These formulas cover fluid power applications such as hydraulics and pneumatics. Key formulas calculate fluid pressure, velocity through pipes, flow through orifices, cylinder force and speed, motor torque and horsepower, pump flow and efficiency, accumulator sizing, and thermal properties of hydraulic systems. Additional information is provided on fluid properties, pipe flow velocities, cylinder intensification and load pressures. Charts for various fluid power values are referenced.
This document provides information about various air standard cycles used in internal combustion engines, including the Otto, Diesel, and Dual cycles. It defines the key processes and equations for each cycle. The Otto cycle involves four processes: isentropic compression, constant volume heat addition, isentropic expansion, and constant volume heat rejection. The Diesel cycle involves: isentropic compression, constant pressure heat addition, isentropic expansion, and constant volume heat rejection. The Dual cycle combines aspects of the Otto and Diesel cycles, involving five processes. Thermodynamic relationships between pressure, volume, temperature and other variables are defined through equations for each cycle.
This document summarizes different types of fans and blowers used to move air or gas. It describes axial and centrifugal fans that move air parallel or perpendicular to the fan shaft. Common fan applications include ventilation, cooling towers, and industrial processes. The document also covers blower types, compression equations, efficiency calculations, performance relationships, and laws governing how fan characteristics change with speed, size, and density.
A cooling tower cools water by evaporating a portion of the water as it is exposed to air circulating through the tower. Hot water enters the top of the tower and is cooled as it falls through fillings, exposing new surfaces to the air. Cooled water exits the bottom while moist air exits from the top after partially saturating with evaporated water. The document provides equations for calculating cooling tower performance parameters like actual cooling range, approach, efficiency, enthalpy, humidity ratio, and mass and energy balances.
This document provides information on refrigeration including:
1. Refrigeration is defined as the process of cooling a substance below the temperature of its surroundings. Major uses include air conditioning, food preservation, and industrial processes.
2. A ton of refrigeration is defined as the heat required to melt 1 ton of ice at 0°C in 24 hours.
3. The Carnot refrigeration cycle consists of heat addition, heat rejection, expansion, and compression processes between a high and low temperature.
4. A vapor compression cycle uses a compressor, condenser, expansion valve, and evaporator to circulate refrigerant between high and low pressures and temperatures.
5. Cascade systems combine two vapor compression units
This document contains solved problems from chapter 12 on positive displacement machines. Problem 12.1 calculates the indicated power and delivery temperature for air compression in a single-stage reciprocating compressor under isentropic, isothermal and polytropic processes. Problem 12.2 calculates the bore size required for the compressor running at 1000 rpm with a stroke to bore ratio of 1.2:1. Problem 12.3 calculates various parameters like bore, stroke, volumetric efficiency and indicated power for a single-stage single-acting air compressor running at 1000 rpm.
This document contains equations and rules of thumb for HVAC systems. It includes equations for cooling and heating load calculations, ductwork sizing, fan and pump laws, expansion tank sizing, air balancing, efficiencies, cooling towers, moisture condensation, and electricity. The equations are presented along with brief explanations of the variables.
This document provides procedures for conducting a Gross Turbine Cycle Heat Rate (GTCHR) test on a steam turbine. The test is used to measure the overall efficiency of the turbine cycle and its auxiliaries. Key steps include operating the unit at a steady load and temperature conditions, collecting instrumentation data like steam and water temperatures and pressures, and calculating the turbine cycle heat rate in kcal/kWh based on enthalpy values and steam and water flows. The test report includes computation of main steam, reheat, and extraction steam flows along with the final heat rate value.
The document discusses a combined separating and throttling calorimeter, which is used to find the dryness fraction (x) of steam. It measures x using two methods - a separating calorimeter that calculates x1 as the ratio of steam mass to total sample mass, and a throttling calorimeter that uses enthalpy calculations before and after throttling to find x2. The overall dryness fraction x is calculated as the product of x1 and x2.
This document provides information about various air standard cycles used in internal combustion engines, including the Otto, Diesel, and Dual cycles. It defines the key processes and equations for each cycle. The Otto cycle involves four processes: isentropic compression, constant volume heat addition, isentropic expansion, and constant volume heat rejection. The Diesel cycle involves: isentropic compression, constant pressure heat addition, isentropic expansion, and constant volume heat rejection. The Dual cycle combines aspects of the Otto and Diesel cycles, involving five processes. Thermodynamic relationships between pressure, volume, temperature and other variables are defined through equations for each cycle.
This document summarizes different types of fans and blowers used to move air or gas. It describes axial and centrifugal fans that move air parallel or perpendicular to the fan shaft. Common fan applications include ventilation, cooling towers, and industrial processes. The document also covers blower types, compression equations, efficiency calculations, performance relationships, and laws governing how fan characteristics change with speed, size, and density.
A cooling tower cools water by evaporating a portion of the water as it is exposed to air circulating through the tower. Hot water enters the top of the tower and is cooled as it falls through fillings, exposing new surfaces to the air. Cooled water exits the bottom while moist air exits from the top after partially saturating with evaporated water. The document provides equations for calculating cooling tower performance parameters like actual cooling range, approach, efficiency, enthalpy, humidity ratio, and mass and energy balances.
This document provides information on refrigeration including:
1. Refrigeration is defined as the process of cooling a substance below the temperature of its surroundings. Major uses include air conditioning, food preservation, and industrial processes.
2. A ton of refrigeration is defined as the heat required to melt 1 ton of ice at 0°C in 24 hours.
3. The Carnot refrigeration cycle consists of heat addition, heat rejection, expansion, and compression processes between a high and low temperature.
4. A vapor compression cycle uses a compressor, condenser, expansion valve, and evaporator to circulate refrigerant between high and low pressures and temperatures.
5. Cascade systems combine two vapor compression units
This document contains solved problems from chapter 12 on positive displacement machines. Problem 12.1 calculates the indicated power and delivery temperature for air compression in a single-stage reciprocating compressor under isentropic, isothermal and polytropic processes. Problem 12.2 calculates the bore size required for the compressor running at 1000 rpm with a stroke to bore ratio of 1.2:1. Problem 12.3 calculates various parameters like bore, stroke, volumetric efficiency and indicated power for a single-stage single-acting air compressor running at 1000 rpm.
This document contains equations and rules of thumb for HVAC systems. It includes equations for cooling and heating load calculations, ductwork sizing, fan and pump laws, expansion tank sizing, air balancing, efficiencies, cooling towers, moisture condensation, and electricity. The equations are presented along with brief explanations of the variables.
This document provides procedures for conducting a Gross Turbine Cycle Heat Rate (GTCHR) test on a steam turbine. The test is used to measure the overall efficiency of the turbine cycle and its auxiliaries. Key steps include operating the unit at a steady load and temperature conditions, collecting instrumentation data like steam and water temperatures and pressures, and calculating the turbine cycle heat rate in kcal/kWh based on enthalpy values and steam and water flows. The test report includes computation of main steam, reheat, and extraction steam flows along with the final heat rate value.
The document discusses a combined separating and throttling calorimeter, which is used to find the dryness fraction (x) of steam. It measures x using two methods - a separating calorimeter that calculates x1 as the ratio of steam mass to total sample mass, and a throttling calorimeter that uses enthalpy calculations before and after throttling to find x2. The overall dryness fraction x is calculated as the product of x1 and x2.
This document contains solutions to multiple problems involving gas turbine cycles. Problem 9.1 involves calculating the power output, efficiency and work ratio of a gas turbine with given specifications. Problem 9.2 calculates the pressure between turbine stages, efficiency and shaft power of a marine gas turbine. Problem 9.3 calculates the efficiency of the turbine from Problem 9.2 when a heat exchanger is added. Problem 9.4 involves a more complex cycle with two compression stages, intercooling, reheat and heat exchange, calculating power output and overall efficiency. Problem 9.5 presents another gas turbine problem without showing the full solution.
Compressors raise the pressure of a flowing fluid by mechanical work. There are two main types: reciprocating for high pressure/low flow, and rotative for low pressure/high flow. Compressed air has many industrial applications. Compressor performance is evaluated based on factors like motor efficiency, mechanical efficiency, compression efficiency, volumetric efficiency, and overall efficiency. Problems involve calculating mass flow rate, power requirements, and other parameters for given compressor specifications and operating conditions.
The document contains formulas and information related to HVAC systems. It defines key terms like tons of refrigeration, horsepower, voltage, amperage, resistance, watts, capacitance, gas laws, and geometric formulas. It also includes formulas for calculating areas, volumes, BTUs, airflow, efficiency, and sizing components like ducts, grilles, burners, and nozzles.
