Fluid properties can be described qualitatively and quantitatively. Key parameters that describe fluids include density, specific weight, specific volume, specific gravity, viscosity, compressibility via the bulk modulus, and speed of sound. Gases follow the ideal gas law, and vapor pressure determines when boiling occurs as the fluid pressure reaches vapor pressure. Surface tension arises from molecular cohesive forces at fluid interfaces.
Unit 6 discusses losses in pipes, including major and minor losses. Major losses are due to friction and calculated using Darcy-Weisbach or Chezy's formulas. Minor losses are due to changes in pipe direction, size, or obstructions and are also calculated using specific formulas. The document also discusses equivalent pipes, pipes in series, pipes in parallel, and two and three reservoir pipe flow analysis problems. Head losses are calculated using friction and minor loss formulas, and continuity and energy equations are used to analyze pipe flows.
This document discusses laminar and turbulent fluid flow in pipes. It defines the Reynolds number and explains that laminar flow occurs at Re < 2000, transitional flow from 2000 to 4000, and turbulent flow over 4000. The entrance length for developing pipe flow profiles is discussed. Fully developed laminar and turbulent pipe flows are compared. Equations are provided for average velocity, shear stress at the wall, and pressure drop based on conservation of momentum and energy analyses. The Darcy friction factor is defined, and methods for calculating it for laminar and turbulent flows are explained, including the Moody chart. Types of pipe flow problems and accounting for minor losses and pipe networks are also summarized.
The properties of a gas mixture depend on the properties of its individual components and their relative amounts. There are two ways to describe the composition of a mixture: molar analysis specifies the moles of each component, and gravimetric analysis specifies the mass of each component. For ideal gas mixtures, Dalton's law and Amagat's law can be used to determine pressure and volume behavior. For real gas mixtures, these laws are approximate and equations of state must be used. The properties of gas mixtures can be determined by weighted averages of the component properties.
120218 chapter 8 momentum analysis of flowBinu Karki
The document discusses momentum analysis of fluid flow. It contains the following key points:
1) The momentum equation is based on the law of conservation of momentum, which states that the net force acting on a fluid mass is equal to the rate of change of momentum of the fluid.
2) The momentum principle can be written as an impulse-momentum equation: the impulse of a force acting on a fluid mass over a short time interval is equal to the change in momentum of the fluid.
3) The momentum equation is used to determine the resultant force exerted by a flowing fluid on a pipe bend based on the fluid's velocity, pressure, area, and external forces at two sections of the pipe.
This document provides an overview of boundary layer concepts and laminar and turbulent pipe flow. It defines boundary layer thickness, displacement thickness, and momentum thickness. It describes how boundary layers develop on surfaces and transition from laminar to turbulent. It also discusses Reynolds number effects, momentum integral estimates for flat plates, and examples calculating boundary layer thickness in air and water flow. Finally, it introduces concepts of laminar and turbulent pipe flow.
The document discusses turbulent flow of fluids in pipes and annuli. It defines laminar and turbulent flow, and introduces the Reynolds number used to characterize flow regimes. It then provides methods to determine friction factors and pressure losses for Newtonian fluids in pipes and annuli under both laminar and turbulent flow conditions. Non-Newtonian fluid models including Bingham plastic and power law models are also covered.
Fluid properties can be described qualitatively and quantitatively. Key parameters that describe fluids include density, specific weight, specific volume, specific gravity, viscosity, compressibility via the bulk modulus, and speed of sound. Gases follow the ideal gas law, and vapor pressure determines when boiling occurs as the fluid pressure reaches vapor pressure. Surface tension arises from molecular cohesive forces at fluid interfaces.
Unit 6 discusses losses in pipes, including major and minor losses. Major losses are due to friction and calculated using Darcy-Weisbach or Chezy's formulas. Minor losses are due to changes in pipe direction, size, or obstructions and are also calculated using specific formulas. The document also discusses equivalent pipes, pipes in series, pipes in parallel, and two and three reservoir pipe flow analysis problems. Head losses are calculated using friction and minor loss formulas, and continuity and energy equations are used to analyze pipe flows.
This document discusses laminar and turbulent fluid flow in pipes. It defines the Reynolds number and explains that laminar flow occurs at Re < 2000, transitional flow from 2000 to 4000, and turbulent flow over 4000. The entrance length for developing pipe flow profiles is discussed. Fully developed laminar and turbulent pipe flows are compared. Equations are provided for average velocity, shear stress at the wall, and pressure drop based on conservation of momentum and energy analyses. The Darcy friction factor is defined, and methods for calculating it for laminar and turbulent flows are explained, including the Moody chart. Types of pipe flow problems and accounting for minor losses and pipe networks are also summarized.
The properties of a gas mixture depend on the properties of its individual components and their relative amounts. There are two ways to describe the composition of a mixture: molar analysis specifies the moles of each component, and gravimetric analysis specifies the mass of each component. For ideal gas mixtures, Dalton's law and Amagat's law can be used to determine pressure and volume behavior. For real gas mixtures, these laws are approximate and equations of state must be used. The properties of gas mixtures can be determined by weighted averages of the component properties.
120218 chapter 8 momentum analysis of flowBinu Karki
The document discusses momentum analysis of fluid flow. It contains the following key points:
1) The momentum equation is based on the law of conservation of momentum, which states that the net force acting on a fluid mass is equal to the rate of change of momentum of the fluid.
2) The momentum principle can be written as an impulse-momentum equation: the impulse of a force acting on a fluid mass over a short time interval is equal to the change in momentum of the fluid.
3) The momentum equation is used to determine the resultant force exerted by a flowing fluid on a pipe bend based on the fluid's velocity, pressure, area, and external forces at two sections of the pipe.
This document provides an overview of boundary layer concepts and laminar and turbulent pipe flow. It defines boundary layer thickness, displacement thickness, and momentum thickness. It describes how boundary layers develop on surfaces and transition from laminar to turbulent. It also discusses Reynolds number effects, momentum integral estimates for flat plates, and examples calculating boundary layer thickness in air and water flow. Finally, it introduces concepts of laminar and turbulent pipe flow.
The document discusses turbulent flow of fluids in pipes and annuli. It defines laminar and turbulent flow, and introduces the Reynolds number used to characterize flow regimes. It then provides methods to determine friction factors and pressure losses for Newtonian fluids in pipes and annuli under both laminar and turbulent flow conditions. Non-Newtonian fluid models including Bingham plastic and power law models are also covered.
