1、SAE Technical Standards Board Rules provide that: “This report is published by SAE to advance the state of technical and engineering sciences. The use of this report is entirelyvoluntary, and its applicability and suitability for any particular use, including any patent infringement arising therefro
2、m, is the sole responsibility of the user.”SAE reviews each technical report at least every five years at which time it may be reaffirmed, revised, or cancelled. SAE invites your written comments and suggestions.Copyright 2003 SAE InternationalAll rights reserved. No part of this publication may be
3、reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE.TO PLACE A DOCUMENT ORDER: Tel: 877-606-7323 (inside USA and Canada)Tel: 724-776-4970 (outside USA)Fax: 724
4、-776-0790Email: custsvcsae.orgSAE WEB ADDRESS: http:/www.sae.orgAEROSPACE INFORMATION REPORTAIR1657REV.BIssued 1981-01Revised 2003-09Superseding AIR1657A(R) Handbook of Hydraulic Metric CalculationsFOREWORDHydraulic calculations may be done directly in the International System (SI) metric units. Cal
5、culations in SI metric units could not be simpler. Data, however, are not always in these units, and conversions are necessary. It is generally preferable to convert the data and then proceed with calculations in the SI metric units. Numerical examples are provided to follow as a guide for avoiding
6、confusion.Changes in the Revision B are primarily editorial.In this document, terminology is defined in each section where required. This is done to avoid any misunderstanding of dual uses of symbols such as N = Newton or N = rpm.Copyright SAE International Provided by IHS under license with SAENot
7、for ResaleNo reproduction or networking permitted without license from IHS-,-SAE AIR1657 Revision B- 2 -TABLE OF CONTENTS1. SCOPE .32. REFERENCES .32.1 SAE Publications .32.2 ASTM Publications.32.3 NAS Publications .32.4 NFPA Publications .32.5 ISO Publications 42.6 Other Publications42.7 U.S. Gover
8、nment Publications.43. TECHNICAL REQUIREMENTS43.1 Metric Units 43.2 Hydrostatics .103.2.1 Static Head.103.2.2 Axial Force .113.3 Hydrodynamics 133.3.1 Bernoullis Theorem .133.3.2 Viscosity.153.3.3 Reynolds Number 213.3.4 Friction Loss.243.3.5 Momentum .283.3.6 Pressure Momentum Equation.313.3.7 Pump
9、 Efficiency .343.4 Thermodynamics363.4.1 Warm-up of Hydraulic Fluid363.4.2 Thermal Expansion 413.4.3 Adiabatic Tangent Bulk Modulus413.4.4 Hydraulic Actuation System Oscillations483.4.5 Adiabatic Secant Bulk Modulus Effects523.4.6 Cooling of Hydraulic Fluid 553.5 Fluid Properties623.5.1 Source of th
10、e Data .623.5.2 Effect of Temperature on Bulk Modulus .634. CONCLUSIONS634.1 Consistent Units.634.2 Simple Calculations634.3 Practical Units 635. NOTES64Copyright SAE International Provided by IHS under license with SAENot for ResaleNo reproduction or networking permitted without license from IHS-,-
11、SAE AIR1657 Revision B- 3 -1. SCOPE:Metric (SI and CGS) and English units related to aerospace hydraulics are summarized. Conversion of units is provided as required. Fundamental fluid properties and physical laws governing fluid motion, pressure and other significant aspects are described in SI met
12、ric units. Examples of application to typical aerospace hydraulic system components are demonstrated. 2. REFERENCES:The following publications form a part of this document to the extent referenced herein. The latest issue of all documents shall apply. In the event of conflict between this document a
13、nd the references cited herein, the text of this document takes precedence. Nothing in this document, however, supersedes applicable laws and regulations unless a specific exemption has been obtained.2.1 SAE Publications:Available from SAE, 400 Commonwealth Drive, Warrendale, PA 15096-0001.AS1241 Fi
14、re Resistant Phosphate Ester Fluid for AircraftAIR1362 Physical Properties of Hydraulic FluidsTSB 003 Rules for SAE Use of SI (Metric) Units2.2 ASTM Publications:Available from ASTM, 100 Barr Harbor, West Conshohocken, PA 19428-2959.ASTM E 38-79 Standard for Metric Practice2.3 NAS Publications:Avail
15、able from Aerospace Industries Association of America, Inc., 1000 Wilson Boulevard, Suite 1700, Arlington, VA 22209-3901.NAS 10001 Preferred Metric Units for Aerospace2.4 NFPA Publications:Available from National Fluid Power Association, Inc., 3333 N. Mayfair Road, Milwaukee, WI 53222-3219.NFPA/T2.1
16、0.1 Metric Units for Fluid Power ApplicationsCopyright SAE International Provided by IHS under license with SAENot for ResaleNo reproduction or networking permitted without license from IHS-,-SAE AIR1657 Revision B- 4 -2.5 ISO Publications:Available from ANSI, 25 West 43rd Street, New York, NY 10036
17、-8002.ISO/R 31 Basic Quantities and Units of SIISO 10090 SI Units and Recommendations for Use of Multiples2.6 Other Publications:2.6.1 Lubrication Engineering, Vol. 44, 4, 324-329, May 1987, Pump Evaluation of Polyalphaolefin Candidates for a 54 C to 135 C Fire-Resistant Aircraft Hydraulic Fluid, L.