This document summarizes an experimental study on the impact of fouling on vapor compression refrigeration systems (VCRS). It describes the test rig setup, which includes thermocouples, a condenser, evaporator, display devices, stirrers, pressure gauges, expansion valve, compressor, and drier. It then provides properties of the refrigerant used, details the actual refrigeration cycle, and discusses various losses in VCRS. Mathematical calculations are shown for system components like the expansion valve, evaporator, compressor, and condenser. Graphs illustrate how COP, refrigeration effect, and compressor work vary with parameters like mass flow rate and heat exchanger U-values. The results are then compared to experimental data
Steam exists in different states depending on temperature and pressure. It can be wet steam with water particles, dry saturated steam where all water is vaporized, or superheated steam which is dry steam heated above its saturation temperature. Calorimeters are used to measure the dryness fraction or quality of steam, which indicates the ratio of dry steam to total steam mass. Different types of calorimeters operate by condensing steam and measuring temperature changes, using a throttling valve to reduce pressure and exploit the constant enthalpy principle, or combining separating and throttling methods for improved accuracy.
The document discusses performance assessment of compressors through field testing. It describes methods to measure free air delivery, isothermal power, volumetric efficiency and specific power requirement. The nozzle method and pump up method are explained to measure free air delivery. Calculations are provided as examples to determine isothermal efficiency and specific power consumption. Periodic performance assessment is important to minimize compressed air costs and improve system efficiencies.
This document provides an introduction to heat transfer in food processing. It discusses calculating convective heat transfer coefficients, estimating overall heat transfer coefficients, and designing tubular heat exchangers. Key equations are presented for calculating heat transfer areas needed based on process conditions like inlet/outlet temperatures and flow rates of fluids in countercurrent and parallel flow configurations. An example problem applies these concepts and calculations to determine exit temperatures, heat transfer rates, and length of tubing needed.
The document discusses various air standard cycles that are used to model internal combustion engine processes, including the Otto, Diesel, and dual cycles. It provides details on the assumptions and thermodynamic processes that define each cycle. The Otto cycle consists of four processes: constant-pressure intake, isentropic compression, constant-volume combustion, and isentropic expansion. The Diesel cycle models combustion as a constant-pressure process rather than constant volume. The dual cycle models combustion as both constant-volume and constant-pressure processes. Comparisons are made between the cycles in terms of their heat transfer and thermal efficiencies.
Applied thermodynamics by mc conkey (ed 5, ch-12)anasimdad007
A reciprocating compressor takes in a gas and delivers it at a higher pressure through the cyclic action of pistons in cylinders. There are two main types - single-acting and double-acting. The compression process can follow different thermodynamic paths like isothermal, polytropic, or isentropic on a pressure-volume or temperature-entropy diagram. Isothermal compression provides the minimum work and highest efficiency. The indicated power and efficiency of a reciprocating compressor depends on parameters like mass flow rate, inlet and outlet pressures and temperatures, and the compression process path.
This document provides guidance on computing safe purge rates for flare stacks and blowdown stacks in refineries. It presents an equation and experimental data from studies at an American Oil Company refinery. The key findings are:
1) Experiments showed that the product of purge velocity and the height of the stack above a given oxygen concentration level (3-6%) is constant, allowing derivation of an equation to calculate safe purge rates.
2) The equation was simplified to a graphical method, with safe purge rates plotted based on stack diameter and purge gas molecular weight.
3) Minimum safe purge rates for flare stacks were found to produce a barely-visible flame, and for blowdown stacks to maintain less than 6%
This document outlines calculations for a mechanical smoke ventilation system for a basement floor with a store. It determines the heat release rate and smoke mass flow rate based on the fire area and assumptions. It then calculates the required air flow rate, duct size, and fan specifications. The system will include two exhaust fans of 18,500 CFM each and two fresh air intake fans of 10,500 CFM each, all located on the roof. The ducts will be sized to accommodate the required air flow rates. The entrance areas are determined to provide sufficient fresh air intake.
This document contains problems from board exams on dryers. The first problem asks to calculate: (1) the required flow of heated air mixture to dry cassava flour, (2) the capacity of the forced draft fan on the dryer, (3) the heat required for heating the air mixture, and (4) the percentage of fresh air in the mixture. The second problem asks to calculate various properties of air before and after passing through an adiabatic drier. The third problem asks to calculate: (a) the required amount of air and (b) the fan capacity to handle the air for drying sand in a dryer.
This document discusses the Diesel and Brayton thermodynamic cycles. It provides details on:
- The history and development of the Diesel cycle, invented by Rudolf Diesel in 1893, including its use of compression ignition and the differences from the Otto cycle.
- The thermodynamic processes that characterize the Diesel cycle and how it has evolved from early constant pressure combustion to the modern dual cycle with both constant pressure and volume combustion.
- The Brayton cycle, introduced in 1872, which uses separate compression and expansion cylinders and constant combustion.
- The ideal processes that make up the Brayton cycle and how to analyze it thermally using pressure and temperature ratios along with the concepts of back
Passivhaus Compendium for Exam and Daily UseAndré Harrmann
The document can be purchased from:
www.15kwh10w.com/passive-house-tools
Harrmann Consulting compiled all relevant Passive House formulas and related information on a few pages. These cheat sheets are handy for Passive House exam preparation and very useful for the day of the exam.
They are also valuable for quick consultation when working on Passive House projects.
References are made throughout the document to the Passive House Planning Package (PHPP Version 8, 2013, metric and imperial) – making the compendium an indispensable tool for every Passive House Consultant.
NOTE: The compendium is being further developed -- suggestions for improvements are welcome -- the extracted pages might not represent the latest version.
HOT TOPIC
TON OF REFRIGERATION,
WORK, U FACTOR, LRA (Locked rotor amps)
RPM of motor, HEAT FORMULA, GAS PIPING (Sizing – CF/hr.), CALCULATING OIL NOZZLE SIZE (GPH):
PYTHAGOREAN THEOREM, Linear Measurement Equivalents (U.S. Conventional - SI Metric)
This document contains solutions to multiple problems related to nozzles and jet propulsion. Problem 10.8 asks the reader to calculate the required nozzle exit area, net thrust developed, air-fuel ratio, and specific fuel consumption for a turbojet aircraft given various parameters such as air mass flow rate, compressor pressure ratio, maximum cycle temperature, efficiencies, and fuel calorific value. Diagrams are provided to illustrate the problem.
This document contains solved problems from Chapter 12 on positive displacement machines. Problem 12.1 calculates the indicated power and delivery temperature for air compression in a single-stage reciprocating compressor under isentropic, isothermal, and polytropic processes. Problem 12.2 calculates the bore size required for the compressor from Problem 12.1 running at 1000 rpm. Problem 12.3 calculates bore size, stroke, volumetric efficiency, indicated power, and isothermal efficiency for a single-stage single-acting air compressor.
IRJET- Enhancement of COP of Vapor Compression Refrigeration Cycle using CFDIRJET Journal
This document discusses enhancing the coefficient of performance (COP) of a vapor compression refrigeration cycle using computational fluid dynamics (CFD).
It presents a study that uses a diffuser between the compressor and condenser to reduce the kinetic energy of the refrigerant leaving the compressor. This lowers the power input to the compressor, thereby improving the COP. Experimental results found adding a 15 degree divergence angle diffuser increased the COP from 3.83 to 5.55, a 31% enhancement.
The experimental results are validated using CFD modeling and analysis software. Modeling and meshing is done in ICEMCFD, analysis in CFX, and post-processing in CFD POST to verify the COP improvement
The document discusses the performance calculation of a gas turbine. It provides definitions of gas turbine performance, assumptions made in the ideal gas turbine cycle calculations, and equations used. It then lists input parameters such as temperatures, pressures, and flows. The calculations determine values like isentropic temperatures and enthalpies. Performance metrics of the compressor, combustion chamber, and turbine are calculated, such as works, efficiencies, heat rates, and fuel consumption. The summary provides the overall performance results including shaft work, thermal efficiency, fuel consumption rate, and plant efficiency.
This document provides formulas and equations for calculating rates, pressures, volumes, densities, and other parameters related to hydraulic fracturing operations. Some key points:
1. Formulas are provided for calculating maximum frac rate, line volume, fluid gradient, bottomhole pressure, frac gradient, horsepower requirements, and other fracturing parameters.
2. Equations are outlined for calculating parameters related to blender operations like clean water weight, sand volumes, slurry volumes, densities, and screw speeds.
3. Pump math formulas define relationships for determining pump capacities based on fluid end geometry, transmission ratios, engine speeds, and other factors.
This document provides formulas and explanations for calculating frac job parameters such as fluid rates, pressures, horsepower requirements, and blender equations. Key points include:
1. Formulas are given for calculating maximum frac rate, line volume, fluid gradient, bottomhole pressure, frac gradient, horsepower, and pipe time.
2. Modes of monitoring bottomhole pressure during fracturing are described.
3. Equations are outlined for calculating parameters related to blender operations like fluid and proppant volumes and densities.
4. Pump math formulas are defined for calculating fluid volumes per revolution and maximum pump rates based on engine speeds and transmission gear ratios.