This document discusses fluid statics and pressure measurement. It defines concepts like absolute pressure, gauge pressure, atmospheric pressure, and Pascal's law. It describes devices used to measure pressure like manometers, piezometers, and Bourdon gauges. Specifically, it provides details on how liquid manometers and differential manometers work, including the principles, setup, and equations to calculate pressure. It also lists the advantages and limitations of using manometers for pressure measurement applications.
1. The document discusses various concepts related to fluid mechanics including pressure, Pascal's law, units of pressure, measurement of pressure using manometers, and example problems. It provides definitions and equations for pressure, hydrostatic pressure, Pascal's law, and discusses different types of manometers and pressure gauges for measuring pressure. Example problems are included for calculating pressure under various conditions.
1) Compressible flow is when the density of a fluid changes during flow, such as gases. Incompressible flow assumes constant density, such as liquids.
2) Examples of compressible flow include gases through nozzles, compressors, high-speed projectiles and planes, and water hammer.
3) Bernoulli's equation relates pressure, temperature, and specific volume and only applies to steady, incompressible flow without friction losses along a single streamline.
Hmt lab manual (heat and mass transfer lab manual)Awais Ali
This document describes procedures for 7 experiments on heat transfer:
1. Investigates Fourier's Law of heat conduction along a brass bar by measuring temperatures at points along the bar for different heat inputs.
2. Studies heat conduction along a composite bar and calculates the overall heat transfer coefficient.
3. Examines the effect of cross-sectional area changes on temperature profiles in a conductor.
4. Determines temperature profiles and heat transfer rates from radial conduction through a cylinder wall.
5. Measures thermal conductivity of non-metallic materials and compares to theory.
6. Determines thermal conductivity of liquids and gases.
7. Investigates the relationship between power input and surface temperature for free convection
1) The document discusses fluid mechanics concepts related to pressure and fluid statics. It covers topics like pressure measurement devices, hydrostatic forces on submerged surfaces, buoyancy, stability of floating and immersed bodies, and fluids in rigid-body motion.
2) Key concepts covered include how pressure varies with depth in fluids, Pascal's law, Archimedes' principle of buoyancy, stability criteria for floating and immersed objects, and how pressure varies in fluids undergoing linear or rotational acceleration.
3) Various pressure measurement devices are described, including manometers, bourdon tubes, and deadweight testers. Equations are provided for calculating hydrostatic forces on plane and curved surfaces.
This document discusses shear stress, shear rate, viscosity, and different types of fluids. It defines Newtonian fluids as having a viscosity that remains constant regardless of external stress. Non-Newtonian fluids do not follow Newton's law of viscosity and can exhibit time-dependent behavior like shear thinning, shear thickening, and thixotropy. Various rheological models are described including Bingham plastic, power law, and Maxwell models. The importance of viscosity measurement in food analysis is discussed for understanding food texture, stability, and consumer acceptability.
This document defines and compares three types of boundary layer thickness:
1. Boundary layer thickness is the distance from the surface where the flow velocity is 99% of the free-stream velocity.
2. Displacement thickness is a theoretical thickness where displacing the surface would result in equal flow rates across sections inside and outside the boundary layer.
3. Momentum thickness is a measure of boundary layer thickness defined as the distance the surface would need to be displaced to compensate for the reduction in momentum due to the boundary layer. It is often used to determine drag on an object.
This document provides an overview of using HTRI software to perform thermal design of heat exchangers. It discusses specifying the geometry, process conditions, and fluid properties required for rating, designing, or simulating shell and tube heat exchangers. Key aspects covered include baffle types, temperature profiles, mean temperature differences, and outputs such as duty, heat transfer area, and pressure drop. The goal is to demonstrate the inputs and calculations used in HTRI to analyze heat exchanger performance.
Turbulent flows are characterized by chaotic, unpredictable changes in velocity. The document discusses turbulence, including defining turbulence, the transition from laminar to turbulent flow, Reynolds averaging to decompose variables into mean and fluctuating components, and the effects of turbulence on the Navier-Stokes equations. It also examines Reynolds stresses, time-averaged conservation equations for turbulent flow, and modeling approaches like Reynolds averaging to account for turbulent fluctuations and closure problems in the equations.
This document provides an overview of fluid mechanics concepts related to flow through pipes. It discusses different types of head losses that can occur through pipes including major losses due to friction and minor losses due to fittings. It also covers topics such as hydraulic grade line, pipes in series and parallel, syphons, power transmission through pipes, flow through nozzles, and water hammer effects in pipes.
This document discusses flow through pipes, including:
- Laminar and turbulent flow characteristics defined by Reynolds number
- Head losses calculated using Darcy-Weisbach and minor loss equations
- Friction factors determined from Moody diagrams for laminar and turbulent flows
- Total head loss in a pipe system equals major losses in pipe sections plus minor losses from fittings
This document presents information about Reynolds number and pressure head. It was presented by 4 students to their teacher. It defines Reynolds number and describes different types based on flow conditions. It also explains pressure head and different types of pressure like absolute, gauge and vacuum pressure. Various pressure measuring devices are discussed along with their principles and applications. Examples of applications of Reynolds number and pressure head in different fields like fluid mechanics and engineering are also provided.
This document presents a project on the design of a centrifugal pump. It includes an introduction to centrifugal pumps and their components. It then provides details of a specific pump design project carried out at Lupin Limited, including specifications for pumping methanol, calculations to determine pipe sizes, pressure losses, power requirements, and cost. Pump curves are presented and the advantages of centrifugal pumps are listed.
This document provides an overview of the key principles of turbomachinery. It begins with an introduction to turbomachines and categorization by flow path and function. The fundamental performance laws are then introduced, focusing on the Euler equation and its applications to different machine types. Compressible flow theory is also covered, along with illustrative examples of how to apply the principles to radial outflow machines, axial pumps/turbines, and compressible flow problems.
This document discusses fluid dynamics and Bernoulli's equation. It begins by defining different forms of energy in a flowing liquid, including kinetic energy, potential energy, pressure energy, and internal energy. It then derives Bernoulli's equation, which states that the total head of a fluid particle remains constant during steady, incompressible flow. The derivation considers forces acting on a fluid particle and uses conservation of energy. Finally, the document presents the general energy equation for steady fluid flow and the specific equation for incompressible fluids using the concepts of total head, head loss, and hydraulic grade line.
