HYDRAUUC DEVICES

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HYDRAUUC DEVICESA Module on Hydraulics and EquilibriumSUNY at BinghamtonMalcolm Goldberg, Westchester Community CollegeJohn P. Ouderkirk, State University of New York Agricultural and Technical College at CantonBruce B. Marsh, State University of New York at AlbanyCarl R. Stannard, State University of New York at BinghamtonBruce B. Marsh, State University of New York at AlbanyProject Co- DirectorsNEW YORKST. LOUISDALLASSAN FRANCISCOAUCKLANDDUSSELDORFJOHANNESBURGKUALA LUMPURLONDONMEXICOMONTREALNEW DELHIPANAMAPARISsAO PAULOSINGAPORESYDNEYTOKYOTORONTO

The Physics of Technology modules were produced by the Tech Physics Project, which wasfunded by grants from the National Science Foundation. The work was coordinated by theAmerican Institute of Physics. In the early planning stages, the Tech Physics Project receiveda small grant for exploratory work from the Exxon Educational Foundation.The modules were coordinated, edited, and printed copy produced by the staff at IndianaState University at Terre Haute. The staff involved in the project included:Philip DiLavore .Julius Sigler . . .Mary Lu McFall.B. W. BarricklowStacy Garrett . .Elsie Green. . . .Donald Emmons·Editor· . . . . . . Rewrite Editor· Copy and Layout Editor. Illustrator·Compositor·Compositor·Technical ProofreaderIn the early days of the Tech Physics Project A. A. Strassenburg, then Director of the AlPOffice of Education, coordinated the module quality- :ontrol and advisory functions of theNational Steering Committee. In 1972 Philip DiLavore became Project Coordinator andalso assumed the responsibilities of editing and producing the final page copy for the modules.The National Steering Committee appointed by the American Institute of Physics hasplayed an important role in the development and review of these modules. Member of thiscommittee are:J. David Gavenda, Chairman, University of Texas, AustinD. Murray Alexander, DeAnza CollegeLewis Fibel, Virginia Polytechnic Institute & State UniversityKenneth Ford, New Mexico Institute of Mining and TechnologyJames Heinselman, Los Angeles City CollegeAlan Holden, Bell Telephone LabsGeorge Kesler, Engineering ConsultantTheodore Pohrte, Dallas County Community College DistrictCharles Shoup, Cabot CorporationLouis Wertman, New York City Community CollegeThis module was written and tested at the State University of New York at Binghamton.In addition to the Project Co-Directors, the professional staff includes Arnold Benton, theAmerican Institute of Physics; Malcolm Goldberg, Westchester Community College; Giovanni Impeduglia, Staten Island Community College; Gabriel Kousourou, QueensboroughCommunity College; Ludwig P. Lange, Broome Community College; John F. Ouderkirk,SUNY ATC, Canton; and Arnold A. Strassenburg, SUNY, Stony Brook.The authors wish to express their appreciation for the help of many people in bringing thismodule to final form. The criticisms of various reviewers and the cooperation of field-testteachers have been most helpful. Several members of the staff of the State University ofNew York at Binghamton also deserve special recognition for their contributions. Theyare: Felix K. Chen, Duane A. Damiano, Eugene C. Deci, Barry R. DeGraff, Max Eibert,Steve I. Finette, Chung-Yu Fu, Jeffrey W. Gray, Leonard R. Kelly, Stevan H. Leiden,Debra M. Simes, Laurie A. Sperling, William Standish, and Howard M. Zendle.Copyright 1975 by the Research Foundation of the State University of New York. Allrights reserved. Printed in the United States of America. No part of this publication may bereproduced, stored in a retrieval system, or transmitted, in any form or by any means,electronic, mechanical, photocopying, recording, or otherwise, without the prior writtenpermission of the publisher.Except for the rights to material reserved by others, the publisher and copyright ownerhereby grant permission to domestic persons of the United States and Canada for use of thiswork without charge in the English language in the United States and Canada after JanuaryI, 1982. For conditions of use and permission to use materials contained herein for foreignpublication or publications in other than the English language, apply to the AmericanInstitute of Physics, 335 East 45th Street, New York, N.Y. 10017.

