The document discusses several problems related to machine design and mechanical components. It includes questions about determining the length of a key based on shear stress, calculating torque on a set screw, finding the size of stud bolts needed to withstand a given cylinder pressure, and calculating tangential load and holding force for various mechanical parts. It also includes questions about determining speeds, stresses, forces and dimensions for components like gears, shafts, pulleys, clutches, beams and other machine elements.
This document discusses various aspects of worm gears, including:
1. Key terms used such as lead, lead angle, pressure angle, and velocity ratio.
2. The three main types of worm gears: straight face, hobbed straight face, and concave face.
3. Formulas for determining efficiency, strength, wear load, and thermal rating of worm gears based on factors like lead angle, coefficient of friction, tooth geometry, and power transmitted.
The document discusses different types of brakes used in vehicles and machinery. It defines key terms related to brakes such as tangential braking force, normal force, coefficient of friction, heat generated during braking. It then describes different types of brakes in detail including single block/shoe brake, pivoted block/shoe brake, band brake, band and block brake, internal expanding brake. Equations are provided for calculating forces, torque, energy absorbed during braking. Materials used for brake linings and their properties are also summarized.
This document contains 4 problems related to the design of mechanical springs. Problem 1 asks the reader to calculate the axial load and deflection per turn for a helical spring with given dimensions and material properties. Problem 2 involves designing a spring for a balance that can measure loads from 0-1000N over 80mm and fits inside a 25mm casing. Problem 3 asks the reader to design a compression spring for 1000N load over 25mm deflection using a spring index of 5. Problem 4 asks the reader to design a close-coiled helical compression spring that can handle loads from 2250-2750N over 6mm deflection with a spring index of 5.
1) Sound is a small pressure wave that travels through a medium and requires a medium, unlike light which can travel through a vacuum.
2) The speed of sound in a medium depends on the properties of that medium and changes as those properties change, such as temperature.
3) The speed of sound is highest in gases with a high kR value, such as helium, and increases with increasing temperature in all gases.
1. The document provides 10 problems related to one-dimensional steady-state heat conduction. The problems involve determining temperature distributions, heat fluxes, heat transfer rates, and thermal resistances for various geometries including walls, pipes, spheres, and cylinders. The materials include aluminum, stainless steel, and other unspecified solids. Boundary conditions include specified temperatures, insulation, convection, and heat generation.
This document contains 11 multi-step physics problems involving fluid mechanics concepts like pressure, viscosity, density, and fluid flow. The problems are solved with relevant equations for ideal gases, compressible fluids, laminar flow, and viscometry. Key values are calculated, such as mass, pressure, shear stress, drag force, velocity, and viscosity.
The document discusses the design of machine elements. It covers factors governing design, general design procedures, stresses in bolts, nuts and keys, and design of cylinder cover bolts. Key points covered include:
1) The factors governing machine element design include strength, cost, reliability, shape, size, friction, corrosion and more.
2) General design procedures include identifying needs, analyzing forces, selecting materials, determining sizes, and producing detailed drawings.
3) Stresses in bolted connections from initial tightening, external loads, and combined loads are analyzed. Formulas to calculate bolt sizes based on allowable stresses are presented.
4) The design of cylinder cover bolts involves calculating the pitch
The document discusses several problems related to machine design and mechanical components. It includes questions about determining the length of a key based on shear stress, calculating torque on a set screw, finding the size of stud bolts needed to withstand a given cylinder pressure, and calculating tangential load and holding force for various mechanical parts. It also includes questions about determining speeds, stresses, forces and dimensions for components like gears, shafts, pulleys, clutches, beams and other machine elements.
This document discusses various aspects of worm gears, including:
1. Key terms used such as lead, lead angle, pressure angle, and velocity ratio.
2. The three main types of worm gears: straight face, hobbed straight face, and concave face.
3. Formulas for determining efficiency, strength, wear load, and thermal rating of worm gears based on factors like lead angle, coefficient of friction, tooth geometry, and power transmitted.
The document discusses different types of brakes used in vehicles and machinery. It defines key terms related to brakes such as tangential braking force, normal force, coefficient of friction, heat generated during braking. It then describes different types of brakes in detail including single block/shoe brake, pivoted block/shoe brake, band brake, band and block brake, internal expanding brake. Equations are provided for calculating forces, torque, energy absorbed during braking. Materials used for brake linings and their properties are also summarized.