Pumps are widely used in process plants to transfer fluid from one point to the other and the Process Engineer is often required to specify the correct size of pumps that will optimize system performance. Though pump sizing can easily be performed using software such as Pipe-Flo®, understanding the basic principle will not only aid one to better interpret the results obtained by pump sizing software but also to better design pumps. Centrifugal pump sizing overview is presented in this tutorial.
This document discusses compressible flow through nozzles. It introduces concepts like stagnation properties, Mach number, and speed of sound. It then derives relationships for isentropic flow of ideal gases through converging and converging-diverging nozzles. The effects of area changes and back pressure on properties like pressure, temperature, density and mass flow rate are examined for both subsonic and supersonic flow regimes. Nozzle design considerations like shapes needed to achieve desired exit velocities are also covered.
This document discusses key concepts in fluid dynamics, including:
1. Fluid flow, viscosity, and Bernoulli's equation are the main properties of fluid dynamics. Fluid flow is the movement of a fluid and can be steady or turbulent. Viscosity is the resistance of fluid layers sliding past one another.
2. Bernoulli's equation relates pressure, velocity, and elevation in fluid systems. It states that the total mechanical energy (pressure + potential + kinetic energy) remains constant in fluid flow. Higher velocities correspond to lower pressures.
3. Other topics covered include streamlines, continuity equation, rate of flow, factors affecting viscosity, and examples applying Bernoulli's equation. The goal is to analyze pressure and velocity in various
1) The document discusses the governing equations for fluid dynamics, which are derived from conservation laws of physics, including conservation of mass, momentum, and energy.
2) These equations can be derived using either a Lagrangian description that follows fluid particles, or an Eulerian description that considers properties at fixed points in space and time.
3) Key equations derived include the continuity equation, momentum equations, and energy equation, which relate the rate of change of properties like density, momentum, and energy to surface and body forces.
This document discusses fluid statics and pressure measurement. It defines concepts like absolute pressure, gauge pressure, atmospheric pressure, and Pascal's law. It describes devices used to measure pressure like manometers, piezometers, and Bourdon gauges. Specifically, it provides details on how liquid manometers and differential manometers work, including the principles, setup, and equations to calculate pressure. It also lists the advantages and limitations of using manometers for pressure measurement applications.
1. The document discusses various concepts related to fluid mechanics including pressure, Pascal's law, units of pressure, measurement of pressure using manometers, and example problems. It provides definitions and equations for pressure, hydrostatic pressure, Pascal's law, and discusses different types of manometers and pressure gauges for measuring pressure. Example problems are included for calculating pressure under various conditions.
1) Compressible flow is when the density of a fluid changes during flow, such as gases. Incompressible flow assumes constant density, such as liquids.
2) Examples of compressible flow include gases through nozzles, compressors, high-speed projectiles and planes, and water hammer.
3) Bernoulli's equation relates pressure, temperature, and specific volume and only applies to steady, incompressible flow without friction losses along a single streamline.
Hmt lab manual (heat and mass transfer lab manual)Awais Ali
This document describes procedures for 7 experiments on heat transfer:
1. Investigates Fourier's Law of heat conduction along a brass bar by measuring temperatures at points along the bar for different heat inputs.
2. Studies heat conduction along a composite bar and calculates the overall heat transfer coefficient.
3. Examines the effect of cross-sectional area changes on temperature profiles in a conductor.
4. Determines temperature profiles and heat transfer rates from radial conduction through a cylinder wall.
5. Measures thermal conductivity of non-metallic materials and compares to theory.
6. Determines thermal conductivity of liquids and gases.
7. Investigates the relationship between power input and surface temperature for free convection
1) The document discusses fluid mechanics concepts related to pressure and fluid statics. It covers topics like pressure measurement devices, hydrostatic forces on submerged surfaces, buoyancy, stability of floating and immersed bodies, and fluids in rigid-body motion.
2) Key concepts covered include how pressure varies with depth in fluids, Pascal's law, Archimedes' principle of buoyancy, stability criteria for floating and immersed objects, and how pressure varies in fluids undergoing linear or rotational acceleration.
3) Various pressure measurement devices are described, including manometers, bourdon tubes, and deadweight testers. Equations are provided for calculating hydrostatic forces on plane and curved surfaces.
This document discusses shear stress, shear rate, viscosity, and different types of fluids. It defines Newtonian fluids as having a viscosity that remains constant regardless of external stress. Non-Newtonian fluids do not follow Newton's law of viscosity and can exhibit time-dependent behavior like shear thinning, shear thickening, and thixotropy. Various rheological models are described including Bingham plastic, power law, and Maxwell models. The importance of viscosity measurement in food analysis is discussed for understanding food texture, stability, and consumer acceptability.
This document defines and compares three types of boundary layer thickness:
1. Boundary layer thickness is the distance from the surface where the flow velocity is 99% of the free-stream velocity.
2. Displacement thickness is a theoretical thickness where displacing the surface would result in equal flow rates across sections inside and outside the boundary layer.
3. Momentum thickness is a measure of boundary layer thickness defined as the distance the surface would need to be displaced to compensate for the reduction in momentum due to the boundary layer. It is often used to determine drag on an object.
This document provides an overview of using HTRI software to perform thermal design of heat exchangers. It discusses specifying the geometry, process conditions, and fluid properties required for rating, designing, or simulating shell and tube heat exchangers. Key aspects covered include baffle types, temperature profiles, mean temperature differences, and outputs such as duty, heat transfer area, and pressure drop. The goal is to demonstrate the inputs and calculations used in HTRI to analyze heat exchanger performance.
Turbulent flows are characterized by chaotic, unpredictable changes in velocity. The document discusses turbulence, including defining turbulence, the transition from laminar to turbulent flow, Reynolds averaging to decompose variables into mean and fluctuating components, and the effects of turbulence on the Navier-Stokes equations. It also examines Reynolds stresses, time-averaged conservation equations for turbulent flow, and modeling approaches like Reynolds averaging to account for turbulent fluctuations and closure problems in the equations.
This document provides an overview of fluid mechanics concepts related to flow through pipes. It discusses different types of head losses that can occur through pipes including major losses due to friction and minor losses due to fittings. It also covers topics such as hydraulic grade line, pipes in series and parallel, syphons, power transmission through pipes, flow through nozzles, and water hammer effects in pipes.