5. Steps for bucket testing chemical pumps to validate
This document contains solutions to multiple problems involving gas turbine cycles. Problem 9.1 involves calculating the power output, efficiency and work ratio of a gas turbine with given specifications. Problem 9.2 calculates the pressure between turbine stages, efficiency and shaft power of a marine gas turbine. Problem 9.3 calculates the efficiency of the turbine from Problem 9.2 when a heat exchanger is added. Problem 9.4 involves a more complex cycle with two compression stages, intercooling, reheat and heat exchange, calculating power output and overall efficiency. Problem 9.5 presents another gas turbine problem without showing the full solution.
Compressors raise the pressure of a flowing fluid by mechanical work. There are two main types: reciprocating for high pressure/low flow, and rotative for low pressure/high flow. Compressed air has many industrial applications. Compressor performance is evaluated based on factors like motor efficiency, mechanical efficiency, compression efficiency, volumetric efficiency, and overall efficiency. Problems involve calculating mass flow rate, power requirements, and other parameters for given compressor specifications and operating conditions.
The document contains formulas and information related to HVAC systems. It defines key terms like tons of refrigeration, horsepower, voltage, amperage, resistance, watts, capacitance, gas laws, and geometric formulas. It also includes formulas for calculating areas, volumes, BTUs, airflow, efficiency, and sizing components like ducts, grilles, burners, and nozzles.
This document summarizes an experimental study on the impact of fouling on vapor compression refrigeration systems (VCRS). It describes the test rig setup, which includes thermocouples, a condenser, evaporator, display devices, stirrers, pressure gauges, expansion valve, compressor, and drier. It then provides properties of the refrigerant used, details the actual refrigeration cycle, and discusses various losses in VCRS. Mathematical calculations are shown for system components like the expansion valve, evaporator, compressor, and condenser. Graphs illustrate how COP, refrigeration effect, and compressor work vary with parameters like mass flow rate and heat exchanger U-values. The results are then compared to experimental data
Steam exists in different states depending on temperature and pressure. It can be wet steam with water particles, dry saturated steam where all water is vaporized, or superheated steam which is dry steam heated above its saturation temperature. Calorimeters are used to measure the dryness fraction or quality of steam, which indicates the ratio of dry steam to total steam mass. Different types of calorimeters operate by condensing steam and measuring temperature changes, using a throttling valve to reduce pressure and exploit the constant enthalpy principle, or combining separating and throttling methods for improved accuracy.
The document discusses performance assessment of compressors through field testing. It describes methods to measure free air delivery, isothermal power, volumetric efficiency and specific power requirement. The nozzle method and pump up method are explained to measure free air delivery. Calculations are provided as examples to determine isothermal efficiency and specific power consumption. Periodic performance assessment is important to minimize compressed air costs and improve system efficiencies.
This document provides an introduction to heat transfer in food processing. It discusses calculating convective heat transfer coefficients, estimating overall heat transfer coefficients, and designing tubular heat exchangers. Key equations are presented for calculating heat transfer areas needed based on process conditions like inlet/outlet temperatures and flow rates of fluids in countercurrent and parallel flow configurations. An example problem applies these concepts and calculations to determine exit temperatures, heat transfer rates, and length of tubing needed.
The document discusses various air standard cycles that are used to model internal combustion engine processes, including the Otto, Diesel, and dual cycles. It provides details on the assumptions and thermodynamic processes that define each cycle. The Otto cycle consists of four processes: constant-pressure intake, isentropic compression, constant-volume combustion, and isentropic expansion. The Diesel cycle models combustion as a constant-pressure process rather than constant volume. The dual cycle models combustion as both constant-volume and constant-pressure processes. Comparisons are made between the cycles in terms of their heat transfer and thermal efficiencies.
Applied thermodynamics by mc conkey (ed 5, ch-12)anasimdad007
A reciprocating compressor takes in a gas and delivers it at a higher pressure through the cyclic action of pistons in cylinders. There are two main types - single-acting and double-acting. The compression process can follow different thermodynamic paths like isothermal, polytropic, or isentropic on a pressure-volume or temperature-entropy diagram. Isothermal compression provides the minimum work and highest efficiency. The indicated power and efficiency of a reciprocating compressor depends on parameters like mass flow rate, inlet and outlet pressures and temperatures, and the compression process path.
This document provides guidance on computing safe purge rates for flare stacks and blowdown stacks in refineries. It presents an equation and experimental data from studies at an American Oil Company refinery. The key findings are:
1) Experiments showed that the product of purge velocity and the height of the stack above a given oxygen concentration level (3-6%) is constant, allowing derivation of an equation to calculate safe purge rates.
2) The equation was simplified to a graphical method, with safe purge rates plotted based on stack diameter and purge gas molecular weight.
3) Minimum safe purge rates for flare stacks were found to produce a barely-visible flame, and for blowdown stacks to maintain less than 6%
This document outlines calculations for a mechanical smoke ventilation system for a basement floor with a store. It determines the heat release rate and smoke mass flow rate based on the fire area and assumptions. It then calculates the required air flow rate, duct size, and fan specifications. The system will include two exhaust fans of 18,500 CFM each and two fresh air intake fans of 10,500 CFM each, all located on the roof. The ducts will be sized to accommodate the required air flow rates. The entrance areas are determined to provide sufficient fresh air intake.
This document contains problems from board exams on dryers. The first problem asks to calculate: (1) the required flow of heated air mixture to dry cassava flour, (2) the capacity of the forced draft fan on the dryer, (3) the heat required for heating the air mixture, and (4) the percentage of fresh air in the mixture. The second problem asks to calculate various properties of air before and after passing through an adiabatic drier. The third problem asks to calculate: (a) the required amount of air and (b) the fan capacity to handle the air for drying sand in a dryer.
This document discusses the Diesel and Brayton thermodynamic cycles. It provides details on:
- The history and development of the Diesel cycle, invented by Rudolf Diesel in 1893, including its use of compression ignition and the differences from the Otto cycle.
- The thermodynamic processes that characterize the Diesel cycle and how it has evolved from early constant pressure combustion to the modern dual cycle with both constant pressure and volume combustion.
- The Brayton cycle, introduced in 1872, which uses separate compression and expansion cylinders and constant combustion.
- The ideal processes that make up the Brayton cycle and how to analyze it thermally using pressure and temperature ratios along with the concepts of back
Passivhaus Compendium for Exam and Daily UseAndré Harrmann
The document can be purchased from:
www.15kwh10w.com/passive-house-tools
Harrmann Consulting compiled all relevant Passive House formulas and related information on a few pages. These cheat sheets are handy for Passive House exam preparation and very useful for the day of the exam.
They are also valuable for quick consultation when working on Passive House projects.
References are made throughout the document to the Passive House Planning Package (PHPP Version 8, 2013, metric and imperial) – making the compendium an indispensable tool for every Passive House Consultant.
NOTE: The compendium is being further developed -- suggestions for improvements are welcome -- the extracted pages might not represent the latest version.
HOT TOPIC
TON OF REFRIGERATION,
WORK, U FACTOR, LRA (Locked rotor amps)
RPM of motor, HEAT FORMULA, GAS PIPING (Sizing – CF/hr.), CALCULATING OIL NOZZLE SIZE (GPH):
PYTHAGOREAN THEOREM, Linear Measurement Equivalents (U.S. Conventional - SI Metric)
This document contains solutions to multiple problems related to nozzles and jet propulsion. Problem 10.8 asks the reader to calculate the required nozzle exit area, net thrust developed, air-fuel ratio, and specific fuel consumption for a turbojet aircraft given various parameters such as air mass flow rate, compressor pressure ratio, maximum cycle temperature, efficiencies, and fuel calorific value. Diagrams are provided to illustrate the problem.
This document contains solved problems from Chapter 12 on positive displacement machines. Problem 12.1 calculates the indicated power and delivery temperature for air compression in a single-stage reciprocating compressor under isentropic, isothermal, and polytropic processes. Problem 12.2 calculates the bore size required for the compressor from Problem 12.1 running at 1000 rpm. Problem 12.3 calculates bore size, stroke, volumetric efficiency, indicated power, and isothermal efficiency for a single-stage single-acting air compressor.
IRJET- Enhancement of COP of Vapor Compression Refrigeration Cycle using CFDIRJET Journal
This document discusses enhancing the coefficient of performance (COP) of a vapor compression refrigeration cycle using computational fluid dynamics (CFD).
It presents a study that uses a diffuser between the compressor and condenser to reduce the kinetic energy of the refrigerant leaving the compressor. This lowers the power input to the compressor, thereby improving the COP. Experimental results found adding a 15 degree divergence angle diffuser increased the COP from 3.83 to 5.55, a 31% enhancement.
The experimental results are validated using CFD modeling and analysis software. Modeling and meshing is done in ICEMCFD, analysis in CFX, and post-processing in CFD POST to verify the COP improvement
The document discusses the performance calculation of a gas turbine. It provides definitions of gas turbine performance, assumptions made in the ideal gas turbine cycle calculations, and equations used. It then lists input parameters such as temperatures, pressures, and flows. The calculations determine values like isentropic temperatures and enthalpies. Performance metrics of the compressor, combustion chamber, and turbine are calculated, such as works, efficiencies, heat rates, and fuel consumption. The summary provides the overall performance results including shaft work, thermal efficiency, fuel consumption rate, and plant efficiency.