This document contains 4 problems related to the design of mechanical springs. Problem 1 asks the reader to calculate the axial load and deflection per turn for a helical spring with given dimensions and material properties. Problem 2 involves designing a spring for a balance that can measure loads from 0-1000N over 80mm and fits inside a 25mm casing. Problem 3 asks the reader to design a compression spring for 1000N load over 25mm deflection using a spring index of 5. Problem 4 asks the reader to design a close-coiled helical compression spring that can handle loads from 2250-2750N over 6mm deflection with a spring index of 5.
1) Sound is a small pressure wave that travels through a medium and requires a medium, unlike light which can travel through a vacuum.
2) The speed of sound in a medium depends on the properties of that medium and changes as those properties change, such as temperature.
3) The speed of sound is highest in gases with a high kR value, such as helium, and increases with increasing temperature in all gases.
1. The document provides 10 problems related to one-dimensional steady-state heat conduction. The problems involve determining temperature distributions, heat fluxes, heat transfer rates, and thermal resistances for various geometries including walls, pipes, spheres, and cylinders. The materials include aluminum, stainless steel, and other unspecified solids. Boundary conditions include specified temperatures, insulation, convection, and heat generation.
This document contains 11 multi-step physics problems involving fluid mechanics concepts like pressure, viscosity, density, and fluid flow. The problems are solved with relevant equations for ideal gases, compressible fluids, laminar flow, and viscometry. Key values are calculated, such as mass, pressure, shear stress, drag force, velocity, and viscosity.
The document discusses the design of machine elements. It covers factors governing design, general design procedures, stresses in bolts, nuts and keys, and design of cylinder cover bolts. Key points covered include:
1) The factors governing machine element design include strength, cost, reliability, shape, size, friction, corrosion and more.
2) General design procedures include identifying needs, analyzing forces, selecting materials, determining sizes, and producing detailed drawings.
3) Stresses in bolted connections from initial tightening, external loads, and combined loads are analyzed. Formulas to calculate bolt sizes based on allowable stresses are presented.
4) The design of cylinder cover bolts involves calculating the pitch
This document provides information about belting, including the transmission of power via belts. It begins by stating the objectives of understanding belting concepts such as the differences between open and closed belts, how power is transmitted by flat and V belts, belt tension ratios, and calculating power transmitted considering centrifugal force. It then provides explanations and examples of calculating the length of open and closed belt drives. Additional sections cover the power transmitted by a belt using the formula of tension difference multiplied by velocity, and determining belt tension ratios. Worked examples are provided throughout to demonstrate application of the concepts.
This document discusses blade nomenclature and axial flow turbines. It defines key differences between turbines and compressors, as well as between axial and radial flow turbines. Axial flow turbines are more commonly used in gas turbines due to their better efficiencies compared to radial turbines. The document then provides the elementary theory of axial flow turbines, including definitions of velocity triangles, assumptions made, calculations of work done, stage efficiency, and flow coefficients. It includes an example problem calculating parameters for a single-stage axial turbine.
This problem involves designing a gear drive system to meet specific power, speed, and ratio requirements.
1. The key specifications are: 15 kW power at 1200 rpm driving a compressor at 300 rpm, with a gear ratio of 4:1. The shafts are 400mm apart. The pinion is forged steel with 210 MPa allowable stress, and the gear is cast steel with 140 MPa stress.
2. A two-stage gear train layout is proposed to achieve a 9:1 ratio from an input of 960 rpm to transmit 2 kW power. The shafts are 200mm apart with coaxial input/output.
3. The solution involves calculating the module, pitch diameter, number
The document contains solutions to several problems involving stresses in cylindrical tanks and shafts.
Problem 7 involves determining stresses in a compressed air tank given its dimensions, wall thickness, internal pressure, and an applied force.
Problem 7.120 calculates stresses in a tank given an applied torque, internal pressure, inner diameter, and wall thickness.
Problem 7.121 determines the torque required to produce a given maximum normal stress in a tank with known pressure, diameter, and thickness.
Problem 7.104 finds the maximum fill height for a water storage tank given the material properties, wall thickness, and a safety factor.