This document discusses flow through pipes, including:
- Laminar and turbulent flow characteristics defined by Reynolds number
- Head losses calculated using Darcy-Weisbach and minor loss equations
- Friction factors determined from Moody diagrams for laminar and turbulent flows
- Total head loss in a pipe system equals major losses in pipe sections plus minor losses from fittings
This document presents information about Reynolds number and pressure head. It was presented by 4 students to their teacher. It defines Reynolds number and describes different types based on flow conditions. It also explains pressure head and different types of pressure like absolute, gauge and vacuum pressure. Various pressure measuring devices are discussed along with their principles and applications. Examples of applications of Reynolds number and pressure head in different fields like fluid mechanics and engineering are also provided.
This document presents a project on the design of a centrifugal pump. It includes an introduction to centrifugal pumps and their components. It then provides details of a specific pump design project carried out at Lupin Limited, including specifications for pumping methanol, calculations to determine pipe sizes, pressure losses, power requirements, and cost. Pump curves are presented and the advantages of centrifugal pumps are listed.
This document provides an overview of the key principles of turbomachinery. It begins with an introduction to turbomachines and categorization by flow path and function. The fundamental performance laws are then introduced, focusing on the Euler equation and its applications to different machine types. Compressible flow theory is also covered, along with illustrative examples of how to apply the principles to radial outflow machines, axial pumps/turbines, and compressible flow problems.
This document discusses fluid dynamics and Bernoulli's equation. It begins by defining different forms of energy in a flowing liquid, including kinetic energy, potential energy, pressure energy, and internal energy. It then derives Bernoulli's equation, which states that the total head of a fluid particle remains constant during steady, incompressible flow. The derivation considers forces acting on a fluid particle and uses conservation of energy. Finally, the document presents the general energy equation for steady fluid flow and the specific equation for incompressible fluids using the concepts of total head, head loss, and hydraulic grade line.
Pumps are widely used in process plants to transfer fluid from one point to the other and the Process Engineer is often required to specify the correct size of pumps that will optimize system performance. Though pump sizing can easily be performed using software such as Pipe-Flo®, understanding the basic principle will not only aid one to better interpret the results obtained by pump sizing software but also to better design pumps. Centrifugal pump sizing overview is presented in this tutorial.
This document discusses compressible flow through nozzles. It introduces concepts like stagnation properties, Mach number, and speed of sound. It then derives relationships for isentropic flow of ideal gases through converging and converging-diverging nozzles. The effects of area changes and back pressure on properties like pressure, temperature, density and mass flow rate are examined for both subsonic and supersonic flow regimes. Nozzle design considerations like shapes needed to achieve desired exit velocities are also covered.
This document discusses key concepts in fluid dynamics, including:
1. Fluid flow, viscosity, and Bernoulli's equation are the main properties of fluid dynamics. Fluid flow is the movement of a fluid and can be steady or turbulent. Viscosity is the resistance of fluid layers sliding past one another.
2. Bernoulli's equation relates pressure, velocity, and elevation in fluid systems. It states that the total mechanical energy (pressure + potential + kinetic energy) remains constant in fluid flow. Higher velocities correspond to lower pressures.
3. Other topics covered include streamlines, continuity equation, rate of flow, factors affecting viscosity, and examples applying Bernoulli's equation. The goal is to analyze pressure and velocity in various
1) The document discusses the governing equations for fluid dynamics, which are derived from conservation laws of physics, including conservation of mass, momentum, and energy.
2) These equations can be derived using either a Lagrangian description that follows fluid particles, or an Eulerian description that considers properties at fixed points in space and time.
3) Key equations derived include the continuity equation, momentum equations, and energy equation, which relate the rate of change of properties like density, momentum, and energy to surface and body forces.
2. 1
Fluid
Definition
. Fluid (유체) : 흐를 수 있는 물질 (기체 나 액체 )
. Flux : 단위시간당 얼마나 많은 유체가 그 면적을 휩쓸고 지나가는지를 나타내는 양
. Pneumatic :
1) using air pressure to move or work.
2) filled with air
. Hydraulic : Liquids under pressure made to do work
. Flow : Fluid 의 흐름 , Flow 의 motion 과 state 는 Velocity, Pressure 및 Density 로 specific 된다
3. 2
Fluid
Compressible VS Incompressible
. Fluid Flow Most liquids are nearly incompressible;
that is, the density of a liquid remains almost constant as the pressure changes.
To a good approximation, then, liquids flow in an incompressible manner.
. In contrast, gases are highly compressible.
However, there are situations in which the density of a flowing gas remains constant enough that the flow can be
considered incompressible.
가스는 기본적으로 compressible 이지만, 흐르는 gas 는 incompressible 이다
. Continuity equation 과 베르누이 정리는 incompressible fluid 에 만 해당한다
4. 3
Flow
Type of Flow Profile
. VISCOSITY : The friction in laminar flow between layer
. REYNOLD number : laminar 와 turbulent 를 구분하는 숫자이다
1) Laminar : Rn < 2000
2) Turbulent : Rn > 4000
. Flow type 에 따라 flow state (유량, 속도 및 압력) 는 차이가 있다
5. 4
Fluid
Viscosity
. Fluid 의 layer 간 마찰력 으로 flow resistance 역할 (흐름방해) 을 한다
. Liquid 는 점성에 의하여 발생되고, Gas 는 분자 간 충돌에 의하여 발생한다
(점성)
6. 5
Fluid
PRESSURE GRADIENT
1) 모든 물질의 흐름은 압력 차 에 의하여 발생한다 : 유체는 압력의 차이에 의하여 가속된다
Fig. Air moves from high to low pressure by pressure gradient force
* 과학상식
-. 대기중의 물질이 주변온도 가 차가우면 fusion (분자 간 밀 결합) 이 발생하여 부피가 커진다
-. 해서 누르는 힘이 커져 대기압력 은 커진다 (Pressure = Force / Area )
2) Fluid Flow 를 위하여 인위적인 압력저하 장치가 Pump 이며, 진공발생을 통한 흡입 과 배출 기능을 지니고 있다.
3) Gas 의 압력을 인위적으로 높이는 것이 Compressor 이다.
Compressed Air 는 압이 높아 사용하려는 장치에 자연적으로 flow 가 발생한다
8. 7
Flow
Flow Rate
. Flow Rate 은 아래와 같이 세가지 구분으로 정량화 된다
1) Volumetric Flow : 유량
2) Mass Flow : 질량유량
3) Average Velocity : 평균유속
. For gases, temperature and pressure have significant effects on the gas density, and thus on the volumetric flow rate,
so mass flow rate is sometimes used instead of volumetric flow rate for gases.