Section AHydraulic DevicesExperiment A-I. DevicesProperties of Liquids .Experiment A-2. HydrometrySummary . . . . .Problems2258· 12· 14· 14Section B . . . . . . .Pressure . . . . .Experiment B-1. Pressure Dependence on DepthPressure versus DepthTall Buildings . . . . . . . . . . . . .Archimedes' Principle.Derivation of Archimedes' PrincipleExperiment B-2. Measuring DensityQuestions for Experiment B-2Atmospheric Pressure . . . . . . . .Gauge Pressure . . . . . . . . . . . .Experiment B-3. A Closed Hydraulic System .Closed Systems-Pascal'sLawFriction .SummaryProblems· 15· 15· 16Section C-1 . .Fluids in Motion: HydrodynamicsExperiment C-1. The Bernoulli Effect.Bernoulli's Principle . . . . . . . . . . .Derivation of the Bernoulli Effect (Optional).34Section C-2.Other Hydraulic Devices.Pressure Measuring Devices (Gauges)Pressure Measurements.Experiment C-2. Blood Pressure MeasurementsHydraulically Actuated Controls .SummaryProblems.WorksheetsExperimentA-I· 18· 19· .42.44.48· 51· 52.5254

-3· .55· .57· . 58.60

Hydraulic DevicesHydraulic devices are used in many waysin our technical society. Many of thesedevices were developed in the nineteenthcentury, before electrical power was available.In those days the engineering work ofteninvolved applications of water and steampower. Hydraulic devices were an outgrowthof the technological needs of the times.Today we still find many hydraulic(fluid-power) devices in our homes, hospitals,and industrial plants. Fluid-powered devicesare relatively cheap, easy to maintain, andhighly reliable; they are still very much a partof our technology. The basic physical principles of hydraulic devices are now wellknown, so most hydraulic engineering todayinvolves only the improvement of materials,methods of manufacture, and the development of new applications of fluid-operateddevices. A few years ago an entirely new useof fluid technology resulted from the development of fluidic amplifiers, which sense andswitch like their electronic counterparts. Theyare extremely reliable and rugged, so they areused in applications which would be too harshfor other kinds of amplifiers.In this module you will study the basicphysics of fluids in order to understand somesimple hydraulic devices. The goals of themodule are outlined here. Read them beforestarting on the module, and refer to them asyou work through the module.The main goal of this module is to helpyou learn the basic principles and concepts ofhydraulics. When you have completed themodule, you should have a knowledge andunderstanding of the following:3.The relationshippressure.betweenforceand4.The way in which pressure increases withdepth in a liquid.5.The way in which pressure is transmittedthrough fluids.7.The mechanical advantage and efficiencyof hydraulic jacks.8.The buoyantby liquids.9.The way in which pressure depends onthe rate of flow of a fluid.forces exerted on objects

A treatment of the properties of liquidsis an important component of this module.You will study several devices in which thestatic (stationary) and dynamic (moving)properties of liquids are used to performuseful functions. The devices to be studiedinclude automobile brakes, the hydraulic jack,the toilet tank, the siphon, the aspirator, thehydrometer,pressure gauges, and thesphygmomanometer.In an automobile brake system, thebrake fluid transmits pedal pressure to a brakeshoe (or a pad for a disc brake). The brakeshoe ru bs against the brake drum and produces a frictional force to slow the auto. A2-ton car, or a 10-ton truck, can be stoppedby applying a force of a few pounds to thebrake pedal. Why is such a small applied forceable to stop a speeding car? What happens ifthere is air in the brake line? You will learn theanswers to these and other questions as youproceed through the module.The toilet tank uses a system of levers torelease the water and a float-lever system toshut off the water supply after the tank hasrefilled. Did you ever watch the operation ofthe tank? What happens to shut off the waterfilling the tank?The aspirator is a pump whose operationdepends on the properties of a flowing liquid.You will see this device in operation in thelaboratory .The hydraulic jack has the effect of"magnifying" a force, so that a heavy object,such as a car, can be lifted with ease.A siphon is a simple device (usually justa piece of tubing) which enables a liquid toflow from one container, over a high point,then down into a lower container, withoutthe aid of a pump. It can be used to drawliquid from the lower part of a containerwhen the surface is contaminated with scum,oil, or other unwanted matter. You might alsouse it to "borrow" gasoline from the tank of acar.Figures I through 6 will serve as part ofthe basis for our discussions of fluid mechanics. You may need to look back at theseillustrations as you work through the module.So far we have used many technicalterms without explaining their meaning. Someyou already know, others are new to you. Wewill explain most of the terms to you as wecome to them in the ISCBRAKEDRUMBRAKE

BALL COCKASSEMBLYWATER SUPPLY-.JFigure 2. The carburetor is a device that makes useof the physical laws which apply to stationary fluids(hydrostatics)and moving fluids (hydrodynamics).LOUTLET

