ME3560 Tentative Schedule–Summer I 2014

Week Number

Date Lecture Topics Covered Assignment

Book Section

Problems Due Date

1

Tuesday

5/6/2014 1

Introduction to course, syllabus and class policies.

Ch. 1. Introduction. Brief history of FM;

definition of a fluid; the Non–Slip condition; classification of fluid flows; system and

control volume.

1.1–1.4, 1.6, 1.7.3, 1.8.

HW 1.1 1.30, 1.31, 1.58, 1.66, 1.78, 1.80, 1.81, 1.85,

1.89.

5/13/2014 5/6/2014 2

Cont. Ch. 1. Dimensions, dimensional homogeneity and units; modeling in

engineering, continuum; density; specific weight; specific gravity.

5/6/2014 3

Cont. Ch. 1. Relation between viscosity and

rate of shearing strain; vapor pressure; cavitation.

Thursday

5/8/2014 4 Cont. Ch. 1. Relation between viscosity and

rate of shearing strain; vapor pressure; cavitation.

2.1–2.6.

HW 2.1 2.33, 2.39,

2.49, SP2.15,

2.52

5/15/2014

5/8/2014 5

Ch. 2. Fluid Statics. Pressure at a point; basic equation for a pressure field; pressure variation

in a fluid at rest.

5/8/2014 6

Cont. Ch. 2. Measurement of pressure;

manometry. Hydrostatic force on a plane surface.

2

Tuesday

5/13/2014 7 Cont. Ch. 2. Hydrostatic force on a plane

surface.

5/13/2014 8 Cont. Ch. 2. Hydrostatic force on a plane

surface. 2.8–2.11.

HW 2.2 2.97, SP2.18,

SP2.19, SP2.20

5/20/2014

5/13/2014 9 Cont. Ch. 2. Hydrostatic force on a curved

surface; buoyancy.

HW 2.3 2.123, 2.130, 2.131, 2.145,

SP2.25, SP2.28, SP2.31.

5/20/2014

Thursday

5/15/2014 10 Cont. Ch. 2. Hydrostatic force on a curved

surface; buoyancy.

5/15/2014 11 Ch. 3. Elementary Fluid Dynamics, Bernoulli’s Equation - Introduction

5/15/2014 12 Ch. 3. Elementary Fluid Dynamics, Bernoulli’s Eq. Newton’s Second Law; F=ma along a streamline; static, stagnation, dynamic

and total pressure. 3.2, 3.2, 3.5, 3.6, 3.6.1–3.

HW 3.1 3.3, 3.19, 3.80, 3.83, 3.64, 3.65,

3.67.

5/27/2014

3

Tuesday

5/20/2014 13

5/20/2014 14 Cont. Ch. 3. Examples of use of the Bernoulli equation (free jets, confined flows, flow rate

measurement).

5/20/2014 15

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.

4.1, 4.1.1–4, 4.2, 4.2.1–3.

Thursday

5/22/2014 16 Cont. Ch. 4. The acceleration field; material

derivative; unsteady effects; convective effects; control Volume and systems

representations; the Reynolds Transport Theorem; selection of a control volume.

4.3, 4.4, 4.4.1–7.

HW 4.1 4.7, 4.9,

4.20, 4.26, 4.31, 4.40,

4.46.

5/29/2014

5/22/2014 17

5/22/2014 18 TEST 1. Chapters 1 and 2

4

Tuesday

5/27/2014 19

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.

5.1, 5.1.1–4. HW 5.1

5.4, 5.6, 5.11, 5.18, 5.23,

SP5.6, 5.46, SP5.10, 5.67,

SP5.21, SP5.22.

6/5/2014

5/27/2014 20 Cont. Ch. 5. Newton’s Second Law–the linear

momentum eqn.; derivation of the linear momentum eqn.; application of the linear

momentum eqn.

5.2, 5.2.1, 5.2.2.

5/27/2014 21

Thursday

5/29/2014 22

Cont. Ch. 5. Newton’s Second Law–the linear momentum eqn.; derivation of the linear momentum eqn.; application of the linear

momentum eqn. 5.3, 5.3.1–3.

HW 5.2 5.122, 5.123, 5.126,

SP5.127, SP5.56

6/5/2014 5/29/2014 23

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. 5/29/2014 24

5

Tuesday

6/3/2014 25 Ch. 6. Differential Analysis of Fluid Flow.

Fluid element kinematics; velocity and acceleration; linear motion and deformation;

angular motion and deformation; conservation of mass; differential form of continuity

equation; the stream function.

6.1, 6.2, 6.2.1, 6.2.3,

Handout 1.

HW 6.1 6.2, 6.12, 6.13, 6.35,

6.36, SP6.4, SP6.26, SP6.27

6/10/2014

6/3/2014 26

6/3/2014 27 TEST 2. Chapters 3 and 4

Thursday

6/5/2014 28 Cont. Ch. 6. Conservation of linear momentum; Description of forces acting on the

differential element; equations of motion; inviscid flow; irrotational flow; the velocity potential; some basic plane potential flows; superposition of basic plane potential flows.

6.3, 6.3.1, 6.3.2, 6.4,

6.4.1, 6.4.3, 6.4.5, 6.5,

6.5.1–4, 6.6, 6.6.1–3,

Handout 2.

HW 6.2.1 6.38, 6.46, 6.56, 6.65, 6.68, 6.75. HW 6.2.2 MATLAB assignment

6/12/2014

6/5/2014 29

6/5/2014 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.

6.8, 6.8.1, 6.8.2, 6.9,

6.9.1–6.9.4, Handout 3.

HW 6.3 6.87, 6.85, 6.88, 6.90.

6.100.

6/12/2014

6

Monday 6/9/2014 Wind Tunnel Testing at WMU Airport

Wind Tunnel Facility. Time to be determined

Tuesday

6/10/2014 31

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.

6/10/2014 32 Introduction to simulation (Fluent) 7.1–7.4

6/10/2014 33

Thursday

6/12/2014 34

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.

7.1–7.4

HW 7.1 7.12, 7.15, 7.19, 7.49, 7.58, 7.68.

6/19/2014

6/12/2014 35

6/12/2014 36

7

Tuesday

6/17/2014 37

TEST 3. Chapters 5 and 6

6/17/2014 38

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.

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.

HW 8.1 8.10, 8.11, 8.18, 8.30, 8.79, 8.81, 8.84, 8.92.

6/24/2014

6/17/2014 39

Thursday

6/19/2014 40 Ch. 8. Cont. Pipe flow examples; single pipes.

6/19/2014 41 Ch. 9. Flow over Immersed bodies. General external flow characteristics; Lift and drag concepts; Characteristics of flow past and

object; Boundary layer characteristics; 6/19/2014

Boundary layer structure and thickness on a flat plate, Drag; Friction drag; Drag coefficient

data and examples; Lift; Surface pressure distribution.

Final Exam: Tuesday 6/24/2014. 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 = lbf/f t^3

(b) What is the specific weight of the mercury? νmer = 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

(e) What is the change in dynamic pressure from section (1) to section (2) (use minus sign if decrease)? ∆Pd = lbf/ft^2

(f) What is the net change in pressure from section (1) to section (2)? ∆Pnet = lbf/ft^2

(g) What is the magnitude of the loss in energy per unit mass from section (1) to section (2)? loss = ft-lbf/slug

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

(b) What is the net force due to pressure for the flow from section (1) to section (2)? Fnet = lbf

(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

(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 = lbf

(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.