. Gas 와 같은 경우는, 온도와 압력에 영향을 주요하게 받음으로, 특정한 경우에는 Mass Flow Rate 으로 정량화 한다
. Average Velocity 를 측정하여, Volumetric Flow 를 산출 하는데 사용한다 (Q=VA)
우리가 흔히 사용하는 Flow meter 및 피토관 은 Average Velocity 를 구하는데 사용한다
. 심볼 및 단위
Flow 정량화 구분 Symbol Units
Volumetric Flow Rate Q ft3/sec, gallons per min, m3/sec
Mass Flow Rate m lb/hr, kg/min
Average Velocity
(Linear Velocity)
V ft/sec or m/sec
9. 8
Flow
Volumetric Flow Rate : the volume of fluid passing a point along the tube per second
. v = Velocity
. d = Distance
. A = Area (cross-section) , 단면적 (3.14*r2)
. V = Volume = Area*Distance
. Volume Flow Rate (Q) = Volume / Time == Velocity*Area
. 특정지점에서 단위시간 (1초) 당 특정면적 을 흐르는 량 을 나타낸다
10. 9
Flow
POISEUILLE’s Law
. Gives the volume flow rate of a fluid flowing through a tube or pipe
. 해당조건 : Incompressible, laminar flow, newtonian fluid
. Newtonian fluid : water and most gases
. 일반적이고 전체적인 Flow Rate 산출에 이용된다
11. 10
Flow
POISEUILLE’s Law
. 전체구간 및 일부 구간 에 대한 Volume Flow Rate 을 산출하는데 현실적 이다
1) 공급압력과 Q 는 비례 한다
2) Pipe Size 와 Q 는 비례 한다
3) Pipe 길이 와 Q 는 반비례 한다
. The fourth power dependency of radius (or diameter)
- 직경이 1d 와 ½ d 차이는 1/16 의 flow rate 차이를 보인다
- Qout = 1/16 = (½ * ½ * ½ * ½ )
12. 11
FLOW Resistance
. The opposition to force or flow
. 증가 시 두 가지 결과로 나타난다
1) Volume Flow Rate 이 감소한다
2) Pressure gradient (P1-P2) 를 감소시킨다
압력의 저하는 특정지점이 아닌 전체 적인 압력의 저하를 보인다
. Fluid Flow Resistance factors:
1) diameter of the pipe
2) length of the pipe
3) inside surface finish of the pipe
4) type of fluid flowing (viscosity) Viscosity
5) Additional : pipe joints pipe, joints valves, valves filters, filters sharp bends
. Pressure regulator 나 Flow Regulator (밸브) 도 결국은 Diameter 를 조절하여 resistance 를 적용한 것이다
ΔP is an independent variable whereas flow is the dependent variable.
. 개념도
Flow
13. 12
FLOW Resistance
. 예1. 관내의 막힘(돌기) 에 의한 Flow Rate 예
. 예2. : Flow resistance 는 100cm*5 보다, 1cm*1 이 6.25배 많다 = 5의4승 / 100
Flow
14. 13
Flow
CONTINUTY EQUATION
. Qin == Qout 을 설명하는 이론 이다
. Incompressible Fluid 인 경우에만 적용된다
. Mass flow 만 해당 된다
. 조건 (Flow Resistance, Pressure Gradient) 이 constant 한 경우에만 적용이 된다
15. 14
Flow
CONTINUITY EQUATION
. 수도꼭지를 조절하면 왜 continuity equation 에 해당 하지 않는가 ?
. The tap works by changing the minimum cross-sectional area of the flow.
For a given pressure difference (upstream pressure minus downstream pressure) flow rate is a function of minimum cross-section
al area. Using your thumb would do the same thing. You can stop the flow with your thumb if you are strong relative to the force of
the flow.
. The Equation of Continuity only means that the mass flow rate in equals the mass flow rate out.
It does not mean that the flow in and the flow out never change.
Flow rate in and flow rate out can change simultaneously
16. 15
Flow
CONTINUITY EQUATION
. 수도꼭지를 조절하면 왜 continuity equation 에 해당 하지 않는가 ?
. When you decrease the aperture in the tap by turning the tap, the water velocity does increase at the aperture (B).
The problem is that the aperture is in the valve stem, where you cant observe this increase in velocity.
You only observe the water trickling out the spout slowly (C) because the cross section has already increased by then.
. If you put your thumb directly at C then you do in fact have direct observation of increase in velocity in relation to decrease in
aperture, as per the continuity law.
. continuity equation does not take into account the pressure required at A to produce a constant flow rate even as the aperture is
decreased. that is where flow factor or flow coefficient comes in. in water systems your water pressure from the provider is fixed,
or in electrical systems your battery voltage is fixed.
so while flow rate through A B C is the same, the actual value depends on the aperture size.
18. 17
Pressure
PRESSURE by KINETIC ENERGY
. Pressure = Force Per Unit Area (P= Force / Area) , 단위면적에 가해지는 힘
. 밀폐된 공간에 존재하는 물질의 (Molecule) 운동 에너지에 의하여 발생
. 물질의 mobility 성질에 의하여 벽과 의 충돌 시 bounce off 될때 발생되는 힘
19. 18
Pressure
압력관련 법칙
1. 보일 (Boyle) 의법칙 : 압력과 부피의 관계
- 분자(원자) 의 밀도 (Density) = 질량 (Mass) / 부피 (Volume)
- 압력은 밀도 와 비례 : 질량에 비례하고 부피에 반비례 한다
- 압축을 시키면 부피는 줄어든다 압력이 높아진다
(기체는 가능 하지만, 액체는 불가능 하다)
- 질량에 따른 압력 (1 mole) : O 159, N 593, NO 752mmHg
2. 아몬톤 (Amonton) 의 법칙 : 압력과 온도의 관계
- 온도가 높아지면 압력은 올라간다
- 외부 에너지에 의하여 물질의 운동이 활발해지는 결과이다
3. 아보가드로 (Avogadro) 의 법칙
- Volume of a gas is directly proportional to the amount of gas
at a constant temperature and pressure.
- the pressure is directly proportional to the number of moles of gas present.
