Based on a control volume analysis for the dashed box, answer the following. Feb 03, 2015 dimensionless numbers can be considered as simple mathematical expressions of the balance between fluid dynamical forces or transport phenomena, based on scaling relationships, that inherently and strongly influence the problem under consideration. Any physical situation, whether it involves a single object or a complete system, can be described in terms of a number of recognisable properties which the object or system possesses. Nondimensional scaling provides a method for developing dimensionless groups that can provide physical insight into the importance of various terms in the system of governing equations. Fundamentals of fluid mechanics chapter 7 dimensional. Dimensionless numbers in fluid mechanics wikipedia free download as pdf file. The grashof number is used to determine the heat transfer coefficient under free convection conditions. It is almost impossible to read an article or listen to a lecture on heat transfer without hearing names like reynolds. Simple ratio of two dimensionally equal quantities. Find materials for this course in the pages linked along the left. Dimension less numbers have important role in fluid mechanics. This book describes typical issues that are taught and cover in first year class of fluid mechanics with various examples. In both procedures the dimensionless numbers just come out of the algebraic manipulation, lacking a strong physical interpretation.
Ce 321 sample laboratory report packet this packet contains the following materials to help you prepare your lab reports in ce 321. Apr 15, 20 some dimensionless numbers in heat transfer 1. Calculates reynolds number or re for a fluid with the given properties for the specified velocity and diameter. Dimensionless numbers of fluid mechanics pqn88p7gjpn1. Topics covered include hydrodynamics, surface tension, boundary layers, potential flow, aerodynamics, viscous flow, and waves. The peclet number is a dimensionless number used in calculations involving convective heat transfer. A closer look at the areas of fluid mechanics and heat transfer reveals that in these fields important dimensionless. Mar 04, 2019 dimensional analysis is a mathematical technique used to predict physical parameters that influence the flow in fluid mechanics, heat transfer in thermodynamics, and so forth. It tells us whether the flow is laminar or turbulent. In many cases, however, the products can be obtained by. Reynolds number, gives the information, whether the flow is inertial or viscous force dominant.
Dimensionless numbers are of very high importance in mechanical engineering and chemical engineering including thermodynamics, fluid mechanics, mass transfer, heat transfer, solid mechanics, momentum transfer and chemical reaction engineering. Here, is a typical spatial variation lengthscale, a typical fluid velocity, and a typical gravitational acceleration assuming that represents a gravitational potential. How many dimensionless numbers are there in fluid mechanics, heat and mass. Dimensionless numbers in hydraulics and fluid mechanics the important dimensionless numbers are reynolds number, froudes number, webers number, eulers number and machs number. Some dimensionless numbers in heat transfer reynolds number nusselt number stanton number peclet number prantdl numberreynolds numberthe dimensionless number that gives the measure of theratio of inertial forces toviscous forces for aparticular fluid stream. Some of the important dimensionless numbers used in fluid mechanics and heat transfer. Dimensionless numbers and their importance in fluid mechanics. Dimensionless numbers used in fluid mechanics mech4study.
Pdf dimensionless numbers are of key importance in parametric analysis of engineering. When any mass is in motion inertia force always exists. Wallaces hints regarding common strengths and weakness of each section of a lab report a sample cover memo. Importance of dimensionless numbers in mass transfer free download as powerpoint presentation.
Pure numbers without any physical units, it does not change if one alters ones system of units of measurement, for example from english units to metric units. Calculates reynolds number or re for a fluid with the given properties for. Dimensionless numbers in fluid mechanics are a set of dimensionless quantities that have an important role in analyzing the behavior of fluids. In fluid mechanics the term static pressure has several uses. Dimensionless numbers in fluid mechanics wikipedia fluid. The nondimensionalization of the governing equations of fluid flow is important for both theoretical and. These nondimensional numbers are helpful tools in heat transfer. Engineering fluid mechanics staffordshire university. Those names are given here because some people use them, and youll probably hear them at some point in your career.
Reynolds numbers express the ratio of inertial forces to viscous forces in a flowing fluid, and represent a way to quantify the importance of these. Dimensionless nonnewtonian fluid mechanics request pdf. It is the ratio of heat transferred to the fluid to the heat transported by the fluid ratio of nusselt number to peclet number used to find heat transfer in forced convection flows. Some important dimensionless numbers used in fluid mechanics and their importance is explained below. The kilogram is the mass of a platinumiridium cylinder kept at sevres in france.
The nondimensionalization of the governing equations of fluid flow is important for both theoretical and computational reasons. If you memorize this material, you will be far along the path to better understanding fluids. Moreover, dimensionless forms also allow us to present the solution in a compact way. Dec 22, 2011 u mean characteristic velocity of the object relative to the fluid. Heat transfer requires circulation, therefore, the grashof number and heat transfer coefficient will rise as the buoyancy forces increase and the viscous forces decrease. Common examples include the reynolds or the mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, flow speed, etc. It is the ratio of the inertia force to the viscous force. The metre is now defined as being equal to 1 650 763. These are the quantities, which actually vary during a given case and can be.