Problem 7.85 uses maximum shear stress to find the force that will cause yielding in
This document discusses different types of joints used in engineering, including bolted, riveted, and welded joints. It provides information on calculating the strength and dimensions of these different joint types. Specific topics covered include threaded fasteners, bolted and riveted joints loaded in shear, shear joints with eccentric loading, and examples of calculating loads on bolted and riveted joints. Design considerations like stress concentrations and failure modes are also addressed.
Me307 machine elements formula sheet Erdi Karaçal Mechanical Engineer Univers...Erdi Karaçal
1. The document discusses various topics related to stress analysis including moment of inertias, stresses from different load cases, principal stresses, stress states, stresses in cylinders, and deflection analysis using Castigliano's theorem.
2. Design considerations for static strength are covered for both ductile and brittle materials using theories such as maximum normal stress and distortion energy.
3. Fatigue strength design includes determining the endurance limit based on material properties and adjusting it using factors for surface finish, size, and loading conditions.
The document discusses torsion in circular shafts. It covers the assumptions in torsion theory including the determination of shear stress, strain, and modulus. It also describes the distribution of shear stress and angle of twist in solid and hollow circular shafts. Key points include:
- Shear stress is highest at the surface and decreases linearly towards the center of a shaft.
- Angle of twist is proportional to both the applied torque and length of the shaft.
- Cross sections remain plane during twisting for circular shafts but may become distorted for non-circular shafts.
This document discusses the design of shafts used in machines. It begins by introducing different types of shafts like stepped, cranked, and flexible shafts. It then discusses the materials used for shafts, focusing on their strength and machinability. The document provides equations to calculate shaft diameter based on the torque transmitted. It also lists permissible stress values for shaft materials under different service conditions. Finally, it discusses how shafts experience both bending and torsional stresses that must be considered in their design.
The document discusses problems related to the design of helical springs, leaf springs, and coned disc springs. It provides examples of spring design problems involving the calculation of spring dimensions, loads, stresses, and deflections given various input parameters such as material properties, load ranges, spring indices, and dimensional constraints. The problems cover topics such as determining wire diameter, number of coils, spring rates, thicknesses of leaf springs, and stresses induced in coned disc springs. Solutions to the problems are presented using relevant spring design equations.
1) The document discusses water passing through a pressure-reducing valve and separating tank, including its state and amount that leaves as vapor.
2) It also discusses heat transfer calculations for air heated in an exchanger and flow rate measurement using a venturi meter.
3) Heat transfer principles and equations are reviewed for various processes, including perfect gas behavior, convection coefficients, radiation from a human body, and insensible evaporation heat loss.
This document describes a student project to design and construct model wind turbines. Each group designed their own airfoil and support structure. This group focused on using triangles in their tower design and aerodynamics in their airfoil. They constructed a four-sided pyramid tower out of yellow pine dowels for its stiffness. Their airfoil was designed in Solidworks to have an asymmetrical cross-section to generate lift from wind. Testing showed the turbine had high stiffness but low power, likely due to the airfoil design being better suited for aircraft than wind turbines.
1) The document discusses the Otto cycle and diesel cycle processes in an internal combustion engine. It provides equations to calculate important parameters like efficiency, temperatures, and pressures at different points in the cycles.
2) An example calculation is provided to determine the air standard thermal efficiency of a diesel engine given data on compression ratio, inlet temperature and pressure, and maximum cycle temperature.
3) The key processes in the Otto cycle are compression, constant volume combustion, expansion, and constant volume heat rejection. The diesel cycle involves compression, constant pressure combustion, expansion, and constant volume heat rejection.
The stresses in thin cylinders and shells subjected to internal pressure or rotational forces are summarized. For thin cylinders under internal pressure, the circumferential (hoop) stress is given by σH=Pd/2t and the longitudinal stress is given by σL=Pd/4t, where P is the internal pressure, d is the internal diameter, and t is the wall thickness. The change in internal volume of the cylinder is given by ΔV=-(5-4v)PV/4tE, where V is the original internal volume, E is Young's modulus, and v is Poisson's ratio. For thin rotating cylinders, the hoop stress is given by σH=ω2R2,
This document provides solutions to design problems involving simple stresses of tension, compression, and shear for various structural elements.
