# Department of Energy Sciences, LTH

Size: px
Start display at page:

Transcription

1 Department of Energy Sciences, LTH MMV11 Fluid Mechanics LABORATION 1 Flow Around Bodies OBJECTIVES (1) To understand how body shape and surface finish influence the flow-related forces () To understand how scaling experiments can be used to determine the forces on a fullscale, real body (3) To understand the basic mechanisms of flow separation (4) To investigate pressure distributions around a circular cylinder and a wing profile SUMMARY The flow-related force vector acting on an immersed body can be divided into three named components, a drag (drag force), which acts in the flow direction, a lift (lift force) and a side force, all perpendicular to each other. The lift usually is in the direction so that it does a useful job, for instance upwards for an airplane in horizontal flight or downwards for inverted wings on race cars. In many cases the (time-mean) side force is zero, for instance when there is flow symmetry about the plane of lift and drag, as for an airplane flying in still air. Further, the components can be divided up with respect to their origin, wall surface pressure and wall friction. The pressure component of the drag, the pressure drag, is often referred to as the form drag since it is strongly dependent on the body form (shape). The remaining part is the friction drag, which is due to shearing viscous forces along the body surface. Flow similarity laws are crucial for model testing experiments. For instance, the Reynolds similarity law says that for incompressible flow about two geometrically similar bodies, without any effects of free surfaces, the flow itself is similar, if tested at the same Reynolds number. The lab session is based on three tests, in air flow. Test 1: Drag measurements Determine the drag for some different axisymmetric bodies and two circular cylinders. Test : Measurements of forces on an airfoil Determine lift and drag for an airfoil model at different angles of attack. Test 3: Pressure measurements Measure the distribution of static wall pressure around a circular cylinder in cross flow and an airfoil model, respectively. Also determine the form drag of the cylinder. PREREQUISITES Read this PM and pages , , , in F. M. White, Fluid Mechanics, 6th Edition 1, 006. REPORT Each student should account for all measurement data and results in the handed-out lab protocol, the report, which is to be finalized during the lab session. Time in lab: approx. 4 hours 1 Pages , , , in 5th edition; further page references are to the 6th edition. C. Norberg, 16/01/010

2 Forces on an immersed body A solid body that is exposed to flow of a viscous fluid is also affected by a flow-induced force. This force is the resultant of the normal and shear forces that acts locally on the body surface. The normal surface force is completely dominated by pressure action, the shear forces are due to viscous stresses only, and are normally referred to as friction forces. Consider a wing-like body of large width in relation to its chord, see Fig. 1. The flow around this body can be considered to be essentially two-dimensional. Figure 1: Forces on an immersed body, two-dimensional flow. The force vector F is divided into two components, the drag D, which acts in the flow direction, and the lift L, which acts normal to the flow. The drag itself is divided into pressure or form drag and friction drag. Form drag is due to the pressure forces acting on the surface (static pressure p); the friction drag is due the surface viscous shearing (frictional) forces (wall shear stress τ). The absolute value of F is normally expressed using a dimensionless coefficient C, defined as F ρ V = C A (1) V - oncoming, free stream velocity A - characteristic area ρ - density of fluid For geometrically similar bodies and for incompressible flows without influences of free surface effects we have the Reynolds similarity law: Flows around geometrically similar bodies are similar for equal Reynolds numbers The Reynolds number, Re, is dimensionless and is defined as Re ρv l V l = = () μ ν V - characteristic velocity, e.g. as above l - characteristic length μ - dynamic viscosity, ν - kinematic viscosity ( ν = μ / ρ ) For a certain geometrical flow situation, the Reynolds similarity law (or rule) means that the dimensionless coefficient C only is a function of the Reynolds number and a dimensionless

3 3 time (e.g. tv / l ), but only if the prerequisites are fulfilled. Thus, the following applies for the time-averaged force F in a stationary flow situation: C = f (Re) (3) If the a flow force on a body is to be determined from experiments, the Reynolds similarity law means that it is not necessary to use the same velocity, body size, fluid medium, fluid temperature, etc. as in the actual flow situation. If only the Reynolds number is the same, or if the Reynolds number is within an interval where C is a constant, the force from the scaled (model) situation can be transferred directly to determine the force on the actual body (fullscale, prototype). For instance, it is possible to transfer results from experiments in air to fullscale water conditions, but only if Reynolds number are equal. Drag The drag component caused by normal forces on the body, the form drag drag due to tangential forces D f, sum up to the total drag, D p, and the friction D = D p + D f (4) Consider Fig. 1 where ϕ is the angle between the surface normal n, at the surface element da, and the oncoming free stream velocity (of magnitude V). The pressure drag then is D p = p da cosϕ = ( p + ρ gz) da cosϕ = A A ρ V p *( x*, y*, z*,re) l da*cosϕ = A * ρ V l p *( x*, y*, z*,re) da*cosϕ = ρ V l f1(re) A * Dimensionless quantities are denoted with a *, e.g. x = x / l. Now introduce the projected area of the body in the free stream direction, or any other characteristic area of the body, and denote it by A. Since this area is proportional to l, it follows that * D p D p ρ V = CD, p A, where C D, p, the pressure drag coefficient, only depends on Re. The total friction drag becomes D f = τ da sinϕ = μ V t V Vt * da sinϕ = μ l n da sinϕ l n = μ μ V l f(re) = ρ V l f(re) = ρ V l f3(re) ρ V l *

