Anna GE 6253 - Basics of Hydraulics – Pascal’s Law

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Basics of Hydraulics Pascal s Law Principles of flow Friction loss All hydraulic systems operate following a defined relationship between area force and pressure hydraulics is generally understood as the generation of forces and motion by hydraulic fluids Hydraulics is the generation of forces and motion using hydraulic fluids which represents the medium for the transmission of power study of fluids the study of water or other fluids at rest or in motion especially with respect to engineering applications like heavy equipments Particles in liquids are close together meaning that liquids are virtually incompressible i e cannot be compacted or squashed together When moving around the particles collide with one another and the walls of the container in which the liquid is housed Pressure and forces can be spread through liquids with the pressure transmitted equally in all directions Liquids in motion or under pressure did useful work for humanity for many scientist centuries before French philosopher Blaise Pascal and Swiss physicist Daniel Bernoulli formulated the hydraulic power technology is based The science of hydraulics can be divided into two branches namely i on which modern laws and ii hydrodynamics hydrostatics ii Hydrodynamics deals with the moving liquids water wheel or turbine the energy water that is used is that created by the motion Hydrostatics deals with the liquids under pressure Examples of the applications of hydrostatics are hydraulic jack or hydraulic press The area of hydraulics that pertains to the transmission of force using a confined fluid Liquid flow Flow rate versus flow velocity The flow rate is the volume of fluid that moves through the system in a given period of time Flow rates determine the speed at which the output device e g a cylinder will operate The flow velocity of a fluid is the distance the fluid travels in a given period of time These two quantities are often confused so care should be taken to note the distinction The following equation relates the flow rate and flow velocity of a liquid to the size area of the conductors pipe tube or hose through which it flows Basic Hydraulic Fluid Principles Elements of Fluid Mechanics Fluid Flow Q general movement of liquid Volumetric rate Lit min Fluid Pressure P Force per square area Kg sq m Fluid Velocity V Distance over time m sec Fluid Temperature T F or C Fluid Viscosity Fluid resistance to flow cSt centistokes Fluid Mechanics Relationships Flow Velocity Q A v Where Q Volumetric Flow Rate A Cross sectional Area v Fluid Velocity Pascal s Principle Pascal s Law which is foundational to the principle of hydraulics The basis for all hydraulic systems is expressed by Pascal s law which states that the pressure exerted anywhere upon an enclosed liquid is transmitted undiminished in all directions to the interior of the container This principle allows large forces to be generated with relatively little effort A static fluid in a closed vessel has the following characteristics as stated by Pascal s principle 1 Pressure works on a plane at a right angle 2 Pressure is transmitted equally in all directions 3 Pressure applied on part of a fluid is transmitted throughout the fluid equally Hydraulic brake lift based on Pascal s law Hydraulic Mechanical Advantage F2 A1 20 in2 Pascal Pressure applied on F1 20 lbf a confined fluid is transmitted in all directions with equal force A1 2 in2 on equal areas Pascal s Law Magnitude transferred of force is in direct proportion to the surface area F P A Pressure Force Area 1 2 3 The bottle is filled with a is not liquid which compressible for example hydraulic oil A 10 lb force applied to a stopper with a surface area of one square inch Results in 10 lb of force inch on every square pressure the container wall of Pascal s Law 4 If the bottom has an area of 20 square each and inches square inch is pushed on by the 10 lb of entire force bottom receives a 200 lb push the 10 lbs x 20 sq in 200 Bernoulli s Law for incompressible fluids fluid is flowing with a significant difference in height between source sink kinetic energy deriving from motion can be partly converted to pressure energy by enlarging the cross section of a pipe which slows down the flow Flow of fluid Laminar When fluid particles move along the same smooth path The path is called a streamline Turbulent When fluid particles flow irregularly causing changes in velocity FLUID FLOW Laminar Flow It is one in which paths taken by the individual partials do not cross one another and moves along well defined paths The laminar flow is characterized by the fluid flowing in smooth layers of lamina This type of flow is also known as streamline or viscous flow Examples 1 Flow of oil in measuring instruments 2 Flow of blood in veins and arteries Turbulent Flow It is that flow in which fluid particles move in a zigzag way It is characterized by continues small fluctuations in the magnitude and direction of the velocity of the fluid particles It causes more resistance to flow Greater energy loss and increase fluid temperature due to greater energy loss Examples High velocity flow in a pipe of large size Reynolds number is a dimensionless quantity that is used to determine the type of flow pattern as laminar or turbulent while flowing through a pipe Reynolds number is defined by the ratio of inertial forces to that of viscous forces This is important because increased mixing and shearing occur in turbulent flow This results in increased viscous losses which affects the efficiency of hydraulic machines The dimensionless Reynolds number predicts whether the fluid flow would be laminar or turbulent referring to several properties such as velocity length viscosity and also type of flow Friction is caused by the fluid molecules rubbing against inside of pipes Friction loss is a measure of the amount of energy your piping system loses because your fluids are meeting resistance the friction loss is related to the flow of liquid through some pipe Thus it is a kind of energy loss due to the friction inside the tube It is therefore related to the velocity and viscosity of the fluid As fluid flows through your pipes it carries energy with it Head Loss in a Pipeline When fluid flows inside a pipeline friction occurs between the moving fluid and the stationary pipe wall This friction converts some of the fluid s hydraulic energy to thermal energy This thermal energy cannot be converted back to hydraulic energy so the fluid experiences

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Anna GE 6253 - Basics of Hydraulics – Pascal’s Law

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