Problem 1 calculates the dimensions of a steel link subjected to tensile loading based on ultimate strength, yield strength, and a specified elongation limit. Problem 2 is similar but for a malleable iron link. Problem 3 calculates dimensions for a gray iron link based on ultimate strength and elongation.
Problem 4 calculates the diameter of a steel piston rod subjected to repeated reversed loading based on ultimate and yield strengths. Problem 5 calculates diameters for a short compression member made of cast steel. Problem 6 does the same for a member made of 4130 steel based on yield and ultimate strengths.
Problem 7 calculates the diameter
1) The document describes the design procedure for a bushed-pin flexible coupling. It begins by explaining the need for flexible couplings to accommodate misalignment between connected shafts.
2) The key steps in the design procedure are: (1) Calculate the shaft diameter based on power and torque equations, (2) Determine flange dimensions using empirical relations of the shaft diameter, (3) Calculate pin diameter based on number of pins and shaft diameter, (4) Find rubber bush dimensions using torque and pitch circle diameter equations, (5) Select a standard key size and check stresses.
3) The main advantage of this flexible coupling is that it can accommodate misalignment between shafts, while the larger pin diameter
This document provides information about belting, including the transmission of power via belts. It begins by stating the objectives of understanding belting concepts such as the differences between open and closed belts, how power is transmitted by flat and V belts, belt tension ratios, and calculating power transmitted considering centrifugal force. It then provides explanations and examples of calculating the length of open and closed belt drives. Additional sections cover the power transmitted by a belt using the formula of tension difference multiplied by velocity, and determining belt tension ratios. Worked examples are provided throughout to demonstrate application of the concepts.
This document discusses blade nomenclature and axial flow turbines. It defines key differences between turbines and compressors, as well as between axial and radial flow turbines. Axial flow turbines are more commonly used in gas turbines due to their better efficiencies compared to radial turbines. The document then provides the elementary theory of axial flow turbines, including definitions of velocity triangles, assumptions made, calculations of work done, stage efficiency, and flow coefficients. It includes an example problem calculating parameters for a single-stage axial turbine.
This problem involves designing a gear drive system to meet specific power, speed, and ratio requirements.
1. The key specifications are: 15 kW power at 1200 rpm driving a compressor at 300 rpm, with a gear ratio of 4:1. The shafts are 400mm apart. The pinion is forged steel with 210 MPa allowable stress, and the gear is cast steel with 140 MPa stress.
2. A two-stage gear train layout is proposed to achieve a 9:1 ratio from an input of 960 rpm to transmit 2 kW power. The shafts are 200mm apart with coaxial input/output.
3. The solution involves calculating the module, pitch diameter, number
The document contains solutions to several problems involving stresses in cylindrical tanks and shafts.
Problem 7 involves determining stresses in a compressed air tank given its dimensions, wall thickness, internal pressure, and an applied force.
Problem 7.120 calculates stresses in a tank given an applied torque, internal pressure, inner diameter, and wall thickness.
Problem 7.121 determines the torque required to produce a given maximum normal stress in a tank with known pressure, diameter, and thickness.
Problem 7.104 finds the maximum fill height for a water storage tank given the material properties, wall thickness, and a safety factor.
Problem 7.85 uses maximum shear stress to find the force that will cause yielding in
This document discusses different types of joints used in engineering, including bolted, riveted, and welded joints. It provides information on calculating the strength and dimensions of these different joint types. Specific topics covered include threaded fasteners, bolted and riveted joints loaded in shear, shear joints with eccentric loading, and examples of calculating loads on bolted and riveted joints. Design considerations like stress concentrations and failure modes are also addressed.
Me307 machine elements formula sheet Erdi Karaçal Mechanical Engineer Univers...Erdi Karaçal
1. The document discusses various topics related to stress analysis including moment of inertias, stresses from different load cases, principal stresses, stress states, stresses in cylinders, and deflection analysis using Castigliano's theorem.
2. Design considerations for static strength are covered for both ductile and brittle materials using theories such as maximum normal stress and distortion energy.
3. Fatigue strength design includes determining the endurance limit based on material properties and adjusting it using factors for surface finish, size, and loading conditions.
The document discusses torsion in circular shafts. It covers the assumptions in torsion theory including the determination of shear stress, strain, and modulus. It also describes the distribution of shear stress and angle of twist in solid and hollow circular shafts. Key points include:
- Shear stress is highest at the surface and decreases linearly towards the center of a shaft.