Your instructor will provide you with aportable hydraulic jack that has a base plateand a load-lifting plate added to it. Thisdevice is a I.S-ton-capacity jack of the typeused to lift a car. Figure 7 shows this manually operated miniature garage jack.Operate the jack; work it up and down.Use it to lift one student standing on the liftplatform. Measure the force needed to movethe handle to lift the student. Use a springbalance and read the dial as the handle movesdownward. Fill in the worksheet for thisexperiment, which is found at the back of themodule.1.How many times greater is the liftedweight than the force applied to thehandle? How shall we describe thisdevice? Inexpensive?Reliable? Liftsheavy loads with a small applied force?Multiplies force?2.Carefully look over the jack,describe briefly what you see.then-Did you notice the two cylinders? Theshaft from the smaller cylinder isattached to the bottom of the handle.The shaft from the larger cylinder transmits the lifting force to the object beinglifted. Look for these now if you didn'tfind them before.Which cylinder is longer? The jackrequires many full strokes of the handleto extend the shaft of the longer cylinder its full travel. Why?3.What do you notice about the handle? Isit a lever? What is the approximatedistance from the pivot to the otherend? What is the approximate distancefrom the pivot to the shaft of the smallercylinder? How many times bigger is thefirst length than the second length? Doyou know the significance of this number? If not, you will soon.What's inside the jack? Can you guess?What reason do you have for youranswer?

This jack weighs less than 6 Ib, costsabout 12, and can lift 3000lb with about100-lb force applied to the handle. How doesit work? The answer is described in thismodule. We will explain the behavior of fluidsin terms of physical laws. When you understand those laws, the. operation of thishydraulic jack and many other devices will beclear.The hydraulic jack illustrates that asimple two-piston hydraulic system can beused for force multiplication.Using the two-pistondemonstrationsystem (Figure 8) with valves and a pressuregauge (0-100 Ib/in2):I.2.nals similar to the oil pressure light orbrake lights in a car.3.Push down on the smaller-diameterpiston until you develop 801b/in2 pressure in the system (you will have to closethe valve between the gauge and thelarger piston to build that pressure). Now,after adjusting the valves properly, pushdown on the larger-diameter piston todevelop an 80 Ib/in 2 pressure in thesystem. Which piston requires a largerforce to produce this pressure? Can youexplain why?4.(Optional) Have a test of strength. Letthe instructor press down on the largepiston. Push down on the small pistonsee who can push his piston all the waydown.5.(Optional) Place a 5-lb weight on thesmall piston. What pressure is developedin the system? Now do it with a I G-IbDemonstrate to yourself that the fluid isalmost incompressible.Observe that simple pressure-activateddevices can be operated to control sig-

and a 15-lb weight. Try the same weightson the larger piston. What pressures areproduced? Can you explain the differences between the two sets of values?6.In a hydraulic system, the amount offluid stays the same if there is no leak. Ifthe fluid is incompressible, then thevolume it occupies also is constant whenthe pressure changes. This may seemquite obvious, but if the system werepneumatic (air operated), the volumewould change as the pressure changed,since air is easily compressed. Using anempty syringe, demonstrate that the airinside is highly compressible by sealingthe exit port with your finger whileoperating the plunger. You should beable to produce a substantial decrease involume. What fraction of the originalvolume is the compressed volume? Whenyou release the plunger, it should returnalmost to the starting point (keeping theexit port sealed). If it doesn't quitereturn, try to explain why and checkyour answer with your instructor.Examine the other hydraulic devicesdisplayed in the lab. As you think about whateach one is for and how it operates, someunanswered questions may come to mind. Foreach device write down one or two questionsyou would like to have answered. Be sure tooperate the aspirator nd the siphon.

