Introduction

In this book a wide range of 24 practical fluid mechanics problems that include heat transfer and mass transfer are investigated. The approach to problem solutions starts with the applicable basic laws of fluid mechanics, heat transfer, and mass transfer. These basic laws are the conservation of matter, the conservation of momentum, the conservation of energy, and the second law of thermodynamics. Each problem solution starts with the simplifying engineering assumptions and identifies the governing equations and dependent and independent variables. In some cases, where solutions to basic equations are not possible, historical experimental studies are utilized. Another critical area is the determination of the appropriate thermophysical properties of the fluid under investigation. Then, the solutions to the governing equations, alongside experimental studies, are presented graphically. These analyses are extended to the sensitivities of dependent variables to independent variables within the boundaries of interest. These sensitivity analyses narrow the field and range of independent variables that should be focused on during the design process.

The development of fluid mechanics started with the well‐known law of Archimedes regarding the buoyancy of submerged bodies in the third century BC. After Newton's laws of motion were introduced, Bernoulli introduced his fluid flow equations for frictionless flow under gravity forces during the eighteenth century. Fluid flow equations, including shear forces due to viscosity, were introduced in the nineteenth century by Navier–Stokes. During the same century, Reynolds differentiated between laminar and turbulent flow regimes. Reynolds named the most important dimensionless group in fluid mechanics: the Reynolds number, the ratio of inertia forces to viscous forces. At the beginning of the twentieth century, Prandtl observed the changes in flow close to a solid boundary, namely the boundary layer. Many engineers, physicists, and mathematicians tried to solve the Navier–Stokes boundary layer equations in laminar and turbulent flow regimes under every conceivable condition for internal and external flows, and tried to verify these solutions with experiments. As computers' speed and memory capacity advanced, so did the solutions to the Navier–Stokes equations and the field took a new name: “computational fluid mechanics.”

Another significant portion of fluid mechanics is the thermophysical properties of fluids, such as density, viscosity, surface tension, and so on under different temperatures and pressures. Historically, these thermophysical properties for different fluids were determined experimentally as the need arose.

I chose a wide variety of simple and fun problems in this book in order to give readers an insight into different approaches to a solution in fluid mechanics, heat transfer, and mass transfer. The sensitivities of the dependent variables to the governing independent variables are investigated under appropriate physical conditions.

Chapter 1 is about draining fluid from a tank, which uses Bernoulli's equation, namely the conservation of mechanical energy along a streamline in a steady flow, along with the experimentally determined discharge velocity coefficient from the discharge hole.

Chapter 2 treats the vertical rise of a weather balloon. Several assumptions are made by neglecting the effects of wind, humidity, clouds, thermals, reduction in gravity, Coriolis forces, and so on, in order to simplify the problem. Then, Archimedes' buoyancy law is used, along with the ideal gas law, all the way through the upper stratosphere.

Chapter 3 treats the stability of a right circular cone‐shaped object floating in water. Again, Archimedes' buoyancy law is used to find the tipping conditions for the cone. Similar applications can be formulated for any object floating on the surface of a fluid.

In Chapter 4 the wind drag forces acting on a person are investigated. All or some of the wind's kinetic energy is converted into pressure energy as a person tries to stagnate the oncoming wind. The Bernoulli equation is applied to determine the wind drag forces on people with different frontal areas. The well‐known Du Bois body surface area formula is utilized as a function of the person's height. Also, for human beings, an approximate experimental drag coefficient of unity is used.

Chapter 5 investigates a limiting case for the Navier–Stokes equations, namely creeping flow past a sphere for different viscosity fluids. During the nineteenth century, Stokes found an exact solution for the Navier–Stokes partial differential equations for a steady, incompressible, and creeping flow past a sphere. Here I expand his work to the sensitivities of the dependent variables, such as the sphere's fall velocity and its diameter, to the governing independent variables.

In Chapter 6 the Venturi meters that are used in pipes as flow meters for incompressible fluids are analyzed. In this analysis, a steady, non‐viscous and irrotational flow is assumed and again the Bernoulli principle is utilized, along with the conservation of volume flow rate. Venturi meters have been used for water and for waste water volume flow rate measurements for centuries. These gages use a converging and diverging nozzle connected in‐line with a pipe. For measurement of the pressure drop in the converging nozzle, the ends of a U‐tube partly filled with a measurement fluid of known density higher than that of water are attached to the upstream of the converging nozzle and to the throat area of the nozzle. There is always a correction factor, called the coefficient of discharge, between the theory and the real flow rate through the Venturi meter. The coefficient of discharge depends on the size, shape, and friction encountered in the Venturi meter.

Chapter 7 analyzes the surface shape of a fluid in a rotating cylindrical tank. In this analysis, the surface tension at the fluid's free surface and the viscous forces between the fluid and the walls of the tank are neglected. Only two forces acting on a fluid's surface particle are considered, namely the gravity force which draws the particle in the downward direction and the centrifugal force which draws the particle away from the center of rotation. Also, the spillover rotational speed is determined.

Chapter 8 investigates a pin floating on the surface of a liquid due to surface tension. Cohesive forces among the liquid molecules close to the surface of a liquid cause the surface tension phenomenon. The surface molecules of a liquid do not have similar molecules above them. As a result, these surface molecules exert greater cohesive forces on the same molecules below the surface, and those next to them on the surface. These excessive cohesive forces of the surface molecules have a tendency to contract to form a membrane‐like surface and minimize their excess surface energy. The maximum pin diameters that surface tension forces will hold on different liquid surfaces were determined.

Chapter 9 tackles the steady‐state behavior of small raindrops or drizzles. Mist and wind effects are neglected. Only raindrops of spherical shape are considered. For a small raindrop with diameter less than 2 mm, the gravity force balances the drag force, while neglecting the atmospheric air's buoyancy force as the raindrops fall to the Earth's surface. Experimental data is used for the drag coefficient of spherical liquid particles falling in air.

In Chapter 10 I investigate one of the most important performance parameters for different aircraft, namely their range, using Brequet's range formula. In this analysis I do not consider an aircraft's takeoff, climb, descent, and landing conditions. For aircraft with turbofan jet engines, I detail Airbus A380 and Boeing 737‐800 cruising conditions. For a propeller‐driven aircraft, I analyze the flight of the Spirit of St. Louis.

Chapter 11 treats the design of a water clock. To measure time, quite a variety of water clocks have been designed and used by humans for more than 6000 years. In this problem I analyze two water clock designs that have water flowing out of a drain hole at the bottom center of a vessel. In the first case a circular vessel's radius varies linearly with respect to time. In the second case the vessel radius is constant (i.e. a cylindrical vessel).

Water's potential energy stored behind a dam in a reservoir has been used very effectively for many decades for a spin water turbine that activates a generator to produce electricity. In Chapter 12 I apply the first law of thermodynamics for open systems, mostly identified as the modified Bernoulli equation, to sensitivities of design parameters for a water turbine system. The hydraulic diameter concept is utilized for non‐circular internal flows. Friction factors are obtained from a Moody diagram, including the water tunnel's wall surface roughness.

Centrifugal acceleration forces have been used very effectively to separate solid particles from fluids or to separate different density fluids. In Chapter 13 I investigate the separation of particles in a fluid flow by centrifugal forces in a centrifuge shaped like a concentric cylinder. The fluid, along with spherical particles of different diameters, enters the centrifuge at the bottom of the centrifuge and high centrifugal forces due to a rotating inner cylinder will separate out the particles from the fluid. All particles with diameters...