4 4 Thus, Since D f ρ V = CD, f A, where the friction drag coefficient C D, f only depends on Re. = C C we then obtain for the total drag: C D D, f + D, p D = C D A ρ V where the (total) drag coefficient C only depends on Re, (Re). Lift The total lift force is determined in a similar fashion, D C D L = C L A ρ V where the lift coefficient C L only depends on Re, C L (Re) Force components measured in a model scale experiment can thus be transferred to any other scale, if there is full geometrical similarity and equal Reynolds numbers (and of course, stationary, incompressible flow without any influence of free surface, e.g., wave interactions). The choice of characteristic area and length For geometrical similar bodies the characteristic length l and the characteristic area A can be chosen arbitrarily. However, as a general rule for bluff bodies, bodies that under normal conditions give rise to large separated wake regions (for instance a sphere, ordinary cars, etc.), the characteristic area is normally chosen as the projected area of the body when viewing it from the upstream, along the free stream velocity; the so-called frontal area. As a characteristic length it is customary to choose a typical cross-stream dimension within the frontal area. For cylinders of circular cross-section the characteristic length is chosen as the diameter d, the frontal, characteristic area then is A = b d, where b is the cylinder length. Also for spheres the characteristic length is chosen as the diameter ( A = π d / 4 ). For slender bodies of the wing type ( wing profiles ) the characteristic length is chosen as the mean chord, ( l = c ), see Fig.. The so-called planform area (projected wing area) is used as characteristic area, A = Ap = bc, where b is the wing span. Figure : Wing profile at angle of attack α.

5 5 Symmetrical bodies In the mean sense, a fully symmetric body, e.g. a sphere, only has a force component in the flow direction, the drag D. According to eq. (1) this drag corresponds to a drag coefficient C D, which under the conditions of Reynolds similarity law only is a function of the Reynolds number (Re). The variations of C D with Re, for the flow around a sphere and a long circular cylinder in cross-flow, are shown in Fig. 3 (smooth surfaces). At very low Reynolds numbers for the sphere the drag coefficient in Fig. 3a approaches a straight line. For low enough Reynolds numbers, see p. 480 in White, the drag can be determined from the Stokes formula, D = 3π μ Vd (5) According to eq. (1) the drag coefficient becomes C D = 4 Re which means a straight line in logarithmic diagram (dotted line in Fig. 3a). 5 Within 5 10 < Re < 3 10 the drag coefficient for a sphere is approximately constant ( = 0.44 ± 0.07 ). Thus the drag within this interval is approximately proportional to the C D velocity squared, D V. At low Re (approx. Re < 1), from Stokes formula, it is proportional to the velocity, D V. Figure 3a: Drag coefficient for a smooth sphere (Fox & McDonald 1994). At high Re the surface roughness has a significant influence on C D, see Fig. 5.3 and D5. in White.

6 6 Figur 3b: Drag coefficient for a long and smooth circular cylinder in cross-flow. We recall that the total drag can be divided into form (pressure) drag and friction (viscous shear) drag. The Reynolds number is a measure of the ratio between inertia forces (mass times acceleration) and viscous forces in the flow field. This means that the viscous forces at large Re become very small in relation to the pressure forces, with pressure forces approximately balancing the inertial forces. Consequently, at high enough Re the form drag dominates, and it can be determined solely from the pressure field acting on the body surface. Fig. 3b shows that the form drag dominates the total drag for the circular cylinder as from about Re = For the cylinder, the friction drag coefficient can be approximated as, C D, f 3.5/ Re (6) C D, f For the circular cylinder and within 3 10 < Re < 3 10, C D = 1.08 ± At Re = the friction part is about 16% of the total drag, at Re = 3 10 it is only about 0.5%. 5 At Re 3 10, for both the sphere and the cylinder and with increasing Re, there is a dramatic decrease in the drag coefficient. In fact, over a short interval, the total drag actually diminishes with increasing velocity. The phenomenon is called drag crisis, and it depends on a change of character for the boundary layer, which influences the separation process; see 6 pages in White. At higher Re, for Re > 4 10 (approx.), the drag coefficient for the cylinder again settles to an approximate constant level, C = 0.6 ± 0.1, see Fig. 3b. 5 D

7 7 4 Figure 4: Pressure distribution round a circular cylinder in cross-flow ( Re 10 ). Fig. 4 shows a schematic of the pressure distribution along the stagnation streamline, for the circular cylinder in cross-flow at relatively high Reynolds numbers (where the drag coefficient is approximately constant, C D 1). The pressure difference Δp is referred to the undisturbed pressure far upstream, in this case the atmospheric pressure, Δp = p patm. Due to deceleration, there is a pressure rise in front of the cylinder. At high Re, the viscous forces in this region are negligible; the pressure rise at the stagnation point then is equal to the dynamic pressure ρv /. Due to acceleration the pressure decreases on the frontal side. Boundary-layer separation occurs at ϕ 80 ; the pressure in the separated (wake) region is approximately constant. Downstream of the cylinder the pressure eventually recovers to the undisturbed value. The pressure distribution around the cylinder surface will be studied further during the laboratory exercise. Wing profiles (aerofoils) Under normal circumstances a wing is subjected not only to a drag but also a lift. Consider the flow around a wide-span wing (a wing profile or aerofoil) exposed to a constant velocity (constant Reynolds number, assumed high), at varying angles of attack α, see Fig.. Since α is part of the geometry both CD and C L will depend on α. Starting at small α, the drag coefficient is approximately constant but then starts to increase; the lift coefficient increases rapidly, almost linear with α. The lift coefficient reaches a maximum at a critical angle of attack, α = αc ; beyond this angle there is a rapid decrease in C L while there is a continuing increase of C D. The occurrence of lift can be explained as follows. At small angles of attack the flow is attached to wing almost to the trailing edge. Due to this viscous adhesive capacity there is a net deflection of the flow downwards 3, which according to the laws of Newton means that there is an opposing force upwards on the wing. The wing profile acts like a turning vane. On the frontal part of the upper side of the wing there is a compression of streamlines, the velocity increases and this means, at high enough Re, that the pressure is lowered (cf. Bernoulli equation). The upper side is thus often called the suction side. On the lower side the streamlines diverge somewhat and the pressure increases slightly (pressure side). At high Re the occurrence of lift is thus due mainly to the pressure difference between the upper and lower side. On the upper side, however, the velocity eventually decreases and the pressure 3 Also the upstream flow is affected, at the wing tip flow is deflected upwards and this also contributes to lift.