This document provides formulas and equations for calculating rates, pressures, volumes, densities, and other parameters related to hydraulic fracturing operations. Some key points:
1. Formulas are provided for calculating maximum frac rate, line volume, fluid gradient, bottomhole pressure, frac gradient, horsepower requirements, and other fracturing parameters.
2. Equations are outlined for calculating parameters related to blender operations like clean water weight, sand volumes, slurry volumes, densities, and screw speeds.
3. Pump math formulas define relationships for determining pump capacities based on fluid end geometry, transmission ratios, engine speeds, and other factors.
This document provides formulas and explanations for calculating frac job parameters such as fluid rates, pressures, horsepower requirements, and blender equations. Key points include:
1. Formulas are given for calculating maximum frac rate, line volume, fluid gradient, bottomhole pressure, frac gradient, horsepower, and pipe time.
2. Modes of monitoring bottomhole pressure during fracturing are described.
3. Equations are outlined for calculating parameters related to blender operations like fluid and proppant volumes and densities.
4. Pump math formulas are defined for calculating fluid volumes per revolution and maximum pump rates based on engine speeds and transmission gear ratios.
5. Steps for bucket testing chemical pumps to validate
The document provides formulas for fluid power, pumps, actuators, thermal properties, accumulators, and volume/capacity equivalents. Key formulas include:
- Fluid pressure (P) equals force (F) divided by area (A).
- Fluid flow rate (Q) equals volume (V) divided by time (T).
- Pump outlet flow equals rpm multiplied by pump displacement divided by 231.
- Cylinder force equals pressure multiplied by net cylinder area.
- Reservoir cooling capacity equals 2 times the temperature difference between reservoir walls and air multiplied by reservoir area.
This document discusses the assumptions and equations used in air-standard cycle analysis of internal combustion engines. It covers:
- The assumptions of the ideal air-standard cycle, including constant specific heats, reversible processes, and no combustion.
- The relevant thermodynamic equations for analyzing the Otto cycle of intake, compression, combustion, expansion, exhaust.
- How real engine cycles differ from the ideal cycle assumptions due to varying composition and properties during combustion, finite combustion duration, valve overlap effects.
- How to account for pump work from intake/exhaust pressures and residual exhaust gases in the clearance volume.
The document provides formulas and definitions for various HVAC concepts. Some key formulas include: the ton of refrigeration which is equal to 288,000 BTU/24 hr or 12,000 BTU/hr; one horsepower equals 33,000 ft-lb of work in one minute or 746 Watts; converting between BTUs, KWs and Watts for heating and cooling equipment. Common gas laws and formulas for area, perimeter, volume and capacitance are also listed.
This document outlines the lecture topics for an internal combustion engine and turbomachinery course. It includes the class policies, a weekly lecture outline, and introductions to key concepts like the Otto cycle, diesel cycle, gas turbines, and turbomachinery terminology. The lecture outline covers topics such as thermodynamic cycles, engine classifications, component design, and performance prediction. Definitions and diagrams are provided for critical turbomachinery elements like stages, velocity diagrams, and flow configurations. Challenges like compressor stall and surge are also discussed.
The document discusses various scenarios that could lead to overpressure in vessels and equipment and the procedures to calculate the size of pressure safety valves (PSVs) to prevent overpressure. It describes scenarios like closed outlets, external fires, failure of automatic controls, hydraulic expansion, heat exchanger tube ruptures, power failures, and more. It provides methods to calculate the relief rates needed for PSVs using equations, charts, and procedures outlined in design codes like ASME and API standards. The goal is to size PSVs correctly to ensure accumulated pressure stays below the maximum allowable to maintain safety.
This document discusses different types of hydraulic pumps, including their basic operating principles and comparisons. It provides equations to calculate pump parameters such as theoretical flow rate, volumetric displacement, efficiency, and torque. For example, it defines that positive displacement pumps capture and transfer fixed amounts of fluid, while centrifugal pumps impart velocity to fluid to create pressure. Gear pump displacement can be calculated based on gear dimensions. Pump efficiency is affected by factors like leakage and viscosity.
1. The document discusses procedures for calculating pressure safety valve (PSV) sizes for various scenarios that could lead to overpressure. It covers scenarios like closed outlets, external fires, control valve failures, hydraulic expansion, heat exchanger tube ruptures, and power or cooling failures.
2. Calculation methods include enthalpy balances for fractionating columns and the use of relief equations specified in codes like API 521. Worst cases are chosen from all possible scenarios to determine the required PSV size.
3. Key scenarios discussed in detail include closed outlets on vessels, external fires, failures of automatic controls, hydraulic expansion, heat exchanger tube ruptures, total and partial power failures, reflux losses,
Refrigeration is the process of cooling a substance below the temperature of its surroundings. Major uses include air conditioning, food preservation, and industrial processes. A ton of refrigeration is the heat required to melt 1 ton of ice in 24 hours. The Carnot refrigeration cycle involves heat addition, heat rejection, and net work to transfer heat from a low temperature reservoir to a high temperature reservoir. The vapor compression cycle uses the same processes as the Carnot cycle and is commonly used in refrigeration systems. It involves compression, condensation, expansion, and evaporation. Refrigerants are circulated through the system's main components: compressor, condenser, expansion valve, and evaporator. Multi-pressure and cascade systems
Centrifugal compressors are considered as a subclass of dynamic turbo machinery. They achieve
the pressure increase by adding kinetic energy to a
continuous flow of fluid. This kinetic energy is
converted to an increase in pressure in the diffuser
where the kinetic energy is converted to pressure
energy by decreasing the gas velocity.
Thermodynamic Cycles for CI engines
- Early CI engines injected fuel at top dead center, resulting in combustion during the expansion stroke. Modern engines inject fuel before top dead center, around 20 degrees.
- The combustion process in early CI engines approximates a constant pressure heat addition process, known as the Diesel cycle. Modern CI engines' combustion approximates a combination of constant volume and constant pressure processes, known as the Dual cycle.
- The air-standard Diesel cycle consists of four processes: isentropic compression, constant pressure heat addition, isentropic expansion, and constant volume heat rejection. Its thermal efficiency is lower than the Otto cycle for the same compression ratio due to the later fuel injection
Improving Gas Turbine – HRSG output using Inlet Air Chilling and Converted Ev...IRJET Journal
This document discusses modifications made to improve the output of a gas turbine-heat recovery steam generator (GT-HRSG) system. The modifications included installing an inlet air chilling system and converting the evaporator section of the HRSG.
The inlet air chilling system cooled the intake air for the gas turbine, allowing it to operate at higher loads while keeping exhaust temperatures low. This provided more flexibility before temperature controls kicked in. Measurements showed the chilled air increased gas turbine mass flow and output.
Supplementary firing in the HRSG was heating the superheater section excessively. To address this, the evaporator section was converted to move the superheater further downstream. This protected the superheater from
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This document discusses various strategies to optimize refrigeration and air conditioning systems to reduce energy consumption and costs. It describes the basic vapor compression refrigeration cycle and how system performance is affected by evaporator and condenser temperatures. Methods to optimize compressor operation include adjusting loading/unloading, variable speed drives, and gas bypass controls. Optimizing cooling water systems, replacing shell and tube condensers with evaporative condensers, and switching to more efficient centrifugal compressors can also improve performance. The document also compares vapor absorption to vapor compression cycles.
The document discusses hydraulic calculations for fire protection systems. Hydraulic calculations ensure piping can deliver enough water to extinguish fires by determining: 1) how much water is needed, 2) if water supply is sufficient, and 3) optimal piping layout and friction losses. Occupancies are classified by fire danger as light, ordinary, or extra hazard. Pipe size calculations and sprinkler coverage are also addressed. Hydraulic calculations use flow rate, pressure, and sprinkler opening relationships to determine pressure and output at each sprinkler and pipe section. A sample calculation is provided to demonstrate the process.
The document provides an overview of different types of reciprocating engine cycles, including definitions of key terms, equations, and efficiency calculations. It describes the ideal Otto, Diesel, and dual combustion cycles. It includes equations to calculate efficiency, temperatures, pressures, work output, and mean effective pressure. It concludes with sample problems to calculate values for each cycle type.
This document discusses performing a heat and mass balance (HMB) study on a cement plant. The objectives are to assess energy consumption, improve thermal efficiency, and identify areas of thermal losses. The study involves defining system boundaries, inputs, outputs, and performing mass balances. A case study on an ABC plant is presented where the overall mass balance was calculated based on measured input and output streams like kiln feed, fuel consumption, cooler vent air, and clinker production. The results can be used to optimize the pyroprocess and thermal energy usage.
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Null Bangalore | Pentesters Approach to AWS IAMDivyanshu
#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
- Gain actionable insights into AWS IAM policies and roles, using hands on approach.
#Prerequisites:
- Basic understanding of AWS services and architecture
- Familiarity with cloud security concepts
- Experience using the AWS Management Console or AWS CLI.
