ME3560 Tentative Schedule–Summer I 2016 Week Number Date Lecture Topics Covered Book Section Assignment Study Problems Due Date Introduction to course, syllabus and class policies. 5/9/2016 1 Monday Quiz 1 2 Cont. Ch. 1. Dimensions, dimensional homogeneity and units; modeling in engineering, continuum; density; specific weight; specific gravity. 5/9/2016 3 Cont. Ch. 1. Relation between viscosity and rate of shearing strain; vapor pressure; cavitation. 5/11/2016 4 Cont. Ch. 1. Relation between viscosity and rate of shearing strain; vapor pressure; cavitation. 5/9/2016 1 Wednesday Quiz 2 Ch. 1. Introduction. Brief history of FM; definition of a fluid; the Non–Slip condition; classification of fluid flows; system and control volume. 5/11/2016 5 Ch. 2. Fluid Statics. Pressure at a point; basic equation for a pressure field; pressure variation in a fluid at rest. 5/11/2016 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. 5/16/2016 5/18/2016 5/16/2016 7 Cont. Ch. 2. Hydrostatic force on a plane surface. 5/16/2016 2.8–2.11. 8 Monday Quiz 3 5/23/2016 Set 2.3 2.123, 2.130, 2.131, 2.145, SP2.25, SP2.28, SP2.31. 5/23/2016 6/1/2016 6/1/2016 5/16/2016 9 Cont. Ch. 2. Hydrostatic force on a curved surface; buoyancy. 5/18/2016 10 Cont. Ch. 2. Hydrostatic force on a curved surface; buoyancy. 5/18/2016 11 Ch. 3. Elementary Fluid Dynamics, Bernoulli’s Equation - Introduction 5/18/2016 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. Set 3.1 3.3, 3.19, 3.80, 3.83, 3.64, 3.65, 3.67. 5/23/2016 13 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. 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. 5.1, 5.1.1–4. 2 Wednesday Quiz 4 Monday Quiz 5 Set 2.2 2.97, SP2.18, SP2.19, SP2.20 5/23/2016 14 5/23/2016 15 3 5/25/2016 16 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. 5/25/2016 17, 18 TEST 1. Chapters 1 and 2 Wednesday Monday 4 Wednesday Quiz 6 5/30/2016 Memorial Day 6/1/2016 19 6/1/2016 20 6/1/2016 21 6/6/2016 22 6/6/2016 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. 6/6/2016 24, 25 TEST 2. Chapters 3 and 4 Monday 5 6/8/2016 26 6/8/2016 27 Wednesday Quiz 7 6 Monday Quiz 8 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. 6/8/2016 28 6/13/2016 29 6/13/2016 30 6/13/2016 31 Set 5.1 5.4, 5.6, 5.11, 5.18, 5.23, SP5.6, 5.46, SP5.10, 5.67, SP5.21, 5.3, 5.3.1–3. SP5.22. 5.2, 5.2.1, 5.2.2. 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. 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. Set 6.3 6.87, 6.85, 6.88, 6.90. 6.100. 6/8/2016 6/13/2016 6/15/2016 6/15/2016 6/20/2016 Wednesday 6/15/2016 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 32, 33, 34 fluid mechanics; modeling and similitude; theory of models; model scales; flow through closed conduits; flow around immersed bodies. 7.1–7.4 Set 7.1 7.12, 7.15, 7.19, 7.49, 7.58, 7.68. 6/22/2016 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. 6/29/2016 Wind Tunnel Testing at WMU Airport Wind Tunnel Facility. Monday 6/20/2016 35 6/20/2016 36 6/20/2016 37 7 Wednesday Monday Quiz 9 8 6/22/2016 38 6/22/2016 6/27/2016 39, 40 41 6/27/2016 42 6/27/2016 43 44 Wednesday 6/29/2016 45 46 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 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 6/29/2016. 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.