Density Is Directly Proportional to Pressure
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Thermodynamics Notes
Thermodynamics Notes Steven K. Krueger Department of Atmospheric Sciences, University of Utah August 2020 Contents 1 Introduction 1 1.1 What is thermodynamics? . .1 1.2 The atmosphere . .1 2 The Equation of State 1 2.1 State variables . .1 2.2 Charles' Law and absolute temperature . .2 2.3 Boyle's Law . .3 2.4 Equation of state of an ideal gas . .3 2.5 Mixtures of gases . .4 2.6 Ideal gas law: molecular viewpoint . .6 3 Conservation of Energy 8 3.1 Conservation of energy in mechanics . .8 3.2 Conservation of energy: A system of point masses . .8 3.3 Kinetic energy exchange in molecular collisions . .9 3.4 Working and Heating . .9 4 The Principles of Thermodynamics 11 4.1 Conservation of energy and the first law of thermodynamics . 11 4.1.1 Conservation of energy . 11 4.1.2 The first law of thermodynamics . 11 4.1.3 Work . 12 4.1.4 Energy transferred by heating . 13 4.2 Quantity of energy transferred by heating . 14 4.3 The first law of thermodynamics for an ideal gas . 15 4.4 Applications of the first law . 16 4.4.1 Isothermal process . 16 4.4.2 Isobaric process . 17 4.4.3 Isosteric process . 18 4.5 Adiabatic processes . 18 5 The Thermodynamics of Water Vapor and Moist Air 21 5.1 Thermal properties of water substance . 21 5.2 Equation of state of moist air . 21 5.3 Mixing ratio . 22 5.4 Moisture variables . 22 5.5 Changes of phase and latent heats . -
Introduction to Hydrostatics
Introduction to Hydrostatics Hydrostatics Equation The simplified Navier Stