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ME3560 Tentative Schedule–Summer I 2015
Week
Number
Date
Lecture
Topics Covered
Book
Section
Assignment
Study
Problems
Due Date
Introduction to course, syllabus and class
policies.
5/11/2015
1
Monday
2
Cont. Ch. 1. Dimensions, dimensional
homogeneity and units; modeling in
engineering, continuum; density; specific
weight; specific gravity.
5/11/2015
3
Cont. Ch. 1. Relation between viscosity and
rate of shearing strain; vapor pressure;
cavitation.
5/13/2015
4
Cont. Ch. 1. Relation between viscosity and
rate of shearing strain; vapor pressure;
cavitation.
5/11/2015
1
Wednesday
Ch. 1. Introduction. Brief history of FM;
definition of a fluid; the Non–Slip condition;
classification of fluid flows; system and
control volume.
5/13/2015
5
Ch. 2. Fluid Statics. Pressure at a point; basic
equation for a pressure field; pressure variation
in a fluid at rest.
5/13/2015
6
Cont. Ch. 2. Measurement of pressure;
manometry. Hydrostatic force on a plane
surface.
1.1–1.4, 1.6,
1.7.3, 1.8.
2.1–2.6.
Set 1.1
1.30, 1.31,
1.58, 1.66,
1.78, 1.80,
1.81, 1.85,
1.89.
Set 2.1
2.33, 2.39,
2.49,
SP2.15,
2.52.
5/18/2015
5/20/2015
5/18/2015
7
Cont. Ch. 2. Hydrostatic force on a plane
surface.
5/18/2015
Set 2.2
2.97, SP2.18,
SP2.19,
SP2.20
5/25/2015
Set 2.3
2.123, 2.130,
2.131, 2.145,
SP2.25,
SP2.28,
SP2.31.
5/25/2015
3.2, 3.2, 3.5,
3.6, 3.6.1–3.
Set 3.1
3.3, 3.19,
3.80, 3.83,
3.64, 3.65,
3.67.
5/27/2015
4.1, 4.1.1–4,
4.2, 4.2.1–3,
4.3, 4.4,
4.4.1–7.
Set 4.1
4.7, 4.9,
4.20, 4.26,
4.31, 4.40,
4.46.
6/3/2015
2.8–2.11.
8
Monday
5/18/2015
9
Cont. Ch. 2. Hydrostatic force on a curved
surface; buoyancy.
5/20/2015
10
Cont. Ch. 2. Hydrostatic force on a curved
surface; buoyancy.
5/20/2015
11
Ch. 3. Elementary Fluid Dynamics,
Bernoulli’s Equation - Introduction
12
Ch. 3. Elementary Fluid Dynamics,
Bernoulli’s Eq. Newton’s Second Law; F=ma
along a streamline; static, stagnation, dynamic
and total pressure.
2
Wednesday
5/20/2015
Monday
5/25/2015
5/27/2015
3
Memorial Day
13
Wednesday
5/27/2015
14
Ch. 4. Fluid Kinematics. Velocity field;
Eulerian vs. Lagrangian flow descriptions; 1–,
2–, and 3–Dimensional flows; steady and
unsteady flows; streamlines, streaklines, and
pathlines. The acceleration field; material
derivative; unsteady effects; convective
effects; control Volume and systems
representations; the Reynolds Transport
Theorem; selection of a control volume.
TEST 1. Chapters 1 and 2
Monday
6/1/2015
15
6/1/2015
16
6/1/2015
17
6/3/2015
18
6/3/2015
19
6/3/2015
20
6/8/2015
21
4
Wednesday
Monday
5
Cont. Ch. 4. Fluid Kinematics. The Reynolds
Transport Theorem; selection of a control
volume.
Ch. 5. Finite Control Volume Analysis.
Conservation of mass–the continuity eqn.;
derivation of the Continuity eqn.; fixed non
deforming C. V.; moving non deforming C. V.;
deforming C. V.
Cont. Ch. 5. Newton’s Second Law–the linear
momentum eqn.; derivation of the linear
momentum eqn.; application of the linear
momentum eqn.
