipe at
1 million N/h, is laminar. Do you agree? A million newtons is a lot, so this sounds like an awfully high
flow rate.
Solution: For SAE 30
Lecture 18 (Navier Stokes Equation)
Differential Equation of Linear Momentum
dV
g p + ij =
dt
u
P xx yx zx
u
u
u
+
+
+
= + u + v + w
t
x
x
y
z
x
y
z
v
P xy yy zy
v
v
v
+
+
+
= + u + v + w
g y
t
y
x
y
z
x
y
z
w
P xz yz zz
w
w
w
+
+
+
=
g z
Lecture 17 (Differential Approach for Mass Conservation)
The Acceleration Field of a Fluid
V (r , t ) = i u ( x, y, z , t ) + j v( x, y, z , t ) + k w( x, y, z , t )
dV V V
V
V V
a=
=
+ u
x + v y + w z = t + V V
dt
t
(
Differential Equation of Mass Con
Lecture 16 (The Energy Equation)
The Energy Equation
dQ dW dE d
=
= edV + e V n dA
dt
dt
dt dt CV
CS
dE
1
1
= (u + V 2 + gz ) dV + (h + V 2 + gz ) V n dA
Q WS WV =
dt t CV
2
2
CS
Friction and Shaft Work in Low-Speed Flow
P V2
P V2
+
= +
2 g + z
Lecture 15 (The Angular Momentum Theorem)
Angular Momentum Theorem
B = Ho
Ho =
( r V )dm
SYST
d Ho
=
= r V
dm
d
dt ( H
)
o SYST
= Mo =
d
( r V ) dV + V r V n dA
dt CV
CS
Lecture 13 (Momentum Flux Correction Factor & Non-Inertial Reference Frame)
Momentum Flux Correction
2
u 2 dA = mVav = AVav
=
u2
1
(Vav ) dA
A
Non-inertial Reference Frame
F a
rel
dm =
CV
arel
d
V dV + V (V r n )dA
dt CV
CS
d2 R d
= 2+
+ 2 V + ( r )
Lecture 12 (The Linear Momentum Equation)
Conservation of Mass
B = m V = d B/ dm = V
d
d
(m V ) SYST = F = V dV + V Vr n dA
dt
dt CV
CS
Control Volume has a Number of One-Dimensional Outlets
F =
d
V dV + (mi Vi ) out (mi Vi ) in
dt CV
Net Pressure
Lecture 11 (Conservation of Mass)
Conservation of Mass
B = m = dm / dm = 1
d
dm
= 0 = dV + Vr n dA
dt CV
dt SYST
CS
Control Volume has a Number of One-Dimensional Outlets
CV
d
dV + ( i AiV ) out ( i AiV ) in
dt
Incompressible Flow
Vr n dA = 0
CS
Lecture 19 (Differential Energy Equation)
Differential Energy Equation
du
+ p ( V ) = (kT ) +
dt
2
2
2
2
2
u 2
v
w v u w u u w
= 2 + 2 + 2 + + +
+ + +
y
z x y y z z x
x
Boundaries Conditions
Continuity:
+ ( V ) = 0
t
Momentum:
dV
g p + ij =
Lecture 20 (Dimensional Homogeneity)
The principle of dimensional homogeneity
If an equation truly expresses a proper relationship between variables in a physical process it will be
dimensionally homogeneous; that is, each of its additive terms will have
Lecture 21 (Variables and Scaling Variables)
Definition
Variables are things we wish to plot, the basic out of the experiment or theory. The scaling variables are
then used to turn the variables into non dimensional numbers
Note that there is more than on
Lecture 22 (Buckingham PI Theorem)
PI Theorem I: expectations in reduction of variables
If a physical process satisfies the principle of dimensional homogeneity and involves n dimensional
variables, it can be reduced to a relation between only k dimension
Chapter 11 Turbomachinery
11.1 Describe the geometry and operation of a human peristaltic PDP which is cherished by every romantic person on earth. How do the two ventricles differ? Solution: Clearly we are speaking of the human heart, driven periodically
Lecture 9 (Reynolds Transport Theorem)
Volume and Mass Rate of Flow:
Q is the volume rate of flow
Q = (V n )dA = Vn dA
S
Reynolds Transport Theorem: Fixed Control Volume
Reynolds transport theorem is the analysis of a property for a given control volume.
Chapter 1 Introduction
1.1 A gas at 20C may be rarefied if it contains less than 1012 molecules per mm3. If Avogadro's number is 6.023E23 molecules per mole, what air pressure does this represent? Solution: The mass of one molecule of air may be computed
rate?
P1.10 flow
The Stokes-Oseen
formula [33] for drag force F on a *P1.14 Figure P1.14 shows the flow of water over a dam. The
homogeneous?
sphere of diameter D in a fluid stream of low velocity V,
volume flow Q is known to depend only on crest
the spec
in a Fluid
2 cm
P2.6
=
1.
xy
xx
A
Air
1.5 m
Gasoline
1m
Glycerin
Oil
diameter
Homework 2, due 01/27/2017
yx
2m
Any pressure reading can be expressed as a length or
head,
P2.4 h " p/"g. What is standard sea-level pressure
expressed in (a) ft of glycerin,
12,000 ft. Assume a standard atmosphere. How high
2m
would the liquid rise in a methanol barometer, assumed
Air
at 20C?
Hint: Dont forget
2 cm the vapor pressure.
Oil
diameter
P2.8 A diamond mine
is two miles below sea level. (a) EstiHomework 2, due 01/27
ME 332 - Fluid mechanics
Spring 2017 (Lecture component)
M, W, F: 11:30AM - 12:20PM
1279 Anthony Hall
Instructor
Dr. Ricardo Mejia-Alvarez
rimejal@egr.msu.edu
(517) 432 - 0814
Office: Engineering Research Complex (ERC), Rm. A117
1449 Engineering Research