20. 19
Pressure
압력관련 법칙
4. 달톤의 법칙 : Partial Law
- 전체질량은 각 개별적인 물질이 지니는 질량의 합이다
5. 찰스 (Charles) 의 법칙 : 온도 와 부피의 관계
- Constant 한 압력 상황에서 온도과 높아지면 동일한 압력을 가져가기
위하여 부피가 커진다
6. Pascal’s Law
. 폐쇠된 내부의 어느 위치에서도 압력은 동일하다
21. 20
압력 과 Density (밀도) 관계
Air density is simply the amount of air molecules in a given space. The more particles there are in a given volume of space, the m
ore dense the air is. Likewise, the less particles there are in given volume of space, the less dense the air is (see the illustration belo
w). However, air density is also positive related to air pressure. The more particles packed in a particular area, the higher the air pr
essure will be. The next paragraph below explains why.
Key Point: Air density is the number of air molecules in a volume of space. Air pressure is the total weight or force of all these part
icles exerting on the earth's surface.
. Density = Mass / Volume
. 압력은 볼륨과 반비례 관계에 있음으로 Density 와는 비례관계를 지닌다
. 액체 와 기체의 차이
When the pressure of a liquid changes, the volume and density, ρ, remain unchanged,
while on the other hand, pressure changes in a gas result in both volume and density change.
Pressure
22. 21
Pressure
Understanding the difference between absolute, gage and differential pressure
. 압력에 대한 정도의 표현은 아래와 같이 세가지 분류로 나뉘어지며, 압력 sensor 도 이 분류로 구분된다.
1) 절대압력 : Pabs= Ppositivegage + Patm
2) Gage 압력 : Patm 를 reference 로 하며 Positive (Ppoa+ Patm) 와 Negative (Patm – Pneg) 값을 지닌다
Negative Gage 를 진공 압력이라도 부른다 (P0 + Pneg)
3) 차이 압력 : Reference 없이 상대적인 두개의 압력을 비교 하는것이다 (PH – PL)
23. 22
Pressure
psi, psig, psid
. 절대압력 이란 완전진공 (0) 을 기준으로 p1 을 측정하며, 이 기준으로 측정된 압력을 psi 라 한다
측정기가 대기중에 노출 되었다면 14.7 psi 를 가르킨다
. Gage 압력이란 대기압을 기준으로 p1 을 측정하며, 정압(+) 고 부압(-) 이 있으며, 이 기준으로 측정된 압력을 psig 라 한다
측정기가 대기중에 노출 되었다면 0 psig 를 가르킨다.
. psid 는 High Pressure (p1) 과 Low Pressure (p2) 간 차압 을 측정하고 (F=F1-F2),
p1>p2 이면 positive 값이고, p1<p2 이면 negative 값이다 - 측정기에 따라 positive 만 측정 하는 것이 대부분이며
압력차이 표현도 psi 로 적용한다
Fig. 절대압력 (psi) Gage 압력 (psig) 차이압력 (psid)
25. 24
Pressure
Local Pressure
. Pascal Law 에 의하여 flow 가 흐르지 않는 상태에서는 모든 부위에 압력은 동일하다
. Flow 가 흐르는 상태에서는 Distributed Resistance (friction) 에 의하여 압력은 길이에 따라가며 낮아진다
26. 25
Pressure Drop
. Flow Restrictor 장치 들에 의하여 압력저하 가 발생된다
. Flow Restrictor 장치 : Orifice, Valve, Capillary tube, Filter, Porous metal,,,
. 동일한 Restriction 조건에서 Volume Flow Rate 는 압력의 차이 와 비례한다
Pressure
27. 26
Pressure
Pressure VS State of Matter
. 온도조건 과 압력조건에 의하여 물질의 상태변화
. Compressed 냉난방기 의 기본원리 :
1) Condensate : 기체 액체 , Release energy , 고압 상태 변화용이
2) Vapor : 액체 기체 , Absorb energy , 저압 상태 변화용이
28. 27
Dew Point
. Dew Point (이슬점)
- HO2 물질이 주변의 온도에 의하여 물질의 상태변화 (기체 액체, condensate) 가 되는 주변온도 점
- 상대습도에 따라 달라진다
- Stack 내의 샘플가스 분석을 위하여 Heated probe 및 Heated tube 를 사용하는 기본원리
. 압력이 높아지면 Dew Point 도 높아진다
Pressure
29. 28
Pressure
Static VS Dynamic Pressure
. Static Pressure
The pressure of a fluid or gas that is stationary (정지된) or not in a motion
. Dynamic pressure
The pressure exerted by a fluid or gas whet it impacts on a surface or an object due to its motion or flow
. Impact pressure (total pressure)
The sum of the static and dynamic pressures on a surface or object
. 베르누이 정리 에 의한 이론화
30. 29
요약
. 요약
베르누이 정리
정의 상대적으로 작은 cross section 으로 fluid flow 가 통과할때
(1) 운동에너지 (velocity) 는 증가한다.
(2) 전체 에너지를 보존하기 위하여 압력은 반드시 내려간다.
조건 It assumes
(1) steady,
(2) incompressible (constant density),
(3) friction-free,
(4) unmotivated flow.
불확실 (1) how to motivate the fluid flow and
(2) that the fluid flow is actually part of the same constant-dens
응용 (1) Flow Meter, Control Valve 및 Pressure Regulator 의 원리
(2) 피토관
실제로 Velocity 와 Pressure는
동일하지 않고 저하를 보일 것이다
31. 30
요약
. 아래 두 가지 법칙으로 정리된다
1) flow 조건이 변한 두 지점간 에너지 보존
- 압력에너지A + 운동에너지A+ 잠재에너지A == 압력에너지B + 운동에너지B + 잠재에너지B
- 압력차 를 이용한 Flow Meter, Control valve 및 Pressure Regulator 의 기본원리로 사용된다
2) 전체압력 (Stagnation Pressure)
- 압력에너지 = Static Energy, 운동에너지 = Dynamic Energy (Velocity Energy)
- 전체압력 = Static Energy + Dynamic Energy
- 피토관 유속계의 기본원리 로 사용된다 : V² 를 산출한다
베르누이 정리
32. 31
Velocity 1 산출 에 대한 방정식
. Velocity 1 산출 에 대한 방정식
베르누이 정리
33. 32
Flow Rate (Q) 산출에 대한 방정식-1
As long as the fluid speed is sufficiently subsonic (V < mach 0.3), the incompressibl
e Bernoulli's equation describes the flow reasonably well. Applying this equation to
a streamline traveling down the axis of the horizontal tube gives,
where location 1 is upstream of the orifice, and location 2 is slightly behind the orifi
ce. It is recommended that location 1 be positioned one pipe diameter upstream of
the orifice, and location 2 be positioned one-half pipe diameter downstream of the
orifice. Since the pressure at 1 will be higher than the pressure at 2 (for flow movin
g from 1 to 2), the pressure difference as defined will be a positive quantity.