Cont. Ch. 5. First Law of Thermodynamics–
the energy eqn.; derivation of the energy eqn.;
application of the energy eqn.; comparison of
the energy equation with Bernoulli’s eqn.
6/8/2015
22
Cont. Ch. 5. First Law of Thermodynamics–
the energy eqn.; derivation of the energy eqn.;
application of the energy eqn.; comparison of
the energy equation with Bernoulli’s eqn.
6/8/2015
23
TEST 2. Chapters 3 and 4
6/10/2015
24
6/10/2015
25
Wednesday
6/10/2015
26
Set 5.1
5.4, 5.6, 5.11,
5.18, 5.23,
5.1, 5.1.1–4. SP5.6, 5.46,
SP5.10, 5.67,
SP5.21,
SP5.22.
6/8/2015
5.2, 5.2.1,
5.2.2.
5.3, 5.3.1–3.
5.3, 5.3.1–3.
Set 5.2
5.122,
5.123,
5.126,
SP5.127,
SP5.56
Ch. 6. Differential Analysis of Fluid Flow.
Set 6.1
Fluid element kinematics; velocity and
6.2, 6.12,
6.1, 6.2, 6.2.1,
acceleration; linear motion and deformation;
6.13, 6.35,
6.2.3,
angular motion and deformation; conservation
6.36, SP6.4,
Handout 1.
of mass; differential form of continuity
SP6.26,
equation; the stream function.
SP6.27
6.3, 6.3.1,
Set 6.2.1
Cont. Ch. 6. Conservation of linear
6.3.2, 6.4,
6.38, 6.46,
momentum; Description of forces acting on the
6.4.1, 6.4.3,
6.56, 6.65,
differential element; equations of motion;
6.4.5, 6.5,
6.68, 6.75.
inviscid flow; irrotational flow; the velocity
6.5.1–4, 6.6,
HW 6.2.2
potential; some basic plane potential flows;
6.6.1–3,
MATLAB
superposition of basic plane potential flows.
assignment
Handout 2.
6/15/2015
6/17/2015
6/17/2015
6/15/2015
Monday
27
6/15/2015
28
6/15/2015
29
6
Wednesday
6/17/2015
30
Cont. Ch. 6. Viscous flow; stress deformation
relationships; N–S equations; some simple
solutions for viscous incompressible fluids;
steady laminar flow between fixed parallel
plates; Couette flow; steady laminar flow in
circular tubes; steady, axial, laminar flow in an
annulus.
Ch. 7. Dimensional analysis and similitude.
Dimensional analysis; Buckingham Pi
theorem; determination of Pi terms; selection
of variables; determination of reference
dimensions; common dimensionless groups in
fluid mechanics; modeling and similitude;
theory of models; model scales; flow through
closed conduits; flow around immersed bodies.
6.8, 6.8.1,
6.8.2, 6.9,
6.9.1–6.9.4,
Handout 3.
Set 6.3
6.87, 6.85,
6.88, 6.90.
6.100.
6/22/2015
7.1–7.4
Set 7.1
7.12, 7.15,
7.19, 7.49,
7.58, 7.68.
6/24/2015
8.1, 8.1.1–3,
8.2, 8.2.1, 8.3,
8.3.1, 8.4,
8.4.1, 8.4.2,
8.5, 8.5.1.
Set 8.1
8.10, 8.11,
8.18, 8.30,
8.79, 8.81,
8.84, 8.92.
7/1/2014
Wind Tunnel Testing at WMU Airport
Wind Tunnel Facility.
Monday
6/22/2015
31
6/22/2015
32
6/22/2015
33
6/24/2015
34
7
Wednesday
6/24/2015
35
6/24/2015
36
Introduction to simulation (Fluent)
Ch. 8. Viscous flow in pipes. General
characteristics of pipe flow; laminar or
turbulent flow; entrance region and fully
developed flow; pressure and shear stress;
fully developed laminar flow; from F = ma
applied to a fluid element; fully developed
turbulent flow; transition from laminar to
turbulent flow; dimensional analysis of pipe
flow; major losses; minor losses.