- Angle of twist is proportional to both the applied torque and length of the shaft.
- Cross sections remain plane during twisting for circular shafts but may become distorted for non-circular shafts.
This document discusses the design of shafts used in machines. It begins by introducing different types of shafts like stepped, cranked, and flexible shafts. It then discusses the materials used for shafts, focusing on their strength and machinability. The document provides equations to calculate shaft diameter based on the torque transmitted. It also lists permissible stress values for shaft materials under different service conditions. Finally, it discusses how shafts experience both bending and torsional stresses that must be considered in their design.
The document discusses problems related to the design of helical springs, leaf springs, and coned disc springs. It provides examples of spring design problems involving the calculation of spring dimensions, loads, stresses, and deflections given various input parameters such as material properties, load ranges, spring indices, and dimensional constraints. The problems cover topics such as determining wire diameter, number of coils, spring rates, thicknesses of leaf springs, and stresses induced in coned disc springs. Solutions to the problems are presented using relevant spring design equations.
1) The document discusses water passing through a pressure-reducing valve and separating tank, including its state and amount that leaves as vapor.
2) It also discusses heat transfer calculations for air heated in an exchanger and flow rate measurement using a venturi meter.
3) Heat transfer principles and equations are reviewed for various processes, including perfect gas behavior, convection coefficients, radiation from a human body, and insensible evaporation heat loss.
This document describes a student project to design and construct model wind turbines. Each group designed their own airfoil and support structure. This group focused on using triangles in their tower design and aerodynamics in their airfoil. They constructed a four-sided pyramid tower out of yellow pine dowels for its stiffness. Their airfoil was designed in Solidworks to have an asymmetrical cross-section to generate lift from wind. Testing showed the turbine had high stiffness but low power, likely due to the airfoil design being better suited for aircraft than wind turbines.
1) The document discusses the Otto cycle and diesel cycle processes in an internal combustion engine. It provides equations to calculate important parameters like efficiency, temperatures, and pressures at different points in the cycles.
2) An example calculation is provided to determine the air standard thermal efficiency of a diesel engine given data on compression ratio, inlet temperature and pressure, and maximum cycle temperature.
3) The key processes in the Otto cycle are compression, constant volume combustion, expansion, and constant volume heat rejection. The diesel cycle involves compression, constant pressure combustion, expansion, and constant volume heat rejection.
The stresses in thin cylinders and shells subjected to internal pressure or rotational forces are summarized. For thin cylinders under internal pressure, the circumferential (hoop) stress is given by σH=Pd/2t and the longitudinal stress is given by σL=Pd/4t, where P is the internal pressure, d is the internal diameter, and t is the wall thickness. The change in internal volume of the cylinder is given by ΔV=-(5-4v)PV/4tE, where V is the original internal volume, E is Young's modulus, and v is Poisson's ratio. For thin rotating cylinders, the hoop stress is given by σH=ω2R2,
This document provides solutions to design problems involving simple stresses of tension, compression, and shear for various structural elements.
Problem 1 calculates the dimensions of a steel link subjected to tensile loading based on ultimate strength, yield strength, and a specified elongation limit. Problem 2 is similar but for a malleable iron link. Problem 3 calculates dimensions for a gray iron link based on ultimate strength and elongation.
Problem 4 calculates the diameter of a steel piston rod subjected to repeated reversed loading based on ultimate and yield strengths. Problem 5 calculates diameters for a short compression member made of cast steel. Problem 6 does the same for a member made of 4130 steel based on yield and ultimate strengths.
Problem 7 calculates the diameter
1) The document describes the design procedure for a bushed-pin flexible coupling. It begins by explaining the need for flexible couplings to accommodate misalignment between connected shafts.
2) The key steps in the design procedure are: (1) Calculate the shaft diameter based on power and torque equations, (2) Determine flange dimensions using empirical relations of the shaft diameter, (3) Calculate pin diameter based on number of pins and shaft diameter, (4) Find rubber bush dimensions using torque and pitch circle diameter equations, (5) Select a standard key size and check stresses.
3) The main advantage of this flexible coupling is that it can accommodate misalignment between shafts, while the larger pin diameter
Fluid mechanics is the study of fluids and the forces on them. It looks at liquids and gases in motion and at rest and involves concepts like pressure, density, viscosity, velocity, and temperature. The key topics covered are hydrostatics, dynamics, thermodynamics, and studies of viscous and inviscid flows.
