Drag and Momentum Balance

Slides:

Advertisements

Similar presentations

Boundary layer with pressure gradient in flow direction.

Advertisements

Aula Teórica 11 Integral Budgets: Momentum. General Principle & Mass The rate of accumulation inside a Control Volume balances the fluxes plus production.

Instructor: André Bakker

Experiment #5 Momentum Deficit Behind a Cylinder

ES 202 Fluid and Thermal Systems Lecture 28: Drag Analysis on Flat Plates and Cross-Flow Cylinders (2/17/2003)

Sources of the Magnetic Field

Particle Acceleration Particle t t+dt. Physical Interpretation Total acceleration of a particle Local acceleration Convective acceleration time velocity.

Pipe Flow Example Water flows steadily into the circular pipe with a uniform inlet velocity profile as shown. Due to the presence of viscosity, the velocity.

Electromagnetic Induction Inductors. Problem A metal rod of length L and mass m is free to slide, without friction, on two parallel metal tracks. The.

Flow over immersed bodies. Boundary layer. Analysis of inviscid flow.

Lecture 20 Discussion. [1] A rectangular coil of 150 loops forms a closed circuit with a resistance of 5 and measures 0.2 m wide by 0.1 m deep, as shown.

1 MECH 221 FLUID MECHANICS (Fall 06/07) Tutorial 7.

Fluid Dynamics.

CONSERVATION OF MASS Control Volumes By: Bashir Momodu.

Fluid Mechanics –For Civil Engineers is all about SMU Storing– Moving– Using ( Incompressible fluids - water) To design and manage these systems we need.

Flow Over Immersed Bodies

0.1m 10 m 1 km Roughness Layer Surface Layer Planetary Boundary Layer Troposphere Stratosphere height The Atmospheric (or Planetary) Boundary Layer is.

Mercury Marine Problem Basically what we are doing here is we are gluing a rubber seal on a painted aluminum part. It is sometimes difficult to keep the.

Conservation Vector Review Mass Balance General Statement Simplifications The Control Volume A Useable Form Problems.

1 MAE 5130: VISCOUS FLOWS Momentum Equation: The Navier-Stokes Equations, Part 1 September 7, 2010 Mechanical and Aerospace Engineering Department Florida.

Fluid Flow Pressure, momentum flux and viscosity..

Quanitification of BL Effects in Engineering Utilitites… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Engineering Parameters.

LAMINAR PLANE COUETTE AND OPEN CHANNEL FLOW

The Air-Sea Momentum Exchange R.W. Stewart; 1973 Dahai Jeong - AMP.

Momentum. NEWTON’S LAWS Newton’s laws are relations between motions of bodies and the forces acting on them. –First law: a body at rest remains at rest,

CHAPTER 6 MOMENTUM PRINCIPLE Dr. Ercan Kahya Engineering Fluid Mechanics 8/E by Crowe, Elger, and Roberson Copyright © 2005 by John Wiley & Sons, Inc.

Chapter 11 Fluids. Density and Specific Gravity The density ρ of an object is its mass per unit volume: The SI unit for density is kg/m 3. Density is.

Introduction to Fluid Mechanics

Basic bluff-body aerodynamics II

Practical Applications Wind Turbine Hydropower Turbine The motion of a fluid is altered so that propulsive forces can be generated on the devices. The.

Introduction to Fluid Mechanics

Electric Potential, Electric Potential Energy, and the Generalized Work Energy Theorem.

Newton’s Third Law of Motion

Chapter 22 Gauss’s Law Chapter 22 opener. Gauss’s law is an elegant relation between electric charge and electric field. It is more general than Coulomb’s.

Chapter 14 Fluids What is a Fluid? A fluid, in contrast to a solid, is a substance that can flow. Fluids conform to the boundaries of any container.

Mass Transfer Coefficient

Lecture 4: Isothermal Flow. Fundamental Equations Continuity equation Navier-Stokes equation Viscous stress tensor Incompressible flow Initial and boundary.

Introduction to Fluid Mechanics

Jan cm 0.25 m/s y V Plate Fixed surface 1.FIGURE Q1 shows a plate with an area of 9 cm 2 that moves at a constant velocity of 0.25 m/s. A Newtonian.

1 SYMMETRY OF THE STRESS TENSOR The stress tensor  ij satisfies the symmetry condition This condition is a consequence of the conservation of moment of.

Concept Summary. Momentum  Momentum is what Newton called the “quantity of motion” of an object.

Chapter 14 Fluids.

Electric Fields. The gravitational and electric forces can act through space without any physical contact between the interacting objects. Just like the.

External Flows An internal flow is surrounded by solid boundaries that can restrict the development of its boundary layer, for example, a pipe flow. An.