8 8 thus starts to increase. This is an adverse pressure gradient and it means that there is a potential for flow separation, and for high enough angles of attack this certainly will happen, starting close to the trailing edge. This is about the point of maximum lift ( α = αc ). A slight increase in α then will move the position of flow separation rapidly upstream, the flow deflection diminishes significantly and there is a rapid drop in lift. Eventually the separation is so massive that the flow is barely deflected at all, the force is then dominated by (pressure) drag; see Fig. 5 and Fig. 7.4 in White. Beyond the critical angle α c the wing is said to be stalled; α c is often called the stall angle. The phenomenon of stall is of great importance when landing an airplane, as it is then crucial to have high enough lift with much drag, at a velocity as low as possible. If stall occurs the loss in lift might result in a too steep approach of the landing-ground. Figure 5: Polar diagram for a wing with b / c = 5 (Finnemore & Franzini 00). The angle of attack for which the ratio between lift and drag is a maximum is called the (best) gliding angle ( α g ). The angle of attack at cruising conditions is normally set at around this value. For a glider in still air, maximum sailing distance will occur at this angle of attack. For the cambered wing in Fig. 5, α 1. g End effects, wing-tip vortices All real wings (and cylinders) have limited width (length). Naturally, there will be flow distortions near the ends, end effects. If the width is high enough the end effects will be of minor importance, sometimes even neglected. At limited widths, the end effects can be reduced by using end plates, thin plates mounted at the ends, along the flow and of special design. For real finite-width wings there will be an overflow from the pressure (lower) side of

9 9 the wing to the suction (upper) side. At the wing tips the pressure is equalized (zero lift). The overflow results in so-called wing-tip vortices, which reduces the lift. It also increases the drag. Since this drag is due to lift it is usually called lift-induced drag. For more details, see Chapter 8.7 in White. Experimental equipment Wind tunnel During scientific measurements it is required to have a flow that is highly uniform, unidirectional and non-turbulent. To achieve this in air it is usually recommended to use a closed-return wind tunnel, with a plenum chamber with several gauze screens followed by a well-designed contraction before the test section, driven by low-noise, highly effective fan unit. However, such wind tunnels are very expensive and require much space. During the lab exercise we will instead use two small (and a bit noisy!), open wind tunnels (fan units), which are quite sufficient for our purposes. The wind tunnels used in this lab basically consist of an axial fan within a circular duct followed by a short contraction (nozzle). One unit has a guiding vane ring that will dampen the flow distortions due to the rotating fan blades. This unit also has exchangeable exit nozzles (of different outlet diameter). Prandtl tube (Pitot-static tube) The free stream velocity V is measured by using a so-called Prandtl tube, also called Pitotstatic tube, see pages 404/5 in White. Along a streamline in stationary, incompressible and frictionless flow the Bernoulli equation applies. Along a horizontal streamline or a streamline where effects of gravitation are negligible, it reads V p + ρ = p0 = const. (7) where p is static pressure, ρ the fluid density and V is the local velocity. The combination ρv / is called the dynamic pressure, the difference between the pressure in a zero-velocity state (stagnation pressure p 0 ) and the flowing state along the same streamline. At the tip of the Prandtl tube there is a pressure hole; it also has pressure holes along the perimeter further downstream. When pointing towards the flow, the frontal tip will become a stagnation point ( V = 0, p = p t ). At the position for the perimeter holes, and by careful design, the pressure has recovered exactly to the undisturbed value upstream, the free stream pressure p. If friction effects can be neglected, as they indeed can for high enough Reynolds numbers, the pressure difference between these two positions is equal to the dynamic pressure, since p = by eq. (7). The undisturbed velocity along the stagnation streamline then is t p 0 ( p 0 p) V = (8) ρ The air density can be calculated from the ideal gas law, p ρ =, where R = 87 J/(kg K) (9) RT

10 10 Pressure and force measurements Measurements of pressure differences will be carried out using a differential liquid U-tube manometer, with readings directly in pascal (Pa). A more detailed description and how to use it will be given by the instructor. Drag and lift components are measured using a twocomponent force balance, to be described by the instructor. Outline The laboratory session consists of three parts: 1. Measurements of Drag (axisymmetric bodies) (a) Measure the drag D on a set of axisymmetric bodies (Fig. 6), at a certain air velocity. Figure 6: Axisymmetric bodies. (b) Measure the drag D on two circular cylinders in cross-flow, for two or three velocities. Analysis (1) Compute Re and C D for all cases () Compare the results with Fig. 3 in this PM, and Table 7.3 in White. Measurements of drag and lift (wing profile) For a certain velocity, measure drag D and lift L for a wing profile at different angles of attack, e.g., α = -5 o, - o, 0 o, o, 5 o, 10 o, 15 o, 0 o, 5 o. Analysis (1) Compute the Reynolds number, C D, C L and the lift-to-drag ratio L / D = C L / C D. Why is L / D called the glide ratio? (think about unpowered descent of a plane in still air) What is the gliding angle α g? () Plot C D and C L as a function α (same diagram). What is the approximate stall angle? What happens at stall?