11. 96
4.7 การคํานวณเกี่ยวกับเรื่องปม
จากสมการดุลพลังงานในบทที่ 3
⎛ Δv 2 ⎞
⎜ ⎟ + Δz g + 2 VdP + Σ F
⎜ 2g α ⎟ gc
p
∫p1 = − W'f (3.14)
⎝ c ⎠
แตละเทอมสามารถใชชื่อ “เฮด” เทอมแรกเรียกวา Velocity head เทอมที่สองเรียกวา Potential head
เทอมที่สามเรียก Pressure head เทอมที่สี่เรียก Friction head และ − W'f คืองานที่ปมจะตองใหแก
ของไหลเพื่อเอาชนะ head ตางๆ เมื่อของไหลเขาสูระบบ หรือ W'f คือ งานที่ของไหลออกจากระบบ
และทํางานใหสิ่งแวดลอม คา − W'f ซึ่งเปนงานที่ปมจะตองใหแกของไหล เพื่อเอาชนะคา head
ทุกประเภท ผลรวมทางดานซายมือของสมการ energy balance นี้ในหนังสือบางเลม เรียกวา Total
dynamic head (TDH) หรือ Total discharge head ทุกเทอมในสมการนีมีหนวย N m/kg, ft lbf/lb
้
กําลังและประสิทธิภาพของปม กําลังหมายถึงอัตราการทํางานตอหนวยเวลา หนวยของกําลังที่
นิยมใชไดแก Watt และแรงมา โดยหนึงแรงมามีคาเทากับ 745.7 Watt (745.7 N.m/s) หรือ 550 ft-
่
lbf/s และนักศึกษาอาจพบคําวา แรงมาตามทฤษฎี, Theoretical horse power, และ Water horse
power (Whp)
= − W'f w
Whp
(4.2)
= − W'f ρQ
เมื่อ Q คือคาอัตราไหล ม3/วินาที ρ คือคาความหนาแนนของของไหลและยังมีคา break hourse
power (Bhp) ซึ่งหมายถึงกําลังที่ตองใหกับมอเตอรหรือเครื่องยนตทใชเปนตนกําลังขับเคลื่อนปม ซึ่ง
ี่
ความสัมพันธระหวางกําลังทั้งสอง ไดแก
Whp
Bhp =
η
; เมื่อ η คือคาประสิทธิภาพของปม
ในกรณีทตนกําลังเปนมอเตอร ซึงใชพลังงานไฟฟาเปนกิโลวัตต (kW) คํานวณไดจาก
ี่ ่
kW =
0 . 746
(4.3)
ηของมอเตอร
และประสิทธิภาพรวม = ประสิทธิภาพของปม x ประสิทธิภาพของมอเตอร
4.8 กราฟเฮดของระบบ (System Head Curve)
System Head Curve คือ กราฟแสดงความสัมพันธระหวางอัตราการไหลผานระบบกับ Total
Discharge head หรือพลังงานที่ปมจะตองใหกับระบบเพื่อกอใหเกิดการไหลนั้นกับอัตราการไหลของ
ระบบ โดยปกติบริษัทผูผลิตปมจะใหความสัมพันธของการทํางานของปมกับตัวแปรตาง ๆ เราเรียก
12. 97
กราฟเหลานี้วา Pump Characteristic Curve ซึ่งใหความสัมพันธของอัตราไหล (Q) กับเฮด, กําลัง,
ประสิทธิภาพของปมแตละรุนและขนาดไว เมื่อผูบริโภคจะซื้อปมหนึงตัวที่ถูกตองแลวจะตองวิเคราะห
่
ภาระงานของปมนันวาจะตองทํางานเอาชนะภาระงานใดบางสมการดุลพลังงานตามสมการ
้
⎛ Δv 2 ⎞