From continuity, the velocities can be replaced by cross-sectional areas of the flow
and the volumetric flowrate Q,
Solving for the volumetric flowrate Q gives,
The above equation applies only to perfectly laminar, inviscid flows. For real flows (
such as water or air), viscosity and turbulence are present and act to convert kinetic
flow energy into heat. To account for this effect, a discharge coefficient Cd is intr
oduced into the above equation to marginally reduce the flowrate Q,
베르누이 정리
34. 33
Flow Rate (Q) 산출에 대한 방정식-2
Since the actual flow profile at location 2 downstream of the orifice is quite complex
, thereby making the effective value of A2 uncertain, the following substitution intro
ducing a flow coefficient Cf is made,
where Ao is the area of the orifice. As a result, the volumetric flowrate Q for real flo
ws is given by the equation,
The flow coefficient Cf is found from experiments and is tabulated in reference book
s; it ranges from 0.6 to 0.9 for most orifices. Since it depends on the orifice and pip
e diameters (as well as the Reynolds Number), one will often find Cf tabulated versu
s the ratio of orifice diameter to inlet diameter, sometimes defined as b,
The mass flowrate can be found by multiplying Q with the fluid density,
베르누이 정리
35. 34
피토관 V² 산출 방정식
.
베르누이 정리
Pitot-Static Tube
S type Pitot Tube
Total Pressure
Static Pressure
36. 35
피토관 을 통한 Q 산출과정
.
베르누이 정리
Stack
Gas
Velocity
Volumetric
Flow
Rate (Q) =
V*A
Velocity
37. 36
Application : Control Valve
CONTROL VALVE 란
. A control valve function as variable resistance in a pipe line.
It Provides pressure drop, called throttling, which limits the flow through a pipeline.
. Cross-section area (A) 조절을 통한 flow resistance 역할,
손실된 운동 에너지 만큼 압력의 차이가 발생한다
. 중요한 개념
1) 단면적 Area (Flow resistance) 만 가변으로 조정, 이 조정에 의하여 압력의 차이는 변화된다.
2) Delta P (P1-P2) 는 임의로 조절할수 있는 것이 아니다 – 다만 측정에 의하여 알뿐이다
3) 동일한 Area 가 주어진 경우 Flow Rate 는 압력차에 비례한다
Q 공식은 이것을 의미한다
38. 37
Orifice
. Orifice 에 의하여 단위시간당 (초) Volume 량이 줄어드는 개념적인 그림이다
. Q = Volume / t 임으로 Volume 에 비례하여 Flow rate 도 줄어든다
. Velocity 가 증가되면 Distance 는 증가 되었다고 하더라도, 전체 Volume 은 줄어든다
Application : Control Valve
FLOWVolumeArea
Distance
FLOWArea Volume
39. 38
Volume Flow Rate
. 밸브를 통과된 유량은 압력차이로 인하여 아래와 같이 산출된다
1) Liquid 인 경우
2) Gas 인 경우
Application : Control Valve
40. 39
FLOW COEFFICENT
. The flow coefficient Cv is a valve sizing designation commonly determined by laboratory test.
It corresponds to the flow rate of water through a valve in US gallons per minute at 60°F with a differential pressure drop of
one psi.
. 중요 :
1) 제조사 모델마다 상이하다
2) Valve 의 크기와 Valve Open 에 비례한다 Delta P 만으로 유량이 결정되는 것은 아니다
Application : Control Valve
41. 40
Why Pressure Drop
. Velocity 가 빨라짐으로 Pressure drop 발생 – 베르누이 정리
. Pressure 는 strength 개념이고 (voltage), Flow 는 speed 개념 (Ampere) 이다
. Resistance 에 의하여 한번 Drop 되면 downstream 에 위치한 pipe 가 동일한 area 를 지녀도 100% 회복은 안됨
. Total pressure loss is derived from 2 sources:
1) frictional losses along the entrance
2) throat and inertial losses stemming from the sudden expansion, causing flow separation and eddies (exit losses).
Frictional losses are linearly related to flow, Q (law of Poiseuille), and exit losses increase with the square of the flow caused by
convective acceleration in the narrowed segment (law of Bernoulli). Total pressure gradient (ΔP) is the sum of the two: ΔP= (f1
×Q) + (f2×Q2).
The loss coefficients f1 and f2 are a function of stenosis geometry and rheologic properties of blood (viscosity and density).
The graphical representation of this equation results in a quadratic relationship, where the curvilinear shape demonstrates the pr
esence of nonlinear exit losses.
When no stenosis is present, the second term is zero and the curve becomes a straight line (with a positive slope that depends
on the diameter of the vessel; law of Poiseuille). As indicates area of the stenosis; An, area of the normal segment; and Ls, effect
ive length of stenosis (up to the point of flow separation).
Application : Control Valve
45. 44
VACUUM
. Vacuum (진공) : 밀폐된 내부에 물질이 없어서 압력이 없는 상태
- 완전한 진공이란 없으며, 통상 대기압 보다 이하인 경우를 진공으로 표현한다
- 진공병 은 열 전달 (convection, conduction, radiation) 통로를 차단하는 역할이다.
. 진공발생장치
1) 벤츄리 관 : Ejector
2) Vacuum Cup
3) Pump
DEVICE
46. 45
DEVICE
VALVE
. Fluid Flow 잠금 및 조절 장치
. Check Valve 는 정압 일 경우에만 Fluid Flow 가 허용되는 switch 역할 : 역류방지 와 압력상승방지
47. 46
DEVICE
Pressure Regulator
. 밸브 의 기능적인 하나의 종류이다
. 입력 압력이 가변 하더라도 출력 압력을 낮추어 일정하게 가져가는 장치
- 입력압력을 조절하는 장치를 backpressure regulator 라 한다,
. Flow Rate 도 같이 조절이 된다
48. 47
DEVICE
Solenoid Valve
. A solenoid valve is an electromechanical actuated valve to control the flow of liquids and gases.