11 11 3. Pressure measurements (circular cylinder and wing profile) (a) Pressure distribution around a circular cylinder The surface pressure is measured through a small drilled hole in the surface. Measure the pressure difference Δp ϕ between the surface pressure (at mid-span) and the ambient pressure at various angles from the scale, e.g., -0 o, -10 o, 0 o, 10 o, 0 o, 40 o,.. 80 o, 90 o, 100 o, 10 o,..., 180 o, -0 o. The angular position for the actual stagnation point (where ϕ = 0 ) may not be identical to the scale value. Actual angles can be determined from the (assumed) symmetry condition. The pressure difference Δp ϕ is measured using a differential micro-manometer. Analysis The component that contributes to the pressure drag is stagnation point, The form drag D p Δ p ϕ cosϕ. Since ϕ = 0 is the pϕ = 0 = ρv / (Bernoulli equation, high Re). per unit width is determined from the integration around the perimeter, Δ π D p = 0 Δ p ϕ cosϕ R dϕ Because of symmetry it is enough to integrate over half the perimeter and multiply with, The form drag coefficient is π Δp cosϕ = R Δpϕ cosϕ dϕ = ρv R dϕ (10) Δp D p 0 0 ϕ= 0 π C D, p = D ρ V p R = π Δpϕ cosϕ dϕ Δp 0 ϕ= 0 (11) (b) Pressure measurements along a wing profile Pressure differences Δp x between the wall static pressure at different fixed positions and the ambient pressure are measured; see Fig. 7. The pressure tap at x = 0 is assumed to be at the stagnation point (limited angles of attack). Figure 7: Pressure holes on the wing profile.

12 1 Analysis Compute Reynolds numbers for both the cylinder and the wing profile. (a) Circular cylinder (1) Plot C p ( ϕ) = Δpϕ / Δpϕ = 0 and f ( ϕ) = ( Δpϕ / Δpϕ = 0 )cosϕ = C p cosϕ in the same diagram. Which part of the cylinder contributes most to the drag, frontal side or rear side? () Determine the pressure drag coefficient, C D, p, graphically. (3) Estimate the total drag coefficient, C D = CD, p + CD, f, and compare with results from previous total drag measurements and Fig. 3b in this PM. (b) Wing profile (1) Plot f ( x) = Δpx / Δpx= 0 = Δpx / Δp1, where x is the abscissa for the projected holes; see Fig. 7. Which side contributes most to the lift, the upper side or the lower side? On which surface is there a risk for flow separation? Why? () Estimate the lift coefficient C L REFERENCES Finnemore, E. J. & Franzini, J. B. (00), Fluid Mechanics (with Engineering Applications), Tenth Edition, McGraw-Hill. Fox, R. W. & McDonald, A. T. (1994), Introduction to Fluid Mechanics, Fourth Edition, John Wiley & Sons, Inc. White, F. M. (006), Fluid Mechanics, Sixth Edition, McGraw-Hill.

### Given the water behaves as shown above, which direction will the cylinder rotate?

water stream fixed but free to rotate Given the water behaves as shown above, which direction will the cylinder rotate? ) Clockwise 2) Counter-clockwise 3) Not enough information F y U 0 U F x V=0 V=0

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

### Lecture-4. Flow Past Immersed Bodies

Lecture-4 Flow Past Immersed Bodies Learning objectives After completing this lecture, you should be able to: Identify and discuss the features of external flow Explain the fundamental characteristics

### Department of Mechanical Engineering

Department of Mechanical Engineering AMEE401 / AUTO400 Aerodynamics Instructor: Marios M. Fyrillas Email: eng.fm@fit.ac.cy HOMEWORK ASSIGNMENT #2 QUESTION 1 Clearly there are two mechanisms responsible

### The E80 Wind Tunnel Experiment the experience will blow you away. by Professor Duron Spring 2012

The E80 Wind Tunnel Experiment the experience will blow you away by Professor Duron Spring 2012 Objectives To familiarize the student with the basic operation and instrumentation of the HMC wind tunnel

### Introduction to Aerospace Engineering

4. Basic Fluid (Aero) Dynamics Introduction to Aerospace Engineering Here, we will try and look at a few basic ideas from the complicated field of fluid dynamics. The general area includes studies of incompressible,

### AEROSPACE ENGINEERING DEPARTMENT. Second Year - Second Term ( ) Fluid Mechanics & Gas Dynamics

AEROSPACE ENGINEERING DEPARTMENT Second Year - Second Term (2008-2009) Fluid Mechanics & Gas Dynamics Similitude,Dimensional Analysis &Modeling (1) [7.2R*] Some common variables in fluid mechanics include:

### Aerodynamics. Basic Aerodynamics. Continuity equation (mass conserved) Some thermodynamics. Energy equation (energy conserved)

Flow with no friction (inviscid) Aerodynamics Basic Aerodynamics Continuity equation (mass conserved) Flow with friction (viscous) Momentum equation (F = ma) 1. Euler s equation 2. Bernoulli s equation

### PART 1B EXPERIMENTAL ENGINEERING. SUBJECT: FLUID MECHANICS & HEAT TRANSFER LOCATION: HYDRAULICS LAB (Gnd Floor Inglis Bldg) BOUNDARY LAYERS AND DRAG

1 PART 1B EXPERIMENTAL ENGINEERING SUBJECT: FLUID MECHANICS & HEAT TRANSFER LOCATION: HYDRAULICS LAB (Gnd Floor Inglis Bldg) EXPERIMENT T3 (LONG) BOUNDARY LAYERS AND DRAG OBJECTIVES a) To measure the velocity

### ν δ - 1 -

ν δ - 1 - δ ν ν δ ν ν - 2 - ρ δ ρ θ θ θ δ τ ρ θ δ δ θ δ δ δ δ τ μ δ μ δ ν δ δ δ - 3 - τ ρ δ ρ δ ρ δ δ δ δ δ δ δ δ δ δ δ - 4 - ρ μ ρ μ ρ ρ μ μ ρ - 5 - ρ τ μ τ μ ρ δ δ δ - 6 - τ ρ μ τ ρ μ ρ δ θ θ δ θ - 7

### SPC Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30

SPC 307 - Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30 1. The maximum velocity at which an aircraft can cruise occurs when the thrust available with the engines operating with the