⎜ ⎟ + Δz g +
⎜ 2g α ⎟ gc
p2
∫p1 VdP + Σ F = − W'f (3.14)
⎝ c ⎠
ซึ่งเขียนไวคลุมภาระงานทุกประเภทแตในการปฏิบัติจริงอาจมีเฉพาะบางเทอมเทานันที่มความสําคัญ
้ ี
ตัวอยางเชน การที่ชาวนาสูบน้ําจากบึงมาลงที่นาของตนซึ่งมีระดับความสูงเกือบเทากัน องคประกอบ
ของภาระงานของปมก็อาจจะมีเพียงการเอาชนะความฝดเทานั้นเนื่องจากเทอม Δg , ∫pp2 VdP , Δz gg
2
v
2 c 1 c
มีคาเปนศูนยไปหมดและเนืองจากไมมีการเปลี่ยนแปลงคาความเร็ว (ถาขนาดทอดูดและทอสงเทากัน)
่
ไมมีการเปลี่ยนแปลงคาความดัน (เนื่องจากแหลงน้ําและทอสงเปดสูบรรยากาศ เทอม ΔP จึงเปน
ศูนย) และความตางระดับไมมี Δz เปนศูนย ดังนั้นในกรณีนี้ปมทํางานเพื่อเอาชนะคา Friction Head
เพียงอยางเดียว ตัวอยางเรื่องการสูบน้ําขึ้นถังสูง การสูบน้ําเขาถัง boiler เปนตัวอยางที่จะเห็นวา
นอกจากการเอาชนะความฝดแลว ปมยังตองใหกําลังมากพอเอาชนะเทอมของ Potential head และ
pressure head ตามลําดับ
จาก Graph Pump Characteristic ซึ่งแกน y เปนคา total dynamic head แกน x เปนแกน
อัตราการไหลนั้นมีประเด็นทีนักศึกษาตองระวังคือเรื่องหนวย นักศึกษาตองไมลืมวาคา total discharge
่
head ที่คานวณจากสมการ 3.14 นั้น คา head มีหนวยเปน ft-lbf/lb แตคา head ในแกน y มีหนวยเปน
ํ
ft ซึ่งหมายความวา เมื่อคํานวณหา total
head ไดแลว จะตองคูณดวยคา gc
g
เพื่อให
ft − lb f ⎛ ft ⋅ lb ⎞⎛ s 2 ⎞
หนวยเปน ft; lb
⋅⎜ 2
⎜ s ⋅ lb
⎟⎜
⎟⎜ ft
⎟
⎟
ซึ่ง
⎝ f ⎠⎝ ⎠
กรณีสําหรับขอมูลในระบบ English
engineeringการไมไดคณดวยคา
ู gc
g
กอน
จะไมมีปญหาใด ๆ แตถา graph นั้นเปน
N−m
ระบบ SI ซึ่งมี head มีหนวยเปน kg
,
เมื่อคูณดวย gc
g
จึงจะมีหนวยเปนเมตร
N − m kg − m s 2
⇒ × ⇒m
kg s 2N m
ตัวอยาง 4.1
รูป 4.14 Characteristic Curve of Gear Pump It is necessary to pump a
constant flow of a liquid with density
13. 98
and viscosity similar to water into a reactor at a rate of 90 gal/min. The pump must operate
agains a pressure of 200 psi, as determined by an energy balance on the flow system. A
pump with the characteristics shown in Figure 4.13.is avaible, with a variable-speed drive.
At what speed should the pump be operated? What horsepower would be required to
maintain flow?