- For hands on lab create account on [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
# Scenario Covered:
- Basics of IAM in AWS
- Implementing IAM Policies with Least Privilege to Manage S3 Bucket
- Objective: Create an S3 bucket with least privilege IAM policy and validate access.
- Steps:
- Create S3 bucket.
- Attach least privilege policy to IAM user.
- Validate access.
- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
- Steps:
- Allow user to pass IAM role to EC2.
- Exploit misconfiguration for unauthorized access.
- Access sensitive resources.
- Exploiting IAM AssumeRole Misconfiguration with Overly Permissive Role
- An overly permissive IAM role configuration can lead to privilege escalation by creating a role with administrative privileges and allow a user to assume this role.
- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
- Steps:
- Create role with administrative privileges.
- Allow user to assume the role.
- Perform administrative actions.
- Differentiation between PassRole vs AssumeRole
Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
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Sinan from the Delivery Hero mobile infrastructure engineering team shares a deep dive into performance acceleration with Gradle build cache optimizations. Sinan shares their journey into solving complex build-cache problems that affect Gradle builds. By understanding the challenges and solutions found in our journey, we aim to demonstrate the possibilities for faster builds. The case study reveals how overlapping outputs and cache misconfigurations led to significant increases in build times, especially as the project scaled up with numerous modules using Paparazzi tests. The journey from diagnosing to defeating cache issues offers invaluable lessons on maintaining cache integrity without sacrificing functionality.
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Supermarket management is a stand-alone J2EE using Eclipse Juno program.
This project contains all the necessary required information about maintaining
the supermarket billing system.
The core idea of this project to minimize the paper work and centralize the
data. Here all the communication is taken in secure manner. That is, in this
application the information will be stored in client itself. For further security the
data base is stored in the back-end oracle and so no intruders can access it.
Software Engineering and Project Management - Software Testing + Agile Method...Prakhyath Rai
Software Testing: A Strategic Approach to Software Testing, Strategic Issues, Test Strategies for Conventional Software, Test Strategies for Object -Oriented Software, Validation Testing, System Testing, The Art of Debugging.
Agile Methodology: Before Agile – Waterfall, Agile Development.
Build the Next Generation of Apps with the Einstein 1 Platform.
Rejoignez Philippe Ozil pour une session de workshops qui vous guidera à travers les détails de la plateforme Einstein 1, l'importance des données pour la création d'applications d'intelligence artificielle et les différents outils et technologies que Salesforce propose pour vous apporter tous les bénéfices de l'IA.
Applications of artificial Intelligence in Mechanical Engineering.pdfAtif Razi
Historically, mechanical engineering has relied heavily on human expertise and empirical methods to solve complex problems. With the introduction of computer-aided design (CAD) and finite element analysis (FEA), the field took its first steps towards digitization. These tools allowed engineers to simulate and analyze mechanical systems with greater accuracy and efficiency. However, the sheer volume of data generated by modern engineering systems and the increasing complexity of these systems have necessitated more advanced analytical tools, paving the way for AI.
AI offers the capability to process vast amounts of data, identify patterns, and make predictions with a level of speed and accuracy unattainable by traditional methods. This has profound implications for mechanical engineering, enabling more efficient design processes, predictive maintenance strategies, and optimized manufacturing operations. AI-driven tools can learn from historical data, adapt to new information, and continuously improve their performance, making them invaluable in tackling the multifaceted challenges of modern mechanical engineering.
Prediction of Electrical Energy Efficiency Using Information on Consumer's Ac...PriyankaKilaniya
Energy efficiency has been important since the latter part of the last century. The main object of this survey is to determine the energy efficiency knowledge among consumers. Two separate districts in Bangladesh are selected to conduct the survey on households and showrooms about the energy and seller also. The survey uses the data to find some regression equations from which it is easy to predict energy efficiency knowledge. The data is analyzed and calculated based on five important criteria. The initial target was to find some factors that help predict a person's energy efficiency knowledge. From the survey, it is found that the energy efficiency awareness among the people of our country is very low. Relationships between household energy use behaviors are estimated using a unique dataset of about 40 households and 20 showrooms in Bangladesh's Chapainawabganj and Bagerhat districts. Knowledge of energy consumption and energy efficiency technology options is found to be associated with household use of energy conservation practices. Household characteristics also influence household energy use behavior. Younger household cohorts are more likely to adopt energy-efficient technologies and energy conservation practices and place primary importance on energy saving for environmental reasons. Education also influences attitudes toward energy conservation in Bangladesh. Low-education households indicate they primarily save electricity for the environment while high-education households indicate they are motivated by environmental concerns.
1. Fluid Power Formula
These Formula Cover All Fluid Power Applications
In This Manual
For Computer Programs To Work Problems
By Simply Filling In The Blanks
See
Your Local Fluid Power Distributor
Many Companies Web Site Or CD
Also See
The Fluid Power Data Book
Packaged With This Manual
For Charts and Other Fluid Power Information
2.
3. Fluid Power Formula
1
Miscellaneous Fluid Power Formula
Fluid Pressure= Force (Pounds)
Unit Area (in2
)
Velocity Through Pipes in Feet/Second (FPS)= 0.320833 x GPM (Flow Through Conduit)
Internal Area of Conduit (in2
)
Extra Hydraulic Oil Required to Fill a Volume (in3
)= PSI x Volume (in3
)
250,000 Based on ½ of 1%/1,000 PSI
Compressibility of a Fluid= 1
Bulk Modulus of the Fluid
Specific Gravity of a Fluid= Weight of 1 ft3
of the Fluid
Weight of 1 ft3
of Water
Orifice Flow
Pressure Drop (∆P) Across an Orifice= (Flow in GPM (Q) x SG)2
Cd= Orifice Coefficient
29.81 x d2
x ∆P From 0.61-0.98 According to
Orifice Length and Shape.
0.65 is a Nominal Figure
Flow GPM (Q) Across an Orifice= 29.81 x Cd x d2
∆P
SG SG= Specific Gravity
Range .87-.90 For Hyd. Oil
Diameter of an Orifice d2
= Flow in GPM (Q) x SG .88 is a Nominal Figure
29.81 x Cd x ∆P
Circle Formula:
Circumference of a Circle= πD2
(3.1416 x Diameter Squared)
Area of a Circle (in2
)= π r2
(3.1416 x radius2
) OR π D2
OR .7854 D2
4
Volume Formula:
Volume (in3
) of Round Object= Area (in2
) x Length
Volume of Square or Rectangular Object= Length x Width x Depth
Tube Burst Calculations:
Barlow Formula =
2ST
p
D
p= Burst Pressure PSI
S= Ultimate Strength of Tube Material, PSI
T= Nominal Wall Thickness, Inches
D= Nominal OD of Tubing, Inches
Boyles Law:
=1 1 2 2P V P V P1= Pressure 1 Absolute. (Gauge Pressure Plus 14.7)
2 2
1
1
P V
P
V
= P2= Pressure 2 Absolute. (Gauge Pressure Plus 14.7)
1 1
2
2
P V
P
V
= V1= Actual Gas Volume at Pressure 1
2 2
1
1
P V
V
P
= V2= Actual Gas Volume at Pressure 2
1 1
2
2
P V
V
P
=
4. Fluid Power Formula
2
Miscellaneous Fluid Power Formula (Cont’d.
Charles Law:
=1 2 2 1T V T V T1= Absolute Temperature of Gas at Volume 1 (Temp. F + 459.7)
2 1
1
2
T V
T
V
= T2= Absolute Temperature of Gas at Volume 2 (Temp. F + 459.7)
V1= Volume of Gas at Temperature 1
1 2
2
1
T V
T
V
= V2= Volume of Gas at Temperature 2
1 2
1
2
T V
V
T
=
2 1
2
1
T V
V
T
=
General Gas Law:
1 1 2 2
1 2
P V P V
T T
= P1= Pressure 1 Absolute. (Gauge Pressure Plus 14.7)
P2= Pressure 2 Absolute. (Gauge Pressure Plus 14.7)
2 2 1
1
2 1
P V T
P
T V
= V1= Actual Gas Volume at Pressure 1
V2= Actual Gas Volume at Pressure 2
1 1 2
2
1 2
P V T
P
T V
= T1= Absolute Temperature of Gas at Volume 1(Temp. F + 459.7)
T2= Absolute Temperature of Gas at Volume 2(Temp. F + 459.7)
2 2 1
1
2 1
P V T
V
T P
=
1 1 2
2
1 2
P V T
V
T P
=
2 2
1
1 1 2
P V
T
P V T
=
1 1
2
2 2 1
P V
T
P V T
=
Flow Velocity In Hydraulic Lines:
Suction Line Low Pressure 2-4 Feet/Second
Return Lines Low Pressure 10-15 Feet/Second
Medium Pressure Lines 500-3,000 PSI 15-20 Feet/Second
High Pressure Lines 3,000 PSI up 25-30 Feet/Second
Air-Oil Systems All Pressures 2-4 Feet/Second
Work (in-lbs)= Force (Pounds) x Distance (Inches) (Feet) (Inches) gives Inch Pounds
(ft-lbs) (Feet) gives Foot Pounds
5. Fluid Power Formula
3
Cylinder Formula
Cylinder Force:
Cap End Area (A) = Bore Diameter Squared x 0.7854 (0.7854D2
)
Net Rod End Area = Bore Diameter Squared x 0.7854 Minus Rod Diameter Squared x 0.7854
(0.7854 D2
Bore – 0.7854 D2
Rod)
Force Extend = Cap End Area x PSI
Force Extend Regeneration = Rod Area x PSI
Force Retract = Net Rod End Area x PSI
Note: Always size an air cylinder at least 25% above load balance or work force to get nominal speed
and/or nominal force buildup time.