### Lab 6: Lift and Bernoulli

Lab 6: Lift and Bernoulli Bio427 Biomechanics In this lab, we explore the flows and fluid dynamic forces on wings and other structures. We deploy force measurement techniques, wind meters, and a variety

### Lesson 6 Review of fundamentals: Fluid flow

Lesson 6 Review of fundamentals: Fluid flow The specific objective of this lesson is to conduct a brief review of the fundamentals of fluid flow and present: A general equation for conservation of mass

### SYSTEMS VS. CONTROL VOLUMES. Control volume CV (open system): Arbitrary geometric space, surrounded by control surfaces (CS)

SYSTEMS VS. CONTROL VOLUMES System (closed system): Predefined mass m, surrounded by a system boundary Control volume CV (open system): Arbitrary geometric space, surrounded by control surfaces (CS) Many

### UNIT II CONVECTION HEAT TRANSFER

UNIT II CONVECTION HEAT TRANSFER Convection is the mode of heat transfer between a surface and a fluid moving over it. The energy transfer in convection is predominately due to the bulk motion of the fluid

### Given a stream function for a cylinder in a uniform flow with circulation: a) Sketch the flow pattern in terms of streamlines.

Question Given a stream function for a cylinder in a uniform flow with circulation: R Γ r ψ = U r sinθ + ln r π R a) Sketch the flow pattern in terms of streamlines. b) Derive an expression for the angular

### BERNOULLI EQUATION. The motion of a fluid is usually extremely complex.

BERNOULLI EQUATION The motion of a fluid is usually extremely complex. The study of a fluid at rest, or in relative equilibrium, was simplified by the absence of shear stress, but when a fluid flows over

### Bluff Body, Viscous Flow Characteristics ( Immersed Bodies)

Bluff Body, Viscous Flow Characteristics ( Immersed Bodies) In general, a body immersed in a flow will experience both externally applied forces and moments as a result of the flow about its external surfaces.

### FLUID MECHANICS. Chapter 9 Flow over Immersed Bodies

FLUID MECHANICS Chapter 9 Flow over Immersed Bodies CHAP 9. FLOW OVER IMMERSED BODIES CONTENTS 9.1 General External Flow Characteristics 9.3 Drag 9.4 Lift 9.1 General External Flow Characteristics 9.1.1

UNIT IV BOUNDARY LAYER AND FLOW THROUGH PIPES Definition of boundary layer Thickness and classification Displacement and momentum thickness Development of laminar and turbulent flows in circular pipes

### Visualization of flow pattern over or around immersed objects in open channel flow.

EXPERIMENT SEVEN: FLOW VISUALIZATION AND ANALYSIS I OBJECTIVE OF THE EXPERIMENT: Visualization of flow pattern over or around immersed objects in open channel flow. II THEORY AND EQUATION: Open channel:

### UNIT 4 FORCES ON IMMERSED BODIES. Lecture-01

1 UNIT 4 FORCES ON IMMERSED BODIES Lecture-01 Forces on immersed bodies When a body is immersed in a real fluid, which is flowing at a uniform velocity U, the fluid will exert a force on the body. The

### Lecture 7 Boundary Layer

SPC 307 Introduction to Aerodynamics Lecture 7 Boundary Layer April 9, 2017 Sep. 18, 2016 1 Character of the steady, viscous flow past a flat plate parallel to the upstream velocity Inertia force = ma

### E80. Fluid Measurement The Wind Tunnel Lab. Experimental Engineering.

Fluid Measurement The Wind Tunnel Lab http://twistedsifter.com/2012/10/red-bull-stratos-space-jump-photos/ Feb. 13, 2014 Outline Wind Tunnel Lab Objectives Why run wind tunnel experiments? How can we use

### List of symbols. Latin symbols. Symbol Property Unit

Abstract Aircraft icing continues to be a threat for modern day aircraft. Icing occurs when supercooled large droplets (SLD s) impinge on the body of the aircraft. These droplets can bounce off, freeze

### INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad

INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad - 500 043 AERONAUTICAL ENGINEERING TUTORIAL QUESTION BANK Course Name : LOW SPEED AERODYNAMICS Course Code : AAE004 Regulation : IARE

### COURSE ON VEHICLE AERODYNAMICS Prof. Tamás Lajos University of Rome La Sapienza 1999

COURSE ON VEHICLE AERODYNAMICS Prof. Tamás Lajos University of Rome La Sapienza 1999 1. Introduction Subject of the course: basics of vehicle aerodynamics ground vehicle aerodynamics examples in car, bus,

### Friction Factors and Drag Coefficients

Levicky 1 Friction Factors and Drag Coefficients Several equations that we have seen have included terms to represent dissipation of energy due to the viscous nature of fluid flow. For example, in the

### CLASS SCHEDULE 2013 FALL

CLASS SCHEDULE 2013 FALL Class # or Lab # 1 Date Aug 26 2 28 Important Concepts (Section # in Text Reading, Lecture note) Examples/Lab Activities Definition fluid; continuum hypothesis; fluid properties

### Empirical Co - Relations approach for solving problems of convection 10:06:43

Empirical Co - Relations approach for solving problems of convection 10:06:43 10:06:44 Empirical Corelations for Free Convection Use T f or T b for getting various properties like Re = VL c / ν β = thermal

### Measurements using Bernoulli s equation

An Internet Book on Fluid Dynamics Measurements using Bernoulli s equation Many fluid measurement devices and techniques are based on Bernoulli s equation and we list them here with analysis and discussion.

