Fluid Flow Concepts PDF

IDEAL FLUID - Fluids which do not have viscosity and are incompressible are termed as ideal fluid. It flows steadily without friction and do not have shear resistance. It is an imaginary fluid because all the fluid that exists in the environment have some viscosity. So, there is no ideal fluid. REA...

IDEAL FLUID - Fluids which do not have viscosity and are incompressible are termed as ideal fluid. It flows steadily without friction and do not have shear resistance. It is an imaginary fluid because all the fluid that exists in the environment have some viscosity. So, there is no ideal fluid. REAL FLUIDS - Fluids which do possess viscosity are termed as real fluids. These fluids always offer shear resistance. Three physical properties of real fluids that are particularly important: density, viscosity, and surface tension. CLASSIFICATION OF FLUID FLOW 1. STEADY AND UNSTEADY STEADY FLOW AND UNSTEADY FLOW  The flow is said to be STEADY at a point in the flowing fluid if the velocity, pressure and other flow characteristic at that point do not change with time.  The flow is said to be UNSTEADY if the velocity and other such characteristics vary with time at a Now Future point in the flowing fluid. 2. UNIFORM AND NON-UNIFORM UNIFORM AND NON-UNIFORM FLOW  In UNIFORM FLUID FLOW, the velocity at a given instant of time is same at any point of the fluid and has the same magnitude in all directions, the flow depth does not change with distance as well.  In NON-UNIFORM FLUID FLOW, the velocity of the fluid changes at every instant for any point at a given time. Fluid factors like: pressure, velocity and speed keeps on changing continuously. 3. LAMINAR AND TURBULENT LAMINAR FLOW AND TURBULENT  During a LAMINAR FLOW, the velocity of movement is sufficiently low, the individual particles will follow well defined paths that do not cross or intersect one another.  On a TURBULENT FLOW, the separate particles will follow irregular paths which keep on crossing and re-crossing one another to form an intricate pattern of interlacing lines. Turbulent flow is more common at high flow speeds and larger scales For a LAMINAR FLOW in circular pipes, the velocity distribution is three dimensional paraboloid of revolution where the maximum velocity is twice of the mean velocity. The transition from laminar to turbulent flow starts when a certain velocity of flow, known as the CRITICAL VELOCITY, is attained and exceeded. Beyond this critical point, the amount of turbulence increases with the velocity and will ultimately reach a state in which the tur 4. COMPRESSIBLE AND INCOMPRESSIBLE COMPRESSIBLE AND INCOMPRESSIBLE  Flow COMPRESSIBLE flow exists if the density of each fluid particles remains relatively constant as it moves through the flow field. The density is constant which means the density of the fluid does not change from point to point.  INCOMPRESSIBLE flow means flow with variation due to pressure changes. 5. ROTATIONAL AND IRROTATIONAL ROTATIONAL AND IRROTATIONAL The ROTATIONAL FLUID FLOW is defined as the type of fluid flow in which the fluid particles while flowing along streamline rotate about their own axis. Whereas, the IRROTATIONAL FLUID FLOW is defined as the type of fluid flow in which the particles while flowing along streamline do not rotate about their own axis. 6. ONE, TWO, AND THREE DIMENSIONAL FLUID FLOW ONE DIMENSIONAL FLOW is that type of flow in which the flow parameter such as velocity is a function of time and one space coordinate only, say x. It is a flow in which the velocity vector depends on only one space variables. Such flow occurs away from geometry changes in long, straight pipes or between parallel plates. u = f(x), v = 0 and w = 0 where u, v and w are velocity component in x, y and z directions respectively. TWO DIMENSIONAL FLUID FLOW is the type of flow in which velocity is a function of time and two rectangular space coordinate say x, y. It is a flow in which the velocity vector depends on only two space variables. An example is a plane flow, in which the velocity vector depends on only two spatial coordinates x and y. u = f1(x,y), v = f2(x,y), and w =0 THREE DIMENSIONAL FLOW is the type of flow in which velocity is a function of time and three mutually perpendicular directions. The function of three space coordinates (x, y, z). It is a flow in which the velocity vector depends on only three space coordinates. u = f1(x,y,z), v = f2(x,y,z), and w =f3(x,y,z)  PATH LINES, STREAMLINES AND FLOW NETS PATH LINES - It is a locus of points traversed by a given particles as it travels in a field of flow. It provides us with a history of particle’s location. It is a line made by