วิธีทา เมื่อพลอตบนกราฟ 4.14 จุดที่แสดงตําแหนงอัตราไหลและความดันที่ตองการไมตก
ํ
บนเสนกราฟใด แตอยูระหวางกราฟที่มีความเร็วรอบ 400 และ 600 รอบตอนาที การเปลี่ยนแปลง
อัตราไหล และความเร็วดูจะไมเปนกราฟเสนตรง ดูไดจากระยะหางของการเปลี่ยนแปลงจากความเร็ว
รอบ 200-400 กับ 400-600 ดังนันการทํา interpolation จะใหความเร็วรอบประมาณ 520 rpm และ
้
คากําลังของปมประมาณ 21 แรงมาที่ความดันดานจายเทากับ 200 psi
4.9 คุณสมบัติของปมแบบเซนตริอลฟูกอล
เนื่องจากปมแบบเซนตริอลฟูกอล เปนปมชนิดทีมีการใชกันอยางกวางขวางมากที่สุด มีความ
่
รูป4.15 กราฟ H-Q ของปม
เหมาะสมกับงานหลากหลายลักษณะ จึงควรรูถึงลักษณะสําคัญไวบาง
4.9.1 กราฟ H-Q ของปม, กราฟ H-Q head capacity curve ของปม คือกราฟแสดงความสัมพันธ
ระหวางอัตราการสูบกับเฮดที่ปมสามารถทํางานได ตังแตอตราการสูบเปนศูนย จนถึงอัตราการสูบ
้ ั
สูงสุดของปมนั้น โดยปกติบริษัทผูผลิตจะมีขอมูลนี้สําหรับปมแตละรุน เพื่อใหผูใชไดพิจารณาขนาดที่
เหมาะสมหลังจากไดวิเคราะหระบบดวยสมการดุลพลังงานของระบบแลว เวลาเลือกใชงานเราจะเลือก
ปมที่ใหเฮดและอัตราการสูบที่ตองการ โดยคาทั้งสองตรงกับจุดที่มีประสิทธิภาพสูงสุด หรือใกลเคียง
14. 99
กับตําแหนงดังกลาวมากที่สุด จุดที่เลือกเรียกวา Design Operating Point รูปรางของเสน H-Q จะ
ขึ้นกับชนิดของใบพัด
รูป 4.16 Characteristic Curve of Centrifugal Pump, 1750 rpm(upper),
3550 rpm(lower)
ตัวอยาง 4.2
A pump with the characteristics given in Figure 4.16 is to deliver 350 gal/min at a
head of 80 ft. What size impeller should be used? What power will be required?
15. 100
วิธีทา จากกราฟ4.16 ปมขนาดความเร็วรอบ 1750 รอบตอนาที ดูจะเหมาะสม เมื่อกําหนด
ํ
ตําแหนงดวยคาอัตราไหล 350 gal/min, head 80ft จะพบวาจุดตัดของเฮดและอัตราไหลอยูระหวาง
คาของใบพัดเสนผานศูนยกลาง 9 นิ้ว และ 10 นิ้ว ตามลําดับ ใบพัด 9 นิ้ว สงน้ําได 175 gal/min ทีคา
่
เฮด 80 ft ดังนั้นจึงตองใชใบพัด 10 นิ้ว ซึ่งอาจจะใหอตราไหลสูงมากกวาที่ตองการ และอาจแกไขโดย
ั
ใชวงจรควบคุม และประมาณกําลังสําหรับปมใบพัด 10 นิ้วดวยวิธี interpolationได เทากับ 11 แรงมา
4.9.2 ความเร็วจําเพาะ (Specific Speed) คือคาความเร็วรอบใบพัดในหนวยรอบตอนาที ซึงปมตาม
่
ทฤษฎี (แบบเดียวกับปมใชจริง) หมุนไดทประสิทธิภาพสูงสุด ขณะทีสูบน้ําได 1 gal/min ตานกับความ
ี่ ่
ดันดานจายเทากับคาเฮด 1 ฟุต โดยมีสมการคาความเร็วจําเพาะ
n Q
Ns =
H0 .75
(4. 4)
เมื่อ Ns = specific
speed, rpm
n= actual speed, rpm
H = total head per speed, ft
Q = pump
capacity, gal/min at speed n and
total head z
รูปที่ 4.17 ความเร็วจําเพาะ (Specific Speed)
คาความเร็วจําเพาะนี้ใชเปนขอมูลในการเลือกชนิดของเซนตริฟูกอลปมทั้งนี้เพราะลักษณะ
รูปทรงของใบพัด และคาความเร็วรอบ องคประกอบหลักที่มีผลตอคาพลังงานทีปมสามารถถายทอด
่
ใหแกของเหลวได
สมการ Ns เมื่อเปนระบบ SI มีดังนี้
1 . 633 rpm lps
Ns =
H0 .75
โดยที่ Ns, rpm มีหนวยเปน rpm เชนเดียวกับสมการขางตน
ตัวอยาง 4.3
It is necessary to pump a liquid with properties similar to water at a rate of 300
gal/min against a head of 70 ft. Recommed a pump type and size.
วิธีทาํ ชนิดของปมสามารถหาไดจากการตรวจสอบคาความเร็วจําเพาะ
และกราฟ
Characteristic และ Ns ซึ่งจะให guide line ชนิดของ pump ที่เหมาะสม