18、J. Gschwender, C.E. Snyder Aircraft, Missile and Ordinance, NATO Code 515MIL-PRF-6083 Hydraulic Fluid, Petroleum Base, for Preservation and Testing, NATO Code 535MIL-PRF-46170 Hydraulic Fluid, Rust Inhibited, Fire Resistant, Synthetic Hydrocarbon Base, NATO Code H-544MIL-PRF-53119 Hydraulic Fluid, N
19、on Flammable, Chloro-trifluoro-ethylene BaseMIL-PRF-83282 Hydraulic Fluid, Fire Resistant, Synthetic Hydrocarbon Base, Aircraft, NATO Code H-537MIL-PRF-87257 Hydraulic Fluid, Fire Resistant, Low Temperature, Synthetic Hydrocarbon Base, Aircraft and Missile, NATO Code 5383. TECHNICAL REQUIREMENTS:3.1
20、 Metric Units:The SI system is coherent because force, pressure, and power are expressed in terms of basic quantities of mass, length, and time without empirical constants. Kilogram (kg), meter (m), and second (s) are the basic units. Unity (1) is the coefficient of the basic units in their definiti
21、on. Multiples of the basic units are defined by powers of 103(see Table 1).These multiples provide usefulness and convenience for practical purposes. Multiples other than powers of 103are obsolete (see Table 2).Copyright SAE International Provided by IHS under license with SAENot for ResaleNo reprod
22、uction or networking permitted without license from IHS-,-SAE AIR1657 Revision B- 5 -TABLE 1 - Recommended Multiples of SI UnitsTABLE 2 - Not Recommended Multiples of Units3.1 (Continued):The SI metric system was established by the International Organization for Standardization (ISO) and supersedes
23、the CGS metric system, where centimeter (cm), and gram (g) and second (s) were the basic units, and the earlier metric system where kilogram force was the basic unit.Table 3 provides conversion of metric units. NAS 10001, NFPA/T2.10.1 and ANSI/ASTM E 380, and other publications are available for con
24、version of metric and English units.Table 4 provides factors for conversion from English units to SI Metric units.Copyright SAE International Provided by IHS under license with SAENot for ResaleNo reproduction or networking permitted without license from IHS-,-SAE AIR1657 Revision B- 6 -TABLE 3 - Me
25、tric UnitsCopyright SAE International Provided by IHS under license with SAENot for ResaleNo reproduction or networking permitted without license from IHS-,-SAE AIR1657 Revision B- 7 -TABLE 3 - Metric Units (Continued)Copyright SAE International Provided by IHS under license with SAENot for ResaleNo
26、 reproduction or networking permitted without license from IHS-,-SAE AIR1657 Revision B- 8 -TABLE 4 - English UnitsCopyright SAE International Provided by IHS under license with SAENot for ResaleNo reproduction or networking permitted without license from IHS-,-SAE AIR1657 Revision B- 9 -TABLE 4 - E
27、nglish Units (Continued)Copyright SAE International Provided by IHS under license with SAENot for ResaleNo reproduction or networking permitted without license from IHS-,-SAE AIR1657 Revision B- 10 -3.2 Hydrostatics:3.2.1 Static Head:3.2.1.1 Primary Units: The hydrostatic pressure (P) is by definiti