### 10.52 Mechanics of Fluids Spring 2006 Problem Set 3

10.52 Mechanics of Fluids Spring 2006 Problem Set 3 Problem 1 Mass transfer studies involving the transport of a solute from a gas to a liquid often involve the use of a laminar jet of liquid. The situation

### CALIFORNIA POLYTECHNIC STATE UNIVERSITY Mechanical Engineering Department ME 347, Fluid Mechanics II, Winter 2018

CALIFORNIA POLYTECHNIC STATE UNIVERSITY Mechanical Engineering Department ME 347, Fluid Mechanics II, Winter 2018 Date Day Subject Read HW Sept. 21 F Introduction 1, 2 24 M Finite control volume analysis

### Experimental Investigation to Study Flow Characteristics over a Naca0018 Aerofoil and an Automobile Dome-A Comparative Study

Experimental Investigation to Study Flow Characteristics over a Naca0018 Aerofoil and an Automobile Dome-A Comparative Study M. Sri Rama Murthy 1, A. V. S. S. K. S. Gupta 2 1 Associate professor, Department

### Steady waves in compressible flow

Chapter Steady waves in compressible flow. Oblique shock waves Figure. shows an oblique shock wave produced when a supersonic flow is deflected by an angle. Figure.: Flow geometry near a plane oblique

### Flight Vehicle Terminology

Flight Vehicle Terminology 1.0 Axes Systems There are 3 axes systems which can be used in Aeronautics, Aerodynamics & Flight Mechanics: Ground Axes G(x 0, y 0, z 0 ) Body Axes G(x, y, z) Aerodynamic Axes

### Lab Reports Due on Monday, 11/24/2014

AE 3610 Aerodynamics I Wind Tunnel Laboratory: Lab 4 - Pressure distribution on the surface of a rotating circular cylinder Lab Reports Due on Monday, 11/24/2014 Objective In this lab, students will be

### External Forced Convection. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

External Forced Convection Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Drag and Heat Transfer in External flow Fluid flow over solid bodies is responsible

### Fluids. Fluids in Motion or Fluid Dynamics

Fluids Fluids in Motion or Fluid Dynamics Resources: Serway - Chapter 9: 9.7-9.8 Physics B Lesson 3: Fluid Flow Continuity Physics B Lesson 4: Bernoulli's Equation MIT - 8: Hydrostatics, Archimedes' Principle,

### Active Control of Separated Cascade Flow

Chapter 5 Active Control of Separated Cascade Flow In this chapter, the possibility of active control using a synthetic jet applied to an unconventional axial stator-rotor arrangement is investigated.

### Nicholas J. Giordano. Chapter 10 Fluids

Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 10 Fluids Fluids A fluid may be either a liquid or a gas Some characteristics of a fluid Flows from one place to another Shape varies according

### Experimental and Numerical Investigation of Flow over a Cylinder at Reynolds Number 10 5

Journal of Modern Science and Technology Vol. 1. No. 1. May 2013 Issue. Pp.52-60 Experimental and Numerical Investigation of Flow over a Cylinder at Reynolds Number 10 5 Toukir Islam and S.M. Rakibul Hassan

### 6.1 Momentum Equation for Frictionless Flow: Euler s Equation The equations of motion for frictionless flow, called Euler s

Chapter 6 INCOMPRESSIBLE INVISCID FLOW All real fluids possess viscosity. However in many flow cases it is reasonable to neglect the effects of viscosity. It is useful to investigate the dynamics of an

### FE Exam Fluids Review October 23, Important Concepts

FE Exam Fluids Review October 3, 013 mportant Concepts Density, specific volume, specific weight, specific gravity (Water 1000 kg/m^3, Air 1. kg/m^3) Meaning & Symbols? Stress, Pressure, Viscosity; Meaning

### Fundamentals of Fluid Mechanics

Sixth Edition Fundamentals of Fluid Mechanics International Student Version BRUCE R. MUNSON DONALD F. YOUNG Department of Aerospace Engineering and Engineering Mechanics THEODORE H. OKIISHI Department

### FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER

FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER ANKARA UNIVERSITY FACULTY OF AGRICULTURE DEPARTMENT OF AGRICULTURAL MACHINERY AND TECHNOLOGIES ENGINEERING 1 5. FLOW IN PIPES 5.1.3. Pressure and Shear Stress

### CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS NOOR ALIZA AHMAD

CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS 1 INTRODUCTION Flow often referred as an ideal fluid. We presume that such a fluid has no viscosity. However, this is an idealized situation that does not exist.

### Introduction to Aerospace Engineering

Introduction to Aerospace Engineering Lecture slides Challenge the future 3-0-0 Introduction to Aerospace Engineering Aerodynamics 5 & 6 Prof. H. Bijl ir. N. Timmer Delft University of Technology 5. Compressibility

### Fluid Dynamics Exercises and questions for the course

Fluid Dynamics Exercises and questions for the course January 15, 2014 A two dimensional flow field characterised by the following velocity components in polar coordinates is called a free vortex: u r

### Fluid Mechanics II. Newton s second law applied to a control volume

Fluid Mechanics II Stead flow momentum equation Newton s second law applied to a control volume Fluids, either in a static or dnamic motion state, impose forces on immersed bodies and confining boundaries.

### Part A: 1 pts each, 10 pts total, no partial credit.

Part A: 1 pts each, 10 pts total, no partial credit. 1) (Correct: 1 pt/ Wrong: -3 pts). The sum of static, dynamic, and hydrostatic pressures is constant when flow is steady, irrotational, incompressible,

### Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015

Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 I. Introduction (Chapters 1 and 2) A. What is Fluid Mechanics? 1. What is a fluid? 2. What is mechanics? B. Classification of Fluid Flows 1. Viscous

CE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK 3 0 0 3 UNIT I FLUID PROPERTIES AND FLUID STATICS PART - A 1. Define fluid and fluid mechanics. 2. Define real and ideal fluids. 3. Define mass density

### Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay

Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture No. # 35 Boundary Layer Theory and Applications Welcome back to the video course on fluid

### for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory?

1. 5% short answers for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory? in what country (per Anderson) was the first