For fast speed and fast work force buildup time size them up to 100% above load balance.
(More than 100% above load balance gives negligible added cylinder speed.)
Size hydraulic cylinders at least 10% above load balance or work force to get full speed at full
force and/or nominal force buildup time.
Cylinder Speed:
Gallons per Inch (GPI) = A (Area)
231 (in3
/Gallon)
Inches per Minute (IPM) = Stroke Length x 60 (Seconds)
Stroke Time (Seconds)
Inches per Second (IPS) = Stroke Length
Stroke Time (Seconds)
Flow at Speed GPM = GPI x IPM
IPM = GPM/GPI
GPI = GPM/IPM
Also: GPM = A (Area) x Stroke Length x 60 (Seconds)
Stroke Time (Seconds) x 231 (in3
/Gallon)
A (Area) = Stroke Time (Seconds) x 231 (in3
/Gallon) x GPM
Stroke Length x 60 (Seconds
Stroke Length = Stroke Time (Seconds) x 231 (in3
/Gallon) x GPM
A (Area) x 60 (Seconds)
Stroke Time = A (Area) x Stroke Length x 60 (Seconds)
GPM x 231 (in3
/Gallon)
Cylinder Rod End Intensification:
Single Rod End Cylinders = Cylinder Bore A (Area)
Cylinder Net Rod End A (Area)
Double Rod End Cylinders = Net Rod End A (Area) of Large Rod
Net Rod End A (Area) of Small Rod
Cylinder Load Induced Pressure:
Vertical Rod Down Cylinder = Load in Pounds
Net Rod End A (Area)
Vertical Rod Up Cylinder = Load in Pounds
Bore A (Area)
6. Fluid Power Formula
4
Fluid Motor Formula
Hydraulic Motors
Torque, Horsepower, Speed Relations
HP x 63,025
Torque (lb. in.)=
2π
For lb-ft use 5,252 Constant in Place of 63,025
Torque (lb. in .)= PSI x Displacement (in3
/Revolution)
2 π
Torque (lb. in.)= GPM x PSI x 36.77 For more accurate answer use
RPM 36.77071 in place of 36.77
Torque (lb. in.)= Motor Displacement (in3
/Revolution)
0.0628
Rule of Thumb: 1 CIR = 16 lb. In. @ 100 PSI
Horsepower = Torque (lb-in) x RPM For Newton Meters Divide Answers
63,025 lb-in by 8.851
RPM = Horsepower x 63,025 lb-ft. by 0.7375
Torque
Flow Formula:
Flow Rate at 100% Efficiency:
3
3
RPM x CIR (in / Revolution Displacement)
Q (Flow GPM)=
231 (in /Gallon)
Multiply the answer by the manufacturers published efficiency percent for actual speed of a new
motor.
Efficiency Formula:
M
Torque Actual
Mechanical Efficiency E =
Torque Theoretical
M
Q (Flow Actual)
Volumetric Efficiency E =
Q (Flow Theoretical)
M
HP Out
Overall Efficiency E =
HP In
Air Motors
Design for maximum torque at approximately half operating air pressure.
Follow manufacturers recommendations for a given motor type for Starting Torque, Maximum
RPM, Maximum Torque and CFM air inlet flow.
Run the air motor only when doing work. Remember an air motor can pull 7-15 compressor HP for each 1
HP output.
7. Fluid Power Formula
5
Hydraulic Pump Formula
Flow Rate:
Flow Rate at 100% Efficiency:
3
3
RPM x CIR (in / Revolution Displacement)
Q (Flow GPM)=
231 (in /Gallon)
Take Q times manufacturers Overall Efficiency Rating at a given pressure to get actual output.
3
3 Q (Flow GPM) x 231 (in / Gallon)
Pump CIR (in / Revolution Displacement)=
RPM
Horsepower, Torque:
Horsepower to drive a pump @ 100% efficiency HP = GPM x PSI x 0.000583
Horsepower to drive a pump @ 85% efficiency HP = GPM x PSI x 0.000686
Rule of Thumb: 1 GPM @ 1,500 PSI = 1 HP
3
PSI x CIR (in. / RevolutionDisplacement)
Torque (lb. in.)=
2π
(Replace 2π with 24π for lb.ft.)
HP x 63,025
Torque (lb. in.)=
RPM
(Replace 63,025 with 5,252 for lb.ft.)
Efficiency Formula for Pumps:
M
Torque Actual
Mechanical Efficiency E =
Torque Theoretical
Q (Flow Actual)
Volumetric Efficiency Ev=
Q (Flow Theoretical)
OA
HP Out
Overall Efficiency E =
HP In
B10 Bearing Life:
10
Rated Speed (RPM) RatedPressure (PSI)
B Bearing Life (Hours)=Rated Life (Hours) x x
Actual Speed (RPM) Actual Pressure(PSI)
⎛ ⎞ ⎛ ⎞⎟ ⎟⎜ ⎜⎟ ⎟⎜ ⎜⎟ ⎟⎜ ⎜⎟ ⎟⎜ ⎜⎝ ⎠ ⎝ ⎠
Need to Remember Items About Pumps:
Pumps do not make pressure they only make flow. Resistance to flow makes pressure.
Fluid is pushed into a pumps inlet not “sucked.” A pump makes negative pressure at its inlet and
Atmospheric pressure pushes fluid in to fill the void of low pressure.
Where possible mount the pump so its inlet is below fluid level. Install a shutoff valve in the inlet
line to reduce pump repair or replacement time.
In most catalogs Gear and Vane pumps are rated at 1,200 RPM while Piston pumps are rated at
1,800 RPM. Multiply Gear and Vane pumps rated flow by 1.5 to get flow at 1,800 RPM.
Multiply Piston pump flow by 0.6667 to get flow at 1,200 RPM.
For fast priming of a pump in a closed center circuit use an Air Bleed Valve at its outlet. Pipe
the return of the Air Bleed Valve so it terminates below fluid level.
Always fill the case of a pressure compensated pump with hydraulic fluid before startup.
Always pipe Case Drain Flow Lines to terminate below fluid level. When the Case Drain Line
terminates above fluid level poor sealing of the Cylinder Block to the Valve Plate can suck in
bypass fluid faster than it is made and empty the case of lubricating fluid.
8. Fluid Power Formula
6
Thermal Formulas
Heat in a Hydraulic System Generated by Wasted Energy:
Heat (BTU/Hour)=Flow Rate (GPM) x Pressure Drop (PSI)
Heat (BTU/Hour)
Flow Rate (GPM)=
1.485 x Pressure Drop (PSI)
Heat (BTU/Hour)
Pr essure Drop (PSI)=
Flow Rate (GPM x 1.485)
Kilowatts Required to Heat Hydraulic Oil:
Tank Capacity Gallons x (Desired Min. Fluid Temp. F- Min. Ambient Temp. F)
KW
800 x Allowable Time in Hours
=
° °
Note: Allow at least one hour and up to three hours for heating from minimum temperature.
To only maintain heat, reduce the KW rating by 1/2 –2/3rds
in relation to the time in hours
allotted.
Cooling Capacity of a Hydraulic Reservoir at the Poorest Ambient Conditions:
2
HP .001 x (Max. Allowable Fluid Temp. F-Max. Ambient Air Temp. F) x Area in Contact W/Fluid (ft )= ° °
Equivalents
One Horsepower Equals: 1 Bar at Sea Level Equals
746 Watts 14.504 PSI
42.4 BTU/Minute 0.98692 atmospheres
2,545 BTU/Hour 33.6 Ft. Water Column
550 Ft. Lbs/Second 41 Ft Oil Column
33,000 Ft. Lb./Minute
1 PSI Equals
One U.S. Gallon Equals: 2.0416″ Hg
Four Quarts, Eight Pints 27.771″ Water Column
128 Ounces (Liquid) 0.0689 Bar
133.37 Ounces (Weight)
8.3356 Pounds 1 Hg Equals
3.785 Liters 0.490 PSI
231 Cubic Inches 1.131 Ft. Water Column
0.8333 Imperial Gallons
1 Ft. Water Column Equals
One Liter Equals 0.2642 U.S. Gallons 0.432 PSI
1 Atmosphere at Sea Level Equals 1 Ft. Oil Column Equals
1.013 Bar 0.354 PSI
29.291″ Hg
14.696 PSI
760 mm Hg
Atmosphere Decreases Approximately ½ PSI/1,000 Feet of Elevation
9. Fluid Power Formula
7
Accumulator Formula
General Rules for Sizing and Applying Accumulators:
Use dry nitrogen to pre-charge an accumulator. Other gasses may have ample pressure but can be a
safety or explosion hazard.