28、on:(Eq. 1)where:P = pressure (Pa) (ML-1T-2) = mass density (kg/m3) (ML-3)g = gravitational acceleration (m/s2) (LT-2)g = 9.81 m/s2h = head (m) (L)3.2.1.2 Practical Units: By the definition of liter (L):(Eq. 2)Therefore:(Eq. 3)Compare the specific gravity and the density of water:(Eq. 4)The hydrostat
29、ic pressure in practical units is:(Eq. 5)where:P = pressure (kPa) (1 kPa = 1000 Pa) = mass density (kg/L) (1 kg/L = 1000 kg/m3)g = gravitational acceleration (m/s2)g = 9.81 m/s2at sea level, 45 deg latitudeh = head (m)P gh=i.e., ML1T2ML3LT2L=( )1 L 1 m3/1000= mass density (kg/L)=1 kg/L 1000 kg/m3=sp
30、ecific gravity 1=density of water at sea level and 16 C 1 kg/L 1 g/cm3=P gh=Copyright SAE International Provided by IHS under license with SAENot for ResaleNo reproduction or networking permitted without license from IHS-,-SAE AIR1657 Revision B- 11 -3.2.1.3 Application Suction Pressure:Given:MIL-PR
31、F-5606 hydraulic fluid at 20 C.The hydraulic reservoir is at 2.27 m above baseline.An actuator is at 5.32 m above baseline.The hydraulic reservoir open to sea level atmosphere during maintenance. Calculate:a. The suction the actuator seals must be able to withstand without air ingestion.b. The absol
32、ute pressure at the actuator.Density of MIL-PRF-5606 at 20 C and 0 Mpa per Figure 1 is:(Eq. 6)The difference in elevation is:(Eq. 7)The suction pressure (below atmospheric) in kilopascals (kPa):(Eq. 8)The standard sea level atmospheric pressure is 101.3 kPa per ANSI/ASTM 380.The absolute pressure at
33、 the actuator is:(Eq. 9)3.2.2 Axial Force:3.2.2.1 Primary Units: The axial force is:(Eq. 10)where:F = force (Newton, N) (MLT-2)A = area (m2) (L2)P = pressure (pascal, Pa) (ML-1T-2) 0.859 kg/L=h 5.32 2.27 3.05 m=P 0.859 9.81 3.05=P25.7 kPa=101.3 25.7 75.6 kPa=FAP=MLT2L2ML1T2=()Copyright SAE Internati
34、onal Provided by IHS under license with SAENot for ResaleNo reproduction or networking permitted without license from IHS-,-SAE AIR1657 Revision B- 12 -FIGURE 1 - Density Versus Temperature, MIL-PRF-56063.2.2.2 Practical Units: The axial force is:(Eq. 11)where:F = force (Newton, N)A = area (mm2) (1
35、mm2= 10-6m2)P = pressure (megapascal, Mpa) (1 Mpa = 106Pa)FAP=Copyright SAE International Provided by IHS under license with SAENot for ResaleNo reproduction or networking permitted without license from IHS-,-SAE AIR1657 Revision B- 13 -3.2.2.3 Application Hydrostatic Test: A hydraulic cylinder of 5
36、0.8 mm inside diameter is proof pressure tested to 1.5 factor of rated 20.7 Mpa pressure.Calculate the axial force on the cylinder cap.The test pressure is:(Eq. 12)The cap area is:(Eq. 13)The force is:(Eq. 14)3.3 Hydrodynamics:3.3.1 Bernoullis Theorem: The total head in steady state flow of an incom
37、pressible fluid is:(Eq. 15)where:h = static head (m) (L)v = velocity of flow (m/s) (LT-1)g = gravitational acceleration (m/s2) (LT-2)z = elevation of section above datum (m) (L)Bernoullis theorem states that total head (H) along a streamline is constant, provided that the head losses (DH) between se
38、ctions are accounted for:(Eq. 16)P 1.5 20.7 Mpa=P31 Mpa=A 50.8()2/4=A 2027 mm2=F 31 E+6 Pa 2027 E-6 m2=F 62,900 N=F 62.9 kN=Hhv22g z+=LL LT-1()2LT-2L+=h1v122g z1+h2v222g z2DH+=H1H2DH+=Copyright SAE International Provided by IHS under license with SAENot for ResaleNo reproduction or networking permit
39、ted without license from IHS-,-SAE AIR1657 Revision B- 14 -3.3.1 (Continued):where:subscripts 1 and 2 refer to sectionsDH = loss in total head, (m)3.3.1.1 Velocity Head: By definition, the velocity head is:(Eq. 17)3.3.1.2 Application Liquid Column Head: MIL-PRF-5606 fluid at 50 C and 20 Mpa pressure
40、 is flowing in a tube at 3 m/s velocity. What is the velocity head in terms of:a. Liquid column heightb. Pressure?In terms of liquid column height:(Eq. 18)where:v = 3.0 m/sg = 9.81 m/s2Then:(Eq. 19)In terms of pressure head (dynamic pressure):(Eq. 20)where: = 0.85 kg/L - (ML-3)v = 3 m/s - (LT-1)hvv2
41、2g=LLT-1()2LT2=hvv22g=hv3.0229.81( )=hv0.46 m=Pv g hvML1T2ML3LT2L=()=Pv g()v22g()=Pv v2/2 ML1T2ML3LT1()2=Copyright SAE International Provided by IHS under license with SAENot for ResaleNo reproduction or networking permitted without license from IHS-,-SAE AIR1657 Revision B- 15 -3.3.1.2 (Continued):
42、Then:(Eq. 21)3.3.2 Viscosity:3.3.2.1 Dynamic (Absolute) Viscosity: It is by definition, the shear force per unit area due to a unit velocity gradient normal to the flow (when the flow is laminar):(Eq. 22)In primary units: = dynamic viscosity, Pa . s (ML-1T-1)F = force, Newton (MLT-2)A = area, m2 (L2
43、)dV = variation of velocity, m/s (LT-1)dy = normal distance, m (L)In practical units:m = dynamic viscosity, mPa . s (E-3 Pa . s ML-1T-1)F = force, Newton (MLT-2)A = area, mm2 (E-6 m2L2)dV = variation of velocity, m/s (LT-1)dy = normal distance, mm (E-3 L L)Refer to Table 3 where 1 mPa . s = 1 centip
44、oise3.3.2.2 Kinematic Viscosity: It is by definition, the shear force per unit area and per unit mass density due to a unit velocity gradient normal to the flow:(Eq. 23)That is:(Eq. 24)Pv0.85 322=Pv3.83 kPa= F/A/(dV/dy)=(ML1T1= MLT2/L2/(LT1/L) F/(A )/(dV/dy)=(L2T1= MLT2/(L2x /(LT1/L) / =L2T1ML1T1/ML
45、3=()Copyright SAE International Provided by IHS under license with SAENot for ResaleNo reproduction or networking permitted without license from IHS-,-SAE AIR1657 Revision B- 16 -3.3.2.2 (Continued):In basic units: = kinematic viscosity, m2/s (L2T-1)F = force, Newton (MLT-2)A = area, m2 (L2) = mass
46、density, kg/m3 (ML-3)dV = variation of velocity, m/s (LT-1)dy = normal distance, m (L)In practical units: = kinematic viscosity, mm2/s (E-6 m2. s L2T-1)F = force, Newton (MLT-2)A = area, mm2 (E-6 m2L2) = mass density, kg/liter (E-3 kg/m3ML-3)dV = variation of velocity, m/s (LT-1)dy = normal distance
47、, mm (E-3 L L)Refer to Table 3 where 1 mm2/s = 1 centistoke.3.3.2.3 Example: Calculate the absolute viscosity () of MIL-PRF-83282 hydraulic fluid at -30 C and 10 Mpa by solving Equation 24:(Eq. 25)Viscosity = 1400 mm2/s (centistoke) obtained from Figure 2 Density = 0.88 kg/L obtained from Figure 4In
48、 primary units: = 1400 m2E-6 x 880 kg/m3= 1.23 Pa . sIn practical units: = 1400 mm2/s x 0.88 kg/L = 1230 mPa . sIn the usual (CGS) units: = 1400 cst x 0.88 g/cc = 1230 centipoise = 1230 mPa . s =Copyright SAE International Provided by IHS under license with SAENot for ResaleNo reproduction or networking permitted without license from IHS-,-SAE AIR1657 Revision B- 17 -FIGURE
