# ME3560 Tentative Schedule Spring 2019

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1 ME3560 Tentative Schedule Spring 2019 Week Number Date Lecture Topics Covered Prior to Lecture Read Section Assignment Prep Problems for Prep Probs. Must be Solved by 1 Monday 1/7/ Introduction to course, syllabus and class policies. Math Review. Differentiation. Wednesday 1/9/ Math Review. Integration Monday 1/14/ Math Review. Differential Equations 2 Wednesday 1/16/ Ch. 1. Introduction. Brief history of FM*. Definition of a fluid. Continuum. the Non Slip condition*. Classification of flows*. System and control volume*. Dimensions, dimensional homogeneity and units; modeling in engineering. density; specific weight; specific gravity. Relation between viscosity and rate of shearing strain; vapor pressure; cavitation. Monday 1/21/2019 M. L. K. Day 3 Wednesday 1/23/ Cont. Ch. 1. Introduction. 1.1, 1.2, 1.4, 1.6, 1.8. HW , 1.31, 1.57, 1.64, 1.79, 1.80, 1.81, 1.85, /30/2019

2 4 Monday 1/28/ Wednesday 1/30/ Cont. Ch. 1. Introduction. Ch. 2. Fluid Statics. Pressure at a point; basic equation for a pressure field; pressure variation in a fluid at rest. Measurement of pressure. Manometry. Mechanical and Electronic Pressure Measuring Devices. Cont. Ch. 2. Hydrostatic force on a plane surface. Hydrostatic force on a curved surface HW , 2.39, 2.49, 2.54, 2.58, HW , SP2.18, SP2.19, SP2.20 2/4/2019 2/6/ Monday 2/4/ Wednesday 2/6/ Cont. Ch. 2. Hydrostatic force on a curved surface. Buoyancy Ch. 3. Elementary Fluid Dynamics, Bernoulli s Eq. Newton s Second Law; F=ma along a streamline; static, stagnation, dynamic and total pressure. Examples of use of the Bernoulli equation (free jets, confined flows, flow rate measurement). 3.2, 3.2, 3.5, 3.6, HW , 2.127, 2.130, 2.131, 2.145, SP2.25, SP2.28, SP2.31. HW , 3.19, , 3.82, 3.66, 3.67, /11/2019 2/13/ Monday 2/11/ 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, , 4.2, , 4.4, HW , 4.10, 4.20, 4.26, 4.27, 4.33, 4.39, /20/2019 Wednesday 2/13/ TEST 1. Chapters 1 and 2

3 7 8 Monday 2/18/ Wednesday 2/20/ Monday 2/25/ 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. 5.1, , 5.2.1, , HW , 5.6, 5.11, 5.14, 5.22, 5.27, 5.37, SP5.6, 5.46, SP5.10, 5.67, SP5.21, SP5.22. HW , 5.111, 5.116, 5.119, SP5.127, SP5.56 3/11/2019 3/11/2019 Wednesday 2/27/2019 Cont. Ch. 5. First Law of Thermodynamics the energy eqn. Spring Break 9 Monday 3/11/2019 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 , 6.5, 6.7, 6.12, 6.14, , 6.36, SP6.4, SP6.26, SP6.27 3/20/2019 Wednesday 3/13/ TEST 2. Chapters 3 and 4

4 10 Monday 3/18/ Cont. Ch. 6. Conservation of linear momentum; Description of forces acting on the differential element; equations of motion; inviscid flow; irrotational flow; Bernoulli s Eqn. for 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, , 6.6, , Handout 2. HW , 6.43, 6.59, 6.61, 6.56, HW MATLAB assignment 3/27/2019 Wednesday 3/20/ Cont. Ch. 6. Some basic plane potential flows; superposition of basic plane potential flows. 11 Monday 3/25/ 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, , Handout 3. HW , 6.85, 6.88, /1/2019 Wednesday 3/27/ Cont. Ch. 6. Some simple solutions for viscous incompressible fluids. 12 Monday 4/1/ 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. Modeling and similitude; theory of models; model scales; flow through closed conduits; flow around immersed bodies HW , 7.15, 7.19, 7.49, 7.58, /8/2019 Wednesday 4/3/ TEST 3. Chapters 5 and 6

5 13 Monday 4/8/ 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, , 8.2, 8.2.1, 8.3, 8.3.1, 8.4, 8.4.1, 8.4.2, 8.5, HW , 8.11, 8.18, 8.30, 8.79, 8.81, 8.84, /15/2019 Wednesday 4/10/2019 Cont. Ch. 8. Viscous flow in pipes. 14 Monday 4/15/ TEST 4. Chapters 7 and 8 Wednesday 4/17/ Final Review in Preparation for Final Exam Final Exam: Thursday 12:30 pm

6 SP 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/m 3.) SP 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/m 3 and g = 9.81 m/sec 2.)

7 SP 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/ft 3 and g = 32.2 ft/sec 2.) 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/ft 3 and g = 32.2 ft/sec 2. 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.)

8 SP 2.28 Liquid concrete is poured into the form shown (R = 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/m 3 and g = 9.81 m/sec 2.) SP 2.31 A volume of material (V = 1.06 ft 3 ) weighing 67 lbf is allowed to sink in water as shown. A circular wooden rod 10 ft long and 3 in 2 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/ft 3 and g = 32.2 ft/sec 2. )

9 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 ft 3 /sec) if Q = 5.67 gpm. (Assume the specific gravity of water is 1.94 slug/ft 3 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/m 3 and g = 9.81 m/sec 2.)

10 SP 5.10 A jet of water issuing from a stationary nozzle at 14.0 m/sec (Aj = 0.07 m 2 ) strikes a turning vane mounted on a cart as shown. The vane turns the jet through an angle = 60 o. Determine the value of M (in kg) required to hold the cart stationary. (Assume the density of water is 999 kg/m 3 and g = 9.81 m/sec 2.) SP 5.17 The nozzle shown discharges a sheet of water through a 180 o 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 m 3 /sec). b) the y-component of force (in kn) required to hold the nozzle in place. (Assume the density of water is 999 kg/m 3.)

11 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 U 2, where k = 0.79 N-sec 2 /m 2. Evaluate the acceleration of the cart (in m/sec 2 ) at the instant when its speed is U = 10 m/sec. (Assume the density of water is 999 kg/m 3.) 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 = Calculate: a) the acceleration of the slider (in m/sec 2 ) at the instant when U = 10.3 m/sec. b) the terminal speed of the slider (in m/sec). (Assume g = 9.81 m/sec 2.) SP 5.56

12 SP 5.127

13 In addition, answer the following questions.

14 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)? ΔP = lbf/ft^2 (d) What is the pressure difference from section (1) to section (2) due to elevation change (use minus sign if decrease)? ΔPe = lbf/ft^2 (e) What is the change in dynamic pressure from section (1) to section (2) (use minus sign if decrease)? ΔPd = lbf/ft^2 (f) What is the net change in pressure from section (1) to section (2)? ΔPnet = 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

15 (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)? ΔR = 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 -1 sec -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/sec 2 ) 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 4y 2. 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.

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