Use a pre-charge pressure of 85-90% of minimum system pressure. This keeps some fluid in the
accumulator at all times and keeps the bladder or piston from bottoming out during normal
operation.
When pre-charge pressure is less than 50-60% of maximum pressure use a piston type
accumulator. Bladder type accumulators sustain fast bladder chafing damage below the 50% mark.
Piston type accumulators have no problem with low pre-charge pressure as long as the piston is not
forced to bottom out as the nitrogen is compressed.
Use a bladder type accumulator for short, rapid high pressure pulses such as shock absorbing. A
piston type accumulator in this application can have premature seal failure due to lack of
lubrication.
Use the greatest possible difference in maximum system pressure and minimum working pressure
to reduce accumulator size and/or number.
Check accumulator pre-charge pressure daily on a new installation or replacement for first week of
operation. If pressure is holding, check weekly for three weeks and if pressure is holding check
every three to six months. See Chapter 16 Page 16-5 for a simple non-invasive way to check
pressure.
Always provide a means of automatically and/or manually dumping stored energy in the
accumulator when the system is shut down. Also apply warning signs indicating an accumulator is
present and must be checked for stored fluid, at the operating station, control panel and the
accumulator.
Always use a check valve between the pump and accumulator inlet to stop back flow to the pump
when the circuit is shut down.
10. Fluid Power Formula
8
Accumulator Formula (Cont’d.)
Supplementing Pump Flow:
Solving for accumulator size in Gallons V1= _________Gallons
Information Required:
Minimum pressure required to satisfy circuit needs: P2= __________PSI
Maximum pressure available or allowed: P3= __________PSI
Required cycle time of actuator in seconds AC= __________Seconds
Oil volume capacity to cycle the actuator in Cubic Inches VA= __________in3
Dwell time in seconds when no actuators are moving AD= __________Seconds
Normal system operating temperature in F T= __________Temp. F
Solve for minimum flow rate (FR) from pump in Cubic Inches/Second FR= VA
AD + AC
Solve for minimum pump flow (Q) in Cubic Inches/Second Q= .26 x FR
Solve for total cubic inches of fluid from accumulator Vx Vx= VA (3.85 x Q x AC)
Solve for ratio of Minimum to Maximum pressure (a) a= P3
P2
From Chart 1, page 10 select (n) using this formula for “Average Pressure” P2 + P3
and Normal System Operating Temperature from above. 2
Select a figure for (f) from the Charts on pages 11-13 using (a) and (n) above
Solve for (V1) Accumulator Volume in Gallons V1= (Vx / 231)
.807 x f
Pick out an accumulator or accumulators with an empty capacity equal to or greater than
the answer for V1 above. Pre-charge with dry nitrogen at 85% of P2.
Making up for System Leakage:
Solving for accumulator size in in3
V1_________in3
Information Required:
Minimum pressure required to satisfy circuit needs (P2): P2= __________PSI
Maximum pressure available or allowed (P3): P3= __________PSI
Required cycle time of actuator in seconds (LR) LR= __________in3
/Minute
Length in minutes accumulator must hold pressure (TM) TM= __________Minutes
Solve for:
Solve for ratio of Minimum to Maximum pressure (a) a= P3
P2
Since this application is Isothermal, it is not necessary to
the reference Charts on pages 11-13. (f) is found by f = 1 1
a
Volume of oil required from accumulator (Vx) Vx= LR x TM
Solve for Accumulator Volume in in3
(V1) V1= Vx
.807 x f
Pick out an accumulator or accumulators with an empty capacity equal to or greater than
the answer for V1 above. Pre-charge with dry nitrogen at 85% of P2.
11. Fluid Power Formula
9
Accumulator Formula (Cont’d.)
Emergency Power Supply:
Solving for accumulator size in Gallons V1=_________Gallons
Information Required:
Minimum pressure required to satisfy circuit needs: P2= __________PSI
Maximum pressure available or allowed: P3= __________PSI
Oil volume capacity to cycle the actuators in in3
VA= __________in3
Normal system operating temperature in F T= __________Temp. F
Solve for ratio of Minimum to Maximum pressure (a) a= P3
P2
From Chart 1, page 10 select (n) using this formula for “Average Pressure” P2 + P3
and Normal System Operating Temperature from above. 2
Select a figure for (f) from the Charts on pages 11-13 using (a) and (n) above
Solve for (V1) Accumulator Volume in Gallons V1= (VA / 231)
.807 x f
Pick out an accumulator or accumulators with an empty capacity equal to or greater than
the answer for V1 above. Pre-charge with dry nitrogen at 85% of P2.
Hydraulic Line Shock Control:
Solving for accumulator size in in3
V1= _________in3
Information Required:
Normal system operating pressure (P2): P2= __________PSI
Length of pipe generating the shock measured in feet between
the pump and valve. (L): L= __________Feet
Internal area of pipe in 1n2
(A) A= __________in2
Flow rate of pump in GPM (Q) Q= __________GPM
Normal system operating temperature in F T= __________Temp. F
From Chart 1, page 10 select (n) using P2 for “Average Pressure”
and Normal System Operating Temperature from above. n= __________
Solve for total volume in pipe (TV) in ft3
TV= L x A
144
Solve for total weight of fluid in pipe in pounds (TW) TW= TV x 53.04
Solve for fluid velocity in feet/second (FPS) (FV) FV= .3208 x Q
A
Pick a figure from Chart 2 page 10 for (C3) C3= _________
Solve for V1 Accumulator volume in in3
V1= FV2
x TW x (n-1) x .186
P2 x C3
Pick out an accumulator or accumulators with an empty capacity equal to or greater than
the answer for V1 above. Pre-charge with dry nitrogen at 95-105% of P2
12. Fluid Power Formula
10
Accumulator Formula (Cont’d.)
Piston Pump Discharge Shock Control:
Solving for accumulator size in in3
V1= _________in3
Information Required:
Normal system operating pressure (P2): P2= __________PSI
Length of piston stroke in inches.(L): L= __________Inches
Area of piston bores in the pump in in2
(A) A= __________in2
Pump constant (K) K= __________
.60 for single piston single acting pumps. .25 for single piston double acting pumps
.25 for double piston single acting pumps. .15 for double piston double acting pumps.
.13 for triple piston single acting pumps. .06 for triple piston double acting pumps.
Normal system operating temperature in F T= __________Temp. F
From Chart 1, below, select (n) using P2 for “Average Pressure”
and Normal System Operating Temperature from above. n= __________
Pick a figure from Chart 2 below for (C1) C1= _________
Pick a figure from Chart 2 below for (C2) C2= _________
Solve for V1 Accumulator volume in in3
V1= L x A x K x C1
1- C2
Pick out an accumulator or accumulators with an empty capacity equal to or greater than
the answer for V1 above. Pre-charge with dry nitrogen at 95-105% of P2
Chart 1 Chart 2
Average Temperature “n” “c1” “c2” “c3”
Pressure 77 F 108 F 140 F 171 F 200 F 220 F 1.41 Thru 1.45 1.036 .966 .0300
98 1.41 1.46 Thru 1.49 1.035 .967 .0318
123 1.42 1.42 1.50 Thru 1.53 1.034 .968 .0336
148 1.43 1.42 1.54 Thru 1.57 1.033 .969 .0352
172 1.43 1.43 1.43 1.43 1.43 1.43 1.58 Thru 1.62 1.032 .970 .0371
197 1.44 1.43 1.43 1.43 1.43 1.43 1.63 Thru 1.67 1.031 .971 .0389
222 1.44 1.44 1.44 1.44 1.44 1.44 1.68 Thru 1.73 1.030 .972 .0410
246 1.45 1.44 1.44 1.44 1.44 1.44 1.74 Thru 1.79 1.029 .973 .0429
295 1.46 1.45 1.45 1.45 1.45 1.45 1.80 Thru 1.85 1.028 .974 .0447
345 1.47 1.47 1.46 1.46 1.45 1.45 1.86 Thru 1.91 1.027 .975 .0464
395 1.48 1.47 1.46 1.46 1.46 1.46 1.92 Thru 1.94 1.026 .976 .0472
443 1.49 1.48 1.47 1.47 1.46 1.46
492 1.51 1.49 1.48 1.48 1.47 1.47
590 1.53 1.51 1.50 1.50 1.49 1.48
690 1.55 1.53 1.52 1.52 1.50 1.49
788 1.57 1.54 1.53 1.52 1.51 1.50
886 1.60 1.56 1564 1.54 1.53 1.52
985 1.62 1.58 1.56 1.55 1.53 1.52
1230 1.65 1.61 1.59 1.58 1.56 1.55
1476 1.70 1.65 1.63 1.61 1.59 1.57
1723 1.74 1.67 1.64 1.62 1.60 1.58
1970 1.78 1.71 1.68 1.66 1.62 1.61
2215 1.82 1.74 1.71 1.68 1.65 1.62
2462 1.86 1.79 1.75 1.71 1.66 1.63
2800 1.92 1.84 1.79 1.75 1.70 1.66
3000 1.94 1.86 1.81 1.76 1.71 1.67
16. Fluid Power Formula
14
SIZING A HYDRAULIC CIRCUIT
THE FOLLOWING INFORMATION MUST BE KNOWN
1. Maximum force required Usually in pounds or tons of
force
2. Total stroke required Usually in inches
3. High pressure stroke required Usually in inches
4. Total cylinder cycle time Usually in seconds
5. Maximum pressure allowed Arbitrarily decided by the
engineer
SAMPLE PROBLEM
1. Maximum force required 50,000 pounds
2. Total stroke required 42 inches
3. High pressure stroke required Total cylinder stroke
4. Total cylinder cycle time 10 seconds
5. Maximum pressure allowed 2,000 PSI
A.