Abj 4.2.2: Pressure, Pressure Force, and Fluid Motion Without Flow [Q2 and Q3] Area as A Vector Component of Area Vector – Projected Area Net Area.

Reynolds Analogy It can be shown that, under specific conditions (no external pressure gradient and Prandtle number equals to one), the momentum and heat.

OC FLOW: ENERGY CONCEPTS, CHANNEL ANALYSIS

CE 1501 Flow Over Immersed Bodies Reading: Munson, et al., Chapter 9.

A Mathematical Frame Work to Create Fluid Flow Devices…… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Development of Conservation.

Slide 1Fig 29-CO, p.895. Slide 2  The direction of the magnetic field B at any location is the direction in which a compass needle points at that location.

Chapter 11 Angular Momentum. The Vector Product and Torque The torque vector lies in a direction perpendicular to the plane formed by the position vector.

1 CONSTITUTIVE RELATION FOR NEWTONIAN FLUID The Cauchy equation for momentum balance of a continuous, deformable medium combined with the condition of.

Transport process In molecular transport processes in general we are concerned with the transfer or movement of a given property or entire by molecular.

Chapter 14 Lecture 28: Fluid Mechanics: I HW10 (problems):14.33, 14.41, 14.57, 14.61, 14.64, 14.77, 15.9, Due on Thursday, April 21.

Mathematics to Innovate Blade Profile P M V Subbarao Professor Mechanical Engineering Department Also a Fluid Device, Which abridged the Globe into Global.

Ship Hydrodynamics - Resistance

GLOBAL CONSERVATION EQUATIONS

GLOBAL CONSERVATION EQUATIONS

Newton's Third Law of Motion and Momentum

Force and Moment Vectors

Drag and Momentum Balance for Flow Around a Cylinder

INFINITESIMALLY SMALL DIFFERENTIAL CUBE IN SPACE

Subject Name: FLUID MECHANICS

External Flows An internal flow is surrounded by solid boundaries that can restrict the development of its boundary layer, for example, a pipe flow. An.

Lorentz Forces The force F on a charge q moving with velocity v through a region of space with electric field E and magnetic field B is given by: 11/23/2018.

V 1. Conservation of Mass dz dy dx

A long straight conducting wire of length L and mass m carries a current I. The conductor is near the surface of the earth, in a uniform magnetic field.

Introdução à Camada Limite.

Chapter 21, Electric Charge, and electric Field

Newton’s Third Law of Motion

Presentation transcript:

Drag and Momentum Balance Aerodynamic drag is exerted on an object when fluid flow passes through it. This force is due to a combination of the shear and pressure forces acting on the surface of the object. The determination of these forces is difficult since it involves the measurement of both velocity and pressure fields near the surface of the object. However, based on the momentum balance concept, this force can also be determined as carrying out the momentum balance around the object. Drag force on a circular cylinder (unit width 1m) will be given here as an example. As shown below, velocity profiles before and after the cylinder are measured. Determine the drag force acting on the cylinder by assuming uniform pressure at the measuring stations. Vin=50 m/s (2) y u(y)=50 (m/s), |y|>1 =20+30|y| (m/s), |y|1 (5) 1 m x (1) (4) (3)

Control Volume and Control Surfaces Consider a control volume surrounding the cylinder as shown in the previous slide. Assume the flow around the cylinder is symmetric, therefore, only half of the control volume is needed as shown below. There are a total of five control surfaces in this problem. Surface 4 is the symmetric plane, therefore, does not contribute since no flow (therefore momentum) going through it. Surface 5 is the surface surrounding the cylinder, and the integration of the pressure and shear stresses on 5 will give the total force the cylinder is acting on the fluid: Rx. This force should balance with the forces acting on surfaces (1), (2) & (3) plus the momentum flow in & out of those surfaces. (Note: the force in y direction will be zero, why?) The surface forces on surfaces (1) & (3) will be free-stream pressure and they should cancel. Momentum flow in & out of (1) & (3) can be determined by integration. Question: Is there momentum flow out of surface (2)? (3) (1) (2) y 1 m (5) x (4)

Mass Conservation Obviously, since there is more mass flows into (1) than that flows out of (3). Their difference is the mass flow out of surface (2). If there is mass flow then the momentum flow is nozero. Use mass conservation: mass flow in (1) = mass flow out (2) + mass flow out (3)

Momentum Conservation

Lift and Drag Forces The force acting on the cylinder by the fluid is equal in magnitude and opposite in direction: Kx=-Rx=540(N). Drag force is in the positive x direction. MOVIE (NCSC University of Illinois) PIV MOVIE Periodic shedding of vortices into the wake generates alternative up- and down-wash as shown. Consequently, oscillatory loading will be exerted on the cylinder. L t