Case Studies in Fluid Mechanics with Sensitivities to Governing Variables

M. Kemal Atesmen

• Publisher: Wiley-ASME Press Series
• Year: 2018
• Print ISBN: 9781119524786
• eBook ISBN: 9781119524878
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Mechanical Engineering
• Index: Technology & Engineering

Covers a wide range of practical fluid mechanics, heat transfer, and mass transfer problems

This book covers the many issues that occur in practical fluid mechanics, heat transfer, and mass transfer, and examines the basic laws (the conservation of matter, conservation of momentum, conservation of energy, and the second law of thermodynamics) of these areas. It offers problem solutions that start with simplifying engineering assumptions and then identifies the governing equations and dependent and independent variables. When solutions to basic equations are not possible, the book utilizes historical experimental studies. It also looks at determining appropriate thermo-physical properties of the fluid under investigation, and covers solutions to governing equations with experimental studies.

Case Studies in Fluid Mechanics with Sensitivities to Governing Variables offers chapters on: draining fluid from a tank; vertical rise of a weather balloon; wind drag forces on people; Venturi meter; fluid's surface shape in a rotating cylindrical tank; range of an aircraft; designing a water clock; water turbine under a dam; centrifugal separation of particles; ideal gas flow in nozzles and diffusers; water supply from a lake to a factory; convection mass transfer through air-water interface; heating a room by natural convection; condensation on the surface of a vertical plate in laminar flow regime; bubble rise in a glass of beer; and more.

• Covers a broad spectrum of problems in practical fluid mechanics, heat transfer, and mass transfer
• Examines the basic laws of fluid mechanics, heat transfer and mass transfer
• Presents solutions to governing equations with experimental studies

Case Studies in Fluid Mechanics with Sensitivities to Governing Variables will appeal to engineers working in thermo-physical sciences and graduate students in mechanical engineering.

1
Draining Fluid from a Tank

Many fluid mechanics problems can be solved by making several simplifying assumptions and come up with fairly accurate results. If we consider conservation of mechanical energy along a streamline in a steady flow, namely no changes are occurring with respect to time in variables such as pressure, density, and flow velocity along a streamline; frictionless flow, namely there are no shear or viscous forces acting on the fluid; an incompressible fluid, where the fluid's density is a constant and a non‐rotating flow, then the governing fluid mechanics equations simplify to the following Bernoulli's equation along a fluid's streamline:

1.1

See Ref. [13] for more details regarding Bernoulli's equation.

Bernoulli's equation conserves the sum of pressure energy p, the potential energy ρ * g * z, and the kinetic energy 0.5 * ρ * V² along a streamline or along many streamlines, namely positions 1 and 2 as shown for a fluid like water in a large tank with a small discharge hole in Figure 1.1. Both positions 1 and 2 are at atmospheric pressure. Streamlines starting at the top of the fluid surface, position 1, converge at the small drain hole at position 2. We can apply the Bernoulli equation between positions 1 and 2 as follows:

1.2

V₁ ≈ 0, since we assume a large‐diameter cylindrical tank with a small discharge hole, at position 2. Also, the potential energies of the streamlines exiting the tank are zero at position 2. h is the distanc...

Table of contents

• Cover
• Table of Contents
• Series Preface
• Preface
• Acknowledgments
• About the Author
• Introduction
• 1 Draining Fluid from a Tank
• 2 Vertical Rise of a Weather Balloon
• 3 Stability of a Floating Cone in Water
• 4 Wind Drag Forces on People
• 5 Creeping Flow Past a Sphere
• 6 Venturi Meter
• 7 Fluid's Surface Shape in a Rotating Cylindrical Tank
• 8 Pin Floating on Surface of a Liquid
• 9 Small Raindrops
• 10 Range of an Aircraft
• 11 Designing a Water Clock
• 12 Water Turbine Under a Dam
• 13 Centrifugal Separation of Particles
• 14 A Simple Carburetor
• 15 Ideal Gas Flow in Nozzles and Diffusers
• 16 Laminar Flow in a Pipe
• 17 Water Supply from a Lake to a Factory
• 18 Air or Water Flow Required to Cool a PC Board
• 19 Convection Mass Transfer Through Air–Water Interface
• 20 Heating a Room by Natural Convection
• 21 Laminar Flow Through Porous Material
• 22 Condensation on the Surface of a Vertical Plate in a Laminar Flow Regime
• 23 A Non‐Newtonian Fluid Flow in a Pipe
• 24 Bubble Rise in a Glass of Beer
• References
• Index
• End User License Agreement