Maximum Force Re quired x 1.1 / Maximum PSI Allowed
Minimum Cylinder Bore
.7854
=
50,000 Pounds x 1.1/2,000 PSI
.7854
= 5.917” diameter or a 6” Bore
2
PistonArea (in. ) x Stroke (Inches) x 60 Seconds
GPM
Cycle Time (Seconds) x 231 (Cubic Inches/Gal.)
=
28.275 x 84 x 60
GPM
10 x 231
= = 61.7 GPM or a 65 GPM pump
84″ is for cylinder extend and retract. Rod displacement is disregarded in this example.
C. Electric motor horse power = HP = GPM x PSI x .000583
HP = 65 x 2,000 x .000583 = 75.79 or a 75 HP motor
D. Tank size = 2-3 times pump GPM = 2 x 65 = 130 gallons = 150 gallon tank
3 x 65 = 195 gallons = 200 gallon tank
17. Fluid Power Formula
15
SIZING A HYDRAULIC CIRCUIT
On the facing page is an exercise sizing a simple single cylinder hydraulic circuit with straight
forward parameters. The example gives basic requirements for sizing a hydraulic cylinder powered
machine.
In the real world of circuit design, experience, knowing the process, the environment, the skill of the
user, how long will the machine be in service, and other items affect cylinder and power unit choices.
Before designing any circuit it is necessary to know several things.
First is force requirement. Usually, the force to do the work is figured with a formula. In instances
where there is no known mathematical way to figure force, use a mock up part on a shop press or on a
prototype machine for best results. If all else fails, an educated guess may suffice. The sample problem
requires a force of 50,000 pounds.
Second, choose a total cylinder stroke. Stroke length is part of machine function and is necessary to
figure pump size. Use a stroke of 42 inches in this problem.
Third, how much of the stroke requires full tonnage? If only a small portion of the stroke needs full
force, a HI-LO pump circuit and/or a regeneration circuit could reduce first cost and operating cost. This
cylinder requires full tonnage for all 42 inches.
Fourth, what is the total cylinder cycle time? Make sure the time used is for cycling the cylinder.
Load, unload and dwell are part of the overall cycle time, but should not be included when figuring pump
flow. Use a cylinder cycle time of 10 seconds for this problem.
Finally, choose maximum system pressure. This is often a matter of preference of the circuit
designer. Standard hydraulic components operate at 3000 PSI maximum, so choose a system pressure at or
below this pressure. If a company has operating and maximum pressure specifications, adhere to them.
Remember, lower working pressures require larger pumps and valves at high flow to get the desired speed.
On the facing page part A, taking the square root of the maximum thrust, times 110%, for fast
pressure buildup, divided by the maximum system PSI, divided by .7854. This gives a minimum cylinder
bore of 5.244". Choose a standard 6" diameter cylinder for this system.
To figure pump capacity, take the cylinder piston area in square inches, times the cylinder stroke in
inches, times 60 seconds, divided by the cycle time in seconds, times 231 cubic inches per gallon. This
shows a minimum pump flow of 61.7 GPM. A 65 GPM pump is the closest flow available. Never
undersize the pump since this formula figures the cylinder is going maximum speed the whole stroke. The
cylinder must accelerate and decelerate for smooth operation, so travel speed after acceleration and before
deceleration should actually be higher than this formula allows.
Figure horsepower by taking GPM times PSI times a constant of .000583. This comes out to 75.79
HP, and is close to a standard 75 HP motor. This should be sufficient horsepower since the system pressure
does not have to go to 2000 PSI with the cylinder size used.
The tank size should be at least two to three times pump flow, which is three times sixty-five, or 195
gallons, so a 200 gallon tank is satisfactory. When using single acting cylinders or unusually large piston
rods, size the tank for enough oil to satisfy cylinder volume without starving the pump.
18. Fluid Power Formula
16
SIZING A PNEUMATIC CIRCUIT
THE FOLLOWING INFORMATION MUST BE KNOWN
1. Maximum force required Usually in pounds or tons of force
2. Total stroke required Usually in inches
3. Total cylinder cycle time Usually in seconds
4. System operating pressure Arbitrarily 80 PSI for most plants
SAMPLE PROBLEM
1. Maximum force required 150 pounds
2. Total stroke required 14 inches
3. Total cylinder cycle time 4 seconds
4. System operating pressure 80 PSI
A.
Maximum Force Required x 1.25 or 2 / Maximum PSI Allowed
Minimum Cylinder Bore
.7854
=
150 Pounds x 1.25/80 PSI
.7854
= 1.727″ Diameter or a 2” Bore
B.
( )
3
V(Vol. in. ) x Compression Ratio (PSI + 14.7/14.7)
SCFM
Total Cycle Time Seconds x 28.8
=
2 x 2 .7854 x 28 x (80 + 14.7/14.7)
SCFM
4 x 28.8
= = 4.92 SCFM
28” is for cylinder extend and retract. Rod displacement is disregarded in this example
C.
(Flow SCFM) (Abs.Temp.) (Spec.Gravity 1 for air)
A g
v
(Cons tan t) (Pr.Drop) (Outlet Pr.) (Atmos.Pr.)
2 A
Q T x S
Min. Valve C =
22.48 P x (P P )+∆
v
4.92 460 x 1
Min. Valve C =
22.48 x (70 14.7)+10
= .161 = 1/8” ported valve
219# of thrust
2” Bore @ 80 PSI Load
Cylinder will move at nominal speed
19. Fluid Power Formula
17
SIZING A PNEUMATIC CIRCUIT
Sizing air cylinders is similar to sizing hydraulic cylinders. Most air systems operate around 100 to
120 PSI with approximately 80 PSI readily available at the machine site. This gives little or no option for
selecting operating pressure.
Since the compressor is part of plant facilities, the amount of cubic feet per minute (CFM) of air
available for the air circuit usually is many times that required. It is good practice though, to check for
ample CFM flow capabilities at the machine location.
The only items needed to figure an air circuit is maximum force required, cylinder stroke, and cycle
time. With this information, sizing cylinders, valves, and piping is simple.
To figure the cylinder bore required, use the formula given at A. Notice the added multiplier on the
force line. For an air cylinder to move at a nominal rate, it needs approximately 25% greater thrust than the
force required to offset the load. When the cylinder must move fast, figure a force at up to twice that
required to balance the load.
The reason for this added force relates to filling an empty tank from a tank at 100 PSI. When air
first starts transferring, a high pressure difference allows fast flow. As the two tanks get closer to the same
pressure the rate of transfer slows until the gauges almost stop moving. The last five to ten PSI of transfer
takes a long time. As the tanks get close to the same pressure, there is less reason for transfer since
pressure difference is so low.
If an air cylinder needs 78 PSI to balance the load, then it has only 2 PSI differential to move fluid
into the cylinder at a system pressure of 80 PSI. If it moves at all, it is very slow and intermittent. As
pressure differential increases, from higher inlet pressure or less load, the cylinder starts to move smoothly
and steadily. The greater the differential the faster the cylinder movement. Once cylinder force is twice the
load balance, speed increase is minimal.
Using the 1.25 figure in the formula shows a cylinder bore of 1.72" minimum. Choose a 2" bore
cylinder since it is the next size greater than 1.72.”
To size the valve use the "flow coefficient," or Cv rating formula. The Cv factor is an expression of
how many gallons of water pass through a valve, from inlet to outlet, at a certain pressure differential.
There are many ways of reporting Cv valve efficiency and some may be misleading. Always look at
pressure drop allowed when figuring the Cv, to be able to compare different brands intelligently.
The formula shows a valve with 1/8" ports is big enough to cycle the 2" bore cylinder out 14" and
back 14" in 4 seconds.
There are many charts in data books as well as valve manufacturers catalogs that take the drudgery
out of sizing valves and pipes. There are several computer programs as well to help in proper sizing of
components.