single particle as it moves during a particular period of time. STREAK LINES - It is defined as the instantaneous line whose points are occupied by all particles originating from some specified points in the flow field. It tells where the particles are “right now”. STREAMLINES - It is a line in the flow possessing the following property: the velocity vector of each particle occupying a point on the streamline is tangent to the streamline. It is a line which gives the velocity direction of the fluid at each point along the line at a given instant. It refers to an instantaneous picture of the velocity direction of number of particles. STREAM TUBE It is a tube whose walls are streamlines. When streamlines are drawn through a closed curve, they form boundaries across which no fluid could pass. A pipe is a stream tube since its walls are streamline; an open channel is a stream tube since no fluid crosses the walls of the channel. Key Concept: In a steady flow, path lines, streak lines and streamlines are all coincident.  FLUID FLOW EQUATIONS DISCHARGE OR FLOW RATE is the amount of fluid passing through a section per unit time. This expressed as a mass flow rate (kg/s), weight flow rate (kN/s), and volume flow rate (m³/s). Volume flow rate Q = Av Mass flow rate M = ρQ Weight flow rate W = γQ where; Q = discharge in (m³/s) A = cross-sectional area of the flow in m² v = mean velocity of flow in m/s ρ = mass density kg/m³ γ = weight density in N/ m³ THREE BASIC LAW 1. LAW OF CONSERVATION OF MASS The law stating that the mass must be conserved is: “MASS CANNOT BE CREATED NOR DESTROYED IN A CLOSED SYSTEM; IT CAN ONLY CHANGE IN FORM.” This principle is applied to ensure that the amount of fluid entering a system (like a pipe) is equal to the amount of fluid leaving it, assuming there are no leaks or accumulation of mass within the system. This concept is captured by the continuity equation, especially for incompressible fluids, where the flow rate (volume of fluid per unit time) remains constant. 𝐴1𝑣1 = 𝐴2𝑣2 2. FIRST LAW OF THERMODYNAMICS Also known as the law of conservation of energy, which states that “ENERGY CANNOT BE CREATED OR DESTROYED, ONLY TRANSFORMED FROM ONE FORM TO ANOTHER”. In fluid flow, energy can exist in various forms, such as kinetic energy (due to the fluid’s velocity), potential energy (due to elevation), and internal energy (related to temperature and pressure). The First Law tells us that as fluid moves and changes state (for example, flowing from a higher elevation to a lower one), the total energy remains constant, but it may convert between these forms. For instance, as a fluid descends, its potential energy decreases while its kinetic energy increases. 3. NEWTON’S SECOND LAW Newton’s Second Law also called the momentum equation, states that: “THE RESULTANT FORCE ACTING ON A SYSTEM EQUALS THE RATE AT WHICH THE MOMENTUM OF THE SYSTEM IS CHANGING.” CONTINUITY EQUATION A CONTINUITY EQUATION in physics is an equation that describes the transport of a conserved quantity. Since mass, energy, momentum, electric charge, and other natural quantities are conserved under their respective appropriate conditions, a variety of physical phenomena may be described using continuity equations.  ENERGY AND HEADS OF FLUIDS IN MOTION ENERGY is defined as the ability to do work. It exists in several forms and in case of fluids in motion the kinetic, potential and pressure energies. KINETIC ENERGY is the energy possessed by a mass by virtue of its motion or velocity. It is expressed as: Kinetic Energy = W( 𝒗𝟐 𝟐𝒈 ) The unit is Newton-meter (N-m) or Joule (J) in SI Units The KINETIC ENERGY per unit of weight represented by K𝒊𝒏𝒆𝒕𝒊𝒄 𝑬𝒏𝒆𝒓𝒈𝒚 𝑾𝒆𝒊𝒈𝒉𝒕 = 𝒗𝟐 𝟐𝒈 The unit is Newton-meter per Newton (N-m/N) or simply meter (m). In fluid flow, the term 𝒗𝟐 𝟐𝒈 is commonly called as the VELOCITY HEAD. POTENTIAL ENERGY is the energy possessed by a mass by virtue of its position or elevation above some horizontal reference plane. It represents the amount of work which the mass is capable of doing if it is allowed to descend to the reference plane. This energy is the same in magnitude as the amount of work that must be used up in raising the mass from the datum plane to its assigned elevation. Potential Energy For a mass having a weight W and positioned at a distance z above the datum plane, the potential energy is: Potential Energy = Wz The dimension or unit is Newton-meter (N-m) or Joule (J). Another name given to such form of energy is ELEVATION ENERGY. The potential energy per unit weight The dimension or unit is Newton-meter per Newton (N-m/N) or simply meter (m). The height z above the datum plane is known as the ELEVATION HEAD