### Syllabus for AE3610, Aerodynamics I

Syllabus for AE3610, Aerodynamics I Current Catalog Data: AE 3610 Aerodynamics I Credit: 4 hours A study of incompressible aerodynamics of flight vehicles with emphasis on combined application of theory

### High Speed Aerodynamics. Copyright 2009 Narayanan Komerath

Welcome to High Speed Aerodynamics 1 Lift, drag and pitching moment? Linearized Potential Flow Transformations Compressible Boundary Layer WHAT IS HIGH SPEED AERODYNAMICS? Airfoil section? Thin airfoil

### Fluid Mechanics II 3 credit hour. External flows. Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1

COURSE NUMBER: ME 323 Fluid Mechanics II 3 credit hour External flows Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1 External flows The study of external

### Approximate physical properties of selected fluids All properties are given at pressure kn/m 2 and temperature 15 C.

Appendix FLUID MECHANICS Approximate physical properties of selected fluids All properties are given at pressure 101. kn/m and temperature 15 C. Liquids Density (kg/m ) Dynamic viscosity (N s/m ) Surface

### Chemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017

Chemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017 Objective: Text: To introduce the basic concepts of fluid mechanics and heat transfer necessary for solution of engineering

Mestrado Integrado em Engenharia Mecânica Aerodynamics 1 st Semester 212/13 Exam 2ª época, 2 February 213 Name : Time : 8: Number: Duration : 3 hours 1 st Part : No textbooks/notes allowed 2 nd Part :

### ME332 FLUID MECHANICS LABORATORY (PART I)

ME332 FLUID MECHANICS LABORATORY (PART I) Mihir Sen Department of Aerospace and Mechanical Engineering University of Notre Dame Notre Dame, IN 46556 Version: January 14, 2002 Contents Unit 1: Hydrostatics

### The Bernoulli Equation

The Bernoulli Equation The most used and the most abused equation in fluid mechanics. Newton s Second Law: F = ma In general, most real flows are 3-D, unsteady (x, y, z, t; r,θ, z, t; etc) Let consider

### S.E. (Mech.) (First Sem.) EXAMINATION, (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum Marks : 100

Total No. of Questions 12] [Total No. of Printed Pages 8 Seat No. [4262]-113 S.E. (Mech.) (First Sem.) EXAMINATION, 2012 (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum

### Convection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds.

Convection The convection heat transfer mode is comprised of two mechanisms. In addition to energy transfer due to random molecular motion (diffusion), energy is also transferred by the bulk, or macroscopic,

### Chapter Four fluid flow mass, energy, Bernoulli and momentum

4-1Conservation of Mass Principle Consider a control volume of arbitrary shape, as shown in Fig (4-1). Figure (4-1): the differential control volume and differential control volume (Total mass entering

### Day 24: Flow around objects

Day 24: Flow around objects case 1) fluid flowing around a fixed object (e.g. bridge pier) case 2) object travelling within a fluid (cars, ships planes) two forces are exerted between the fluid and the

### COMPUTATIONAL SIMULATION OF THE FLOW PAST AN AIRFOIL FOR AN UNMANNED AERIAL VEHICLE

COMPUTATIONAL SIMULATION OF THE FLOW PAST AN AIRFOIL FOR AN UNMANNED AERIAL VEHICLE L. Velázquez-Araque 1 and J. Nožička 2 1 Division of Thermal fluids, Department of Mechanical Engineering, National University

### HVAC Clinic. Duct Design

HVAC Clinic Duct Design Table Of Contents Introduction... 3 Fundamentals Of Duct Design... 3 Pressure Changes In A System... 8 Example 1... 13 Duct Design Methods... 15 Example 2... 15 Introduction The

### vector H. If O is the point about which moments are desired, the angular moment about O is given:

The angular momentum A control volume analysis can be applied to the angular momentum, by letting B equal to angularmomentum vector H. If O is the point about which moments are desired, the angular moment

### BLUFF-BODY AERODYNAMICS

International Advanced School on WIND-EXCITED AND AEROELASTIC VIBRATIONS OF STRUCTURES Genoa, Italy, June 12-16, 2000 BLUFF-BODY AERODYNAMICS Lecture Notes by Guido Buresti Department of Aerospace Engineering

### Ph.D. Qualifying Exam in Fluid Mechanics

Student ID Department of Mechanical Engineering Michigan State University East Lansing, Michigan Ph.D. Qualifying Exam in Fluid Mechanics Closed book and Notes, Some basic equations are provided on an

### Chapter 14. Lecture 1 Fluid Mechanics. Dr. Armen Kocharian

Chapter 14 Lecture 1 Fluid Mechanics Dr. Armen Kocharian States of Matter Solid Has a definite volume and shape Liquid Has a definite volume but not a definite shape Gas unconfined Has neither a definite

### Mass of fluid leaving per unit time

5 ENERGY EQUATION OF FLUID MOTION 5.1 Eulerian Approach & Control Volume In order to develop the equations that describe a flow, it is assumed that fluids are subject to certain fundamental laws of physics.

### Momentum (Newton s 2nd Law of Motion)

Dr. Nikos J. Mourtos AE 160 / ME 111 Momentum (Newton s nd Law of Motion) Case 3 Airfoil Drag A very important application of Momentum in aerodynamics and hydrodynamics is the calculation of the drag of

### For example an empty bucket weighs 2.0kg. After 7 seconds of collecting water the bucket weighs 8.0kg, then:

Hydraulic Coefficient & Flow Measurements ELEMENTARY HYDRAULICS National Certificate in Technology (Civil Engineering) Chapter 3 1. Mass flow rate If we want to measure the rate at which water is flowing

### Introduction to Fluid Mechanics - Su First experiment: Flow through a Venturi

530.327 - Introduction to Fluid Mechanics - Su First experiment: Flow through a Venturi 1 Background and objectives. In this experiment, we will study the flow through a Venturi section using both flow

### 2.The lines that are tangent to the velocity vectors throughout the flow field are called steady flow lines. True or False A. True B.