TEST 3. Chapters 5 and 6
6/29/2015
Monday
37
6/29/2015
38
6/29/2015
39
8
40
Wednesday
7/1/2015
41
42
Cont. Ch. 8. Pipe flow examples; single pipes.
Ch. 9. Flow over Immersed bodies. General
external flow characteristics; Lift and drag
concepts; Characteristics of flow past and object;
Boundary layer characteristics; Boundary layer
structure and thickness on a flat plate, Drag;
Friction drag; Drag coefficient data and
examples; Lift; Surface pressure distribution.
Final Exam: Wednesday
7/1/2015. Comprehensive
SP 2.15. An inverted U-tube manometer containing oil (SG = 2.3) is located
between two reservoirs as shown in the figure below. The reservoir on the
left, which contains carbon tetrachloride, is closed and pressurized to 9 psi.
The reservoir on the right contains water and is open to the atmosphere. With
the given data, determine the depth of water, h, in ft, in the right reservoir.
(Assume the specific weight of carbon tetrachloride is 99.5 lbf/ft3 and the
specific weight of water is 62.4 lbf/ft3.)
SP 2.18. The rigid gate, OAB, shown in the figure below, is hinged at O and rests against
a rigid support at B. What minimum horizontal force, P, is required to hold the gate closed
if its width is 2.0 m? Neglect the weight of the gate and friction in the hinge. The back of
the gate is exposed to the atmosphere.
(Assume the specific weight of water is 9800 N/m3.)
SP 2.19. The gate shown is hinged at H. The gate is 1.6 m wide normal to the plane of the
diagram. Calculate the force required at A to hold the gate closed.
(Assume the density of water is 999 kg/m3 and g = 9.81 m/sec2.)
SP 2.20. The gate AOC shown is 6.3 ft wide and is hinged along O. Neglecting the weight of the gate, determine the force (in lbf) in bar AB.
The gate is sealed at C.
(Assume the density of water is 1.94 slug/ft3 and g = 32.2 ft/sec2.)
SP 2.25 Determine the hydrostatic force vector (in lbf) acting on the radial gate if the gate is 40 ft long
(normal to the page).
(Assume the density of water is 1.94 slug/ft3 and g = 32.2 ft/sec2. The resultant force vector should be
expressed in the following format:
5i -0.25j ------> (5*i)-(0.25*j)
where i and j are unit vectors in the x- and y-directions.)
SP 2.28 Liquid concrete is poured into the form shown (R = 0.348 m). The form is w = 4.9 m wide
normal to the diagram. Compute:
a) the magnitude of the vertical force exerted on the form by the concrete (in kN),
b) the horizontal distance (in m) from the center of curvature of the form to a point along which the
vertical force acts.
(Assume the specific gravity of concrete is 2.5, the density of water is 1000 kg/m3 and g = 9.81 m/sec2.)
SP 2.31 A volume of material (V = 1.06 ft3) weighing 67 lbf is allowed to sink in water as shown. A
circular wooden rod 10 ft long and 3 in2 in cross section is attached to the weight and also to the wall.
If the rod weighs 3 lbf, what will be the angle, , in degrees, for equilibrium?
(Assume the density of water is 1.94 slug/ft3 and g = 32.2 ft/sec2. )
SP 5.6 A hydraulic accumulator is designed to reduce pressure pulsations in a machine tool hydraulic system. For the instant shown,
determine the rate at which the accumulator gains or loses hydraulic oil (in ft3/sec) if Q = 5.67 gpm.
(Assume the specific gravity of water is 1.94 slug/ft3 and the specific gravity of
hydraulic fluid is 0.88.)
SP 5.8 Water flows steadily from a tank mounted on a cart as shown in the figure below. After the water jet leaves the nozzle of the tank, it
falls and strikes a vane attached to another cart. The cart's wheels are frictionless, and the fluid is inviscid.
a) Determine the speed of the water leaving the tank (in m/sec), V1,
b) Determine the speed of the water leaving the second cart (in m/sec), V2,
c) Determine the tension in rope A (in N), and
d) Determine the tension in rope B (in N)
(Assume the density of water is 999 kg/m3 and g = 9.81 m/sec2.)