With the help of these numbers we can easily predict the flow behavior of fluid. Dimensionless numbers c d discharge coefficient f friction factor pipes. Jul 01, 2016 the grashof number is used to determine the heat transfer coefficient under free convection conditions. Determine a suitable set of pi terms to study this problem experimentally. Nul convective heat transfer conductive heat transfer where l is the characteristic length, k is the thermal conductivity of the fluid, h is the convective heat transfer coefficient of the fluid. The course concentrates on those aspects of fluid mechanics that can be studied analytically. Fluid mechanicsdimensional analysis wikibooks, open books. In order to help you better understand fluid mechanics, we have prepared a glossary of terms, phenomena, dimensionless numbers, etc.
Dimensional analysis advanced fluid mechanics mechanical. V ch characteristic velocity c p specific heat capacity at constant pressure. An annotated sample lab report prepared on a fluids experiment. Dimensionless numbers in fluid mechanics wikipedia. How to remember dimensionless numbers in fluid mechanics. Jun 14, 2016 dimensionless numbers are of very high importance in mechanical engineering and chemical engineering including thermodynamics, fluid mechanics, mass transfer, heat transfer, solid mechanics, momentum transfer and chemical reaction engineering. Mendes 2, nonnewtonian fluid behavior is encountered in almost all studied dimensionless nonnewtonian fluid mechanics the chemical and allied processing industries. What is the easiest way to understand dimensionless numbers.
A complete set of lecture notes for an upperdivision undergraduate fluid mechanics course. Summary of dimensionless numbers of fluid mechanics and heat. Reynolds number re it gives a measure of the ratio of inertial and viscous forces in fluid flow. Dimensionless numbers in incompressible flow it is helpful to normalize the equations of incompressible fluid flow, 1. Some of the important dimensionless numbers used in fluid mechanics and heat transfer are given below. These names refer to very specific dimensionless numbers that are used to characterize and classify the heat transfer problems.
Summary of dimensionless numbers of fluid mechanics and heat transfer 1. For example, in a fluid apparatus in which the flow is isothermal and incompressible, the number of relevant parameters can often be reduced to one. In fluid mechanics, mach number m or ma is a dimensionless quantity representing the ratio of speed of an object moving through a fluid and the local speed of sound. Sep 23, 2016 these nondimensional numbers are helpful tools in heat transfer. A a typical fluid mechanics problemtypical fluid mechanics problem in which experimentation is required consider the experimentation is required consider the steady flow of an steady flow of an incompressible newtonian fluid through a long, smoothincompressible newtonian fluid through a long, smooth walled, horizontal, circular pipe.
In fluid mechanics, dimensionless numbers or nondimensional numbers are those which are useful to determine the flow characteristics of a fluid. How many dimensionless numbers are there in fluid mechanics. Express the interdependence of the dimensionless groups in a function form that allows computation of the nondimensional lift from other nondimensional parameters form nondimensional groups that correspond to wellknown dimensionless numbers in fluid mechanics. The analysis involves the fundamental units of dimensions mlt. Importance of dimensionless numbers in mass transfer.
Here, is a typical spatial variation lengthscale, a typical fluid velocity, and a typical gravitational acceleration assuming. We will cover the topics of mass, momentum and energy conservation. Jul 04, 2014 how to remember dimensionless numbers in fluid mechanics. It is basically a ratio between the buoyancy forces and viscous forces. A closer look at the areas of fluid mechanics and heat transfer reveals that. Dimensionless numbers can be considered as simple mathematical expressions of the balance between fluid dynamical forces or transport phenomena, based on scaling relationships, that inherently and strongly influence the problem under consideration.
Nondimensional scaling provides a method for developing dimensionless groups that can provide physical insight into the importance of. If pe is small, conduction is important and in such a case, the major source of conduction could be down the walls of a tube. This book should be used by many different engineering disciplines. List of all important dimensionless numbers and their. Dimensionless numbers in heat transfer me mechanical. It is the ratio of the thermal energy convected to the fluid to the thermal energy conducted within the fluid. Engineering fluid mechanics 4 contents contents notation7 1 fluid statics 14 1. Dimensionless numbers in fluid mechanics are a set of dimensionless quantities that have. Find the relationship between variables affecting a phenomenon. Consider a steady, incompressible boundary layer with thickness.
The numbers produced by scaling of equation are presented for transport of momentum, heat and mass. Dimensionless numbers used in fluid mechanics may 15, 2018 admin 0 comments. Fluid mechanics problems for qualifying exam fall 2014 1. Assume that the drag, d, that the fluid exerts on the plate is a function of w and h, the fluid viscosity,and. The table shows the definitions of a lot of dimensionless quantities used in chemistry, fluid flow and physics engineering.
Why are dimensionless numbers used in heat transfer and fluid. Nondimensional scaling provides a method for developing dimensionless groups that can. Dimensionless numbers in fluid dynamics chemical engineering. Dimensionless parameter approach for oxygen even before reynolds did his classical work, helmholtz derived groups in which are now called the reynolds, froude, and mach numbers in the course of solving a fluid flow problem.