CHAPTER 03 1. Write Newton's second law of motion. YOUR ANSWER: F = ma 2.The lines that are tangent to the velocity vectors throughout the flow field are called steady flow lines. True or False 3.Streamwise

### Fluid Mechanics. du dy

FLUID MECHANICS Technical English - I 1 th week Fluid Mechanics FLUID STATICS FLUID DYNAMICS Fluid Statics or Hydrostatics is the study of fluids at rest. The main equation required for this is Newton's

### BOUNDARY LAYER FLOWS HINCHEY

BOUNDARY LAYER FLOWS HINCHEY BOUNDARY LAYER PHENOMENA When a body moves through a viscous fluid, the fluid at its surface moves with it. It does not slip over the surface. When a body moves at high speed,

### 6.1 According to Handbook of Chemistry and Physics the composition of air is

6. Compressible flow 6.1 According to Handbook of Chemistry and Physics the composition of air is From this, compute the gas constant R for air. 6. The figure shows a, Pitot-static tube used for velocity

### 2 Navier-Stokes Equations

1 Integral analysis 1. Water enters a pipe bend horizontally with a uniform velocity, u 1 = 5 m/s. The pipe is bended at 90 so that the water leaves it vertically downwards. The input diameter d 1 = 0.1

### Fluids Applications of Fluid Dynamics

Fluids Applications of Fluid Dynamics Lana Sheridan De Anza College April 16, 2018 Last time fluid dynamics the continuity equation Bernoulli s equation Overview Torricelli s law applications of Bernoulli

### R09. d water surface. Prove that the depth of pressure is equal to p +.

Code No:A109210105 R09 SET-1 B.Tech II Year - I Semester Examinations, December 2011 FLUID MECHANICS (CIVIL ENGINEERING) Time: 3 hours Max. Marks: 75 Answer any five questions All questions carry equal

### Iran University of Science & Technology School of Mechanical Engineering Advance Fluid Mechanics

1. Consider a sphere of radius R immersed in a uniform stream U0, as shown in 3 R Fig.1. The fluid velocity along streamline AB is given by V ui U i x 1. 0 3 Find (a) the position of maximum fluid acceleration

### Airfoils and Wings. Eugene M. Cliff

Airfoils and Wings Eugene M. Cliff 1 Introduction The primary purpose of these notes is to supplement the text material related to aerodynamic forces. We are mainly interested in the forces on wings and

### 150A Review Session 2/13/2014 Fluid Statics. Pressure acts in all directions, normal to the surrounding surfaces

Fluid Statics Pressure acts in all directions, normal to the surrounding surfaces or Whenever a pressure difference is the driving force, use gauge pressure o Bernoulli equation o Momentum balance with

### Chapter 9 Flow over Immersed Bodies

57:00 Mechanics of Fluids and Transport Processes Chapter 9 Professor Fred Stern Fall 009 1 Chapter 9 Flow over Immersed Bodies Fluid flows are broadly categorized: 1. Internal flows such as ducts/pipes,

### FE Fluids Review March 23, 2012 Steve Burian (Civil & Environmental Engineering)

Topic: Fluid Properties 1. If 6 m 3 of oil weighs 47 kn, calculate its specific weight, density, and specific gravity. 2. 10.0 L of an incompressible liquid exert a force of 20 N at the earth s surface.

### 5 ENERGY EQUATION OF FLUID MOTION

5 ENERGY EQUATION OF FLUID MOTION 5.1 Introduction In order to develop the equations that describe a flow, it is assumed that fluids are subject to certain fundamental laws of physics. The pertinent laws

### Masters in Mechanical Engineering. Problems of incompressible viscous flow. 2µ dx y(y h)+ U h y 0 < y < h,

Masters in Mechanical Engineering Problems of incompressible viscous flow 1. Consider the laminar Couette flow between two infinite flat plates (lower plate (y = 0) with no velocity and top plate (y =

### Problem 4.3. Problem 4.4

Problem 4.3 Problem 4.4 Problem 4.5 Problem 4.6 Problem 4.7 This is forced convection flow over a streamlined body. Viscous (velocity) boundary layer approximations can be made if the Reynolds number Re

### Fundamental Concepts of Convection : Flow and Thermal Considerations. Chapter Six and Appendix D Sections 6.1 through 6.8 and D.1 through D.

Fundamental Concepts of Convection : Flow and Thermal Considerations Chapter Six and Appendix D Sections 6.1 through 6.8 and D.1 through D.3 6.1 Boundary Layers: Physical Features Velocity Boundary Layer

### Chapter 3 Lecture 8. Drag polar 3. Topics. Chapter-3

Chapter 3 ecture 8 Drag polar 3 Topics 3.2.7 Boundary layer separation, adverse pressure gradient and favourable pressure gradient 3.2.8 Boundary layer transition 3.2.9 Turbulent boundary layer over a

### 12-3 Bernoulli's Equation

OpenStax-CNX module: m50897 1 12-3 Bernoulli's Equation OpenStax Tutor Based on Bernoulli's Equation by OpenStax College This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution

### τ du In his lecture we shall look at how the forces due to momentum changes on the fluid and viscous forces compare and what changes take place.

4. Real fluids The flow of real fluids exhibits viscous effect, that is they tend to stick to solid surfaces and have stresses within their body. You might remember from earlier in the course Newtons law

### ENGINEERING FLUID MECHANICS. CHAPTER 1 Properties of Fluids

CHAPTER 1 Properties of Fluids ENGINEERING FLUID MECHANICS 1.1 Introduction 1.2 Development of Fluid Mechanics 1.3 Units of Measurement (SI units) 1.4 Mass, Density, Specific Weight, Specific Volume, Specific