. Solenoid : Coil 을 원형으로 감아 N회 반복한 형태로서 전기가 흐르면 자기력이 생기는 원리를 이용
. 2/2 Way : 2 ports (inlet, outlet) and 2 positions (open or closed)
. 3/2 Way : 3 ports (inlet, outlet and common) and 2 position
. 4/2 , 5/2 , 5/3 Way
49. 48
DEVICE
Flow Meter
. Generally, five types of flow meters are used
1) Mechanical : Turbine
2) Electronic : Magnetic, Vortex, Ultransonice
3) Differential Pressure : Venturi, Orifice, Nozzle, Pitot Tube
4) Variable Area (Rota Meter)
5) Mass
Pressure Meter
. Types
1) Elastic Material : Bourdon tube, Bellows, Diaphragm
2) Electrical Method : Capacitive, Inductive, Reluctive, Piezoelectric, Strain Gauge, Vibrating Element, Potentiometric
51. 50
DEVICE
PUMP
. Pump 란 Sample 가스를 흡입하여 배출하는 기능을 갖는다
. Pump 란 진공과 고압을 만드는 장치이다
. Positive Displacement Pump (용적식 펌프)
- 일정 공간에 갇혀있는 액체를 왕복 혹은 회전운동으로 압축하여 압력을 높임으로서 액체를 토출측 으로 밀어내는 회전기계
- 회전식 (Rotary) 과 왕복식 이 있다
- 회전식 종류 : Gear, Screw, Vane
- 왕복식 종류 : Piston, Plunger, Diaphragm
. Diaphragm pumps are positive displacement pumps, meaning they use contracting and expanding cavities to move fluids.
Diaphragm pumps work by flexing the diaphragm out of the displacement chamber.
When the diaphragm moves out, the volume of the pump chamber increases and causes the pressure within the chamber to decrease
and draw in fluid.
The inward stroke has the opposite effect, decreasing the volume and increasing the pressure of the chamber to move out fluid.
This operation is very similar to the draw in, push out, concept of human breathing.
The motion of the diaphragm looks like this:
. 일반적인 성능 이외에 Low noise, Low Vibration 및 High Temperature 특성을 지닌다
성능 단위 예
Gas Max Flow l/min 6
Max Vacuum KPa 61.32
Max Discharge Pressure MPa 0.08
53. 52
Air
Air (Gas) Dryer
. Pneumatic 을 이용하는 장치 이거나, Gas 를 분석하는 장비들의 주요한 요구조건 (Condition) 은 다음과 같다
- 수분, 먼지 및 이물질 을 포함하지 않을 것
- 적절한 Flow rate
- 적절한 Flue Gas 온도
. Flue Gas, Ambient Air 및 Compressed Air 중 의 수분을 제거 하기 위한 방법은 아래와 같이 크게 두가지 가 있다
- Refrigerator Air Dryer : 냉장고 원리 Dew Point 수분발생 Drain
- Membrane Air Dryer : Compressed Air 박막 수분을 diffusion 하여 제거
. 참고 : 배출가스의 물질구성
54. 53
Air
Refrigerator Air Dryer
. 물질의 상태변화 시 주변 에너지를 흡수 하거나 발생에너지를 방출하는 원리를 이용
-. 액체 기체 (Vaporize) : 주변 에너지 (열) 을 필요로 한다 주변 열을 흡수하여 차갑게 만든다
-. 기체 액체 (Condensate) : 내부 에너지(열) 을 방출한다
. 기체 액체 : 기체가 고온 상태이면 주변온도에 의하여 액체로 변하고, 고압 상태이면 쉽게 액화할 수 있는 조건을 만들어 준다.
. 액체 기체 : 주변의 잠열에 의하여 기화 되며, 액체가 저압 상태이면 주변온도에 의하여 쉽게 기화할 수 있는 조건이 된다
. 물질은 Freon 을 사용하며 이를 촉매(냉매) 라 한다
Vapor
High PressureVapor
LiquidLiquid + Vapor
Low Pressure
55. 54
Air
Membrane Air Dryer
. Diffusion 원리 : 물질의 concentration 은 이동하여 balance 를 맞춘다
. 박막 (hollow fiber membrane) 으로 내부 와 외부가 구성되어 있으며, 내부에는 Wet gas 가 흐르고
외부에는 상대적으로 concentration 이 작은 Purge (Inst. Air) air 가 반대 방향으로 흐르면서
Vapor 는 외부로 이동한다.
56. 55
Connector
장치와 연결부위 및 호스 와 연결부위를 지님으로 두 가지 규격을 reference 한다
1) Hose (Pipe) 부분 : NPS or DN
2) Thread 부분 : NPT or G
Pipe Thread Standard : 장치에 연결되는 돌출부분
1) NPT : National Pipe Thread (America) or BSP (British Standard Pipe)
2) M thread : Standard in Europe
3) R or G thread (Whitworth) : Cylindrical threads which are mainly used in countries with imperial system
배관 (tube, pipe) 규격
1) IPS (Iron Pipe Size)
2) NPS (Nominal Pipe Size) : 외경(OD) 기준, Inch 사용
3) DN (Diameter Nominal) : NPS 규격 Inch 를 미터법으로 표기
. NPS ¼” : DN 10, NPS 1/8” : DN 6
. DN 4/6 의 외경은 6mm, 내경은 4mm 이다
. DN 6/8 의 외경은 8mm, 내경은 6mm 이다
* Connector 의 PTFE 는 외경, 내경을 따지지만 (내경 부분에 capillary 관이 있다) , SS 는 외경만 따진다
재질
1) PP : Polypropylene
2) PVDF : Polyvinylidene Fluoride
3) PTFE
4) PFA : Polyfluoroakoxy
5) Viton
6) Novoprene
7) Stainless Steel
57. 56
Connector
NIPPLE :
. 장치 와 Tube, Tube 와 Tube 간 연결장치 (Fitting) 이다
. 생김새 가 유두 모양이라 nipple 이라 칭하지만, 회사마다 connector 혹은 fittings 로 칭한다
. 용도에 따라 크게 두 가지로 구분
1) Tube-Pipe Thread(장치)
2) Tube-Tube 형 : 이것을 UNION 이라 칭한다
* Pipe Thread 막는것도 있으며 이를 CAP 이라 한다
. 아래 세가지 조합되어 다양하다
1) 형태 (straight, Tee, Elbow,,)
2) 재질 (SUS, Brass, PVDF)
3) Pipe Thread 규격 및 Tube 규격