SP 5.10 A jet of water issuing from a stationary nozzle at 14.0 m/sec (Aj = 0.07 m2) strikes a turning vane mounted on a cart as shown. The
vane turns the jet through an angle = 60o. Determine the value of M (in kg) required to hold the cart stationary.
(Assume the density of water is 999 kg/m3 and g = 9.81 m/sec2.)
SP 5.17 The nozzle shown discharges a sheet of water through a 180o arc. The water speed is 17.3 m/sec and the jet thickness is 30 mm at a
radial distance of 0.3 m from the centerline of the supply pipe. Find:
a) the volume flow rate of water in the jet sheet (in m3/sec).
b) the y-component of force (in kN) required to hold the nozzle in place.
(Assume the density of water is 999 kg/m3.)
SP 5.21 A steady jet of water is used to propel a small cart along a horizontal track as shown below. Total resistance to motion of the cart
assembly is given by FD = k U2, where k = 0.79 N-sec2/m2. Evaluate the acceleration of the cart (in m/sec2) at the instant when its speed is U =
10 m/sec.
(Assume the density of water is 999 kg/m3.)
SP 5.22 A vane slider assembly moves under the influence of a liquid jet as shown below. The coefficient of kinetic friction for motion of the
slider along the surface is
= 0.37. Calculate:
a) the acceleration of the slider (in m/sec2) at the instant when U = 10.3 m/sec.
b) the terminal speed of the slider (in m/sec).
(Assume g = 9.81 m/sec2.)
SP 5.56
SP 5.127
In addition, answer the following questions.
Concept:
Pressure changes for a flow in a pipe are dependent on the flow velocities, elevation change, the transfer of mechanical work, and frictional
losses.
(a) What is the specific weight of the water? νw =
(b) What is the specific weight of the mercury? νmer =
lbf/ft^3
lbf/ft^3
(c) What is the static pressure difference from section (1) to section (2) as reflected by the manometer (use minus sign if decrease)? ∆P =
lbf/ft^2
(d) What is the pressure difference from section (1) to section (2) due to elevation change (use minus sign if decrease)? ∆Pe =
lbf/ft^2
lbf/ft^2
(e) What is the change in dynamic pressure from section (1) to section (2) (use minus sign if decrease)? ∆Pd =
(f) What is the net change in pressure from section (1) to section (2)? ∆Pnet =
lbf/ft^2
ft-lbf/slug
(g) What is the magnitude of the loss in energy per unit mass from section (1) to section (2)? loss =
SP5.127-Part 2
Solve for the axial force due to friction at the pipe wall acting on the flow.
(a) What is the cross-sectional area of the pipe? A =
ft^2
lbf
(b) What is the net force due to pressure for the flow from section (1) to section (2)? Fnet =
(c) What is the volume of the fluid in the pipe between section (1) and section (2)? V =
ft^3
(d) What is the magnitude of the weight of the fluid in the pipe between section (1) and section (2)? w =
lbf
lbf
(e) What is the component of weight acting in the axial flow direction? wa =
lbf
(f) What is the change in momentum flux between section (1) and section (2)? ∆R =
(g) What is the magnitude of the frictional force acting on the flow? Rx =
lbf
SP 6.4 Consider the following velocity field:
where A = 0.25 m-1sec-1, B is a constant, and the coordinates are measured in meters. The flow is incompressible. Evaluate the
magnitude of the component of acceleration (in m/sec2) of a particle normal to the velocity vector at point (x,y) = (1,4).
SP 6.26 The stream function for an incompressible, two-dimensional flow field is ψ = 8y – 4y2. Is this an irrotational flow?
SP 6.27 A two-dimensional, incompressible flow is given by u = - y and v = x. Determine the equation of the streamline passing through the
point x = 6 and y = 0.