letter p (rho) is the commonlysymbol for mass density:The behavior of liquids has top billing inthis module. It is important that we establishseveral of the basic properties of liquids.Some of these liquid properties will be veryfamiliar, others will be new and interesting.1.A liquid conforms to the shape of itscontainer. This fact is one of the maindifferences between liquids and solids.2.A liquid seeks its own level. When aliquid is poured into an open vessel, thesurface of the liquid will reach the samelevel in all parts of the vessel.usedM'Vp -where M mass of the sample in kilograms (kg) and V the volume of thesample in cubic meters (m3). Mass density is measured in kg/m 3. Since this is alarge unit, mass density is more oftendescribed in g/cm3. 1 g/cm3 103kg/m3.In the English system of units it is morecommon to use weight density. which isthe ratio of weight to volume.WD -V--- --------------------------------- ------------------------------------------- ---Figure 9. A liquid reaches the same level in all partsof an open vessel.3.Liquids are incompressible. No matterhow hard you squeeze, you cannotnoticeablychange the volume of asample of liquid. (There is a tiny bit ofchange at high pressures, but it can beneglected.) This is the most importantdifference between a liquid and a: gas. Agas is easily compressed into a smallervolume. Because of its incompressibility,the ratio of the mass to the volume is adistinctive property of a given liquid.This useful and easily measured propertyis called the mass density. The Greekwhere D is the weight density, W is theweight, and V is the volume. Typicalunits used for weight density are Ib/ft3or ton/yd3. Table I lists density values forseveral commonsubstances.Severalsolids are included, even though thismodule emphasizes liquids.A word of caution: the density of amaterial depends on its temperature.Because the volume of a substanceusually changes when its temperaturechanges, while the mass and weightremain unchanged,the density alsochanges. To be precise, one shouldalways give temperature data along withthe density.Weight density and mass density arerelated because the weight of an object isrelated to its mass:where g is the acceleration due to gravity(9.8 m/s2 or 32 ft/s2). Therefore, theweight density is simply related to themass density byMD -gV pg

Weight DensityMass 79049.41.4*1,400*87.5*Ethylene Glycol rpentine0.8787054.413,500843.891056.9LIQUIDSMaple SyrupMercuryOlive d3.2*3,200*200.0*Wood0.7*700*43.8*

Example 1. A sample of metal has a volumeof 0.10 m 3 and a mass of 790 kg. Determineits density, and check Table I to see whatmaterial it might be.Solution. Because mass is specified, we canmost readily determine mass density.Mp -790 kgmnumber which compares the density of thesubstance to the density of water.Of·.Sdensity of substanceSpeCI ICgraVity Go -------density of water Specific gravity is a dimensionless number.Since the density of water is 1.0 g/cm3, wecan easily calculate the density of any substance if we know its specific gravity.V 0.1Sometimes a material is described by itsspecific gravity. The specific gravity is a3From the table we see that this is the densityof iron.Example 3. By law, maple syrup must meetminimum density standards. The specificgravity of a sample of maple syrup is 1.412.What is its density?Example 2. How many tons of water arethere in a swimming pool 15ft wide, 30 ftlong, and 4 ft deep?S.G.Solution. The weight can be determined fromthe volume of the pool and the weight densityof water:W1.412 density of waterdensity of syrup/31.0gcmdensity of syrup 1.412 g/cm3D -VThe volume of the pool can be determinedfrom the dimensions:From Table I, the weight density of water is62.41b/fe.W (62.41b/ft3)density of syrup ------(1800 ft3)One practical use of specific gravity is inthe measurement of the "proof' of alcoholicsolutions, as Table II shows. Notice that thetemperature is specified.There are many other practical uses formeasurements of specific gravity. For example, since the specific gravity of the acid in acar battery depends on the condition ofcharge, the battery can be tested simply bymeasuring that specific gravity. Likewise, thepercentage of antifreeze in the cooling systemcan be determined through a specific-gravitymeasurement. The specific gravity of a liquidcan be measured easily by using a simpleinstrument called a hydrometer.

Alcohol Strength and Specific Gravity,As Measured in the United StatesPercent by volumeProofSpecific 1750.0100.00.934260.0120.00.913370.0140.00.8899

A. A hydrometer is a simple device formeasuring the specific gravity of a liquid.Hydrometers are used in the chemical industry for process-control and testing. They areused in the maple syrup, wine, whiskey, andmilk industries for quality control tests.In its simplest form, the hydrometer is arod of wood, or a hollow glass tube, weightedslightly at one end so that it floats in anupright position. A scale is usually marked onit. Each hydrometer, of course, has a certainfixed mass. When floated in a beaker of water,it will sink to a certain depth. The water lineis marked 1.0 on the hydrometer, since this isthe specific gravity of water. If the hydrometer is placed into any other liquid and itcomes to rest with the liquid surface at the1.0 line, then that liquid also has a specificgravity of 1.0 and a density of 1 g/cm3.Ques

hydrometer, pressure gauges, and the sphygmomanometer. In an automobile brake system, the brake fluid transmits pedal pressure to a brake shoe (or a pad for a disc brake). The brake shoe rubs against the brake drum and pro-duces a frictional force to slow the auto. A 2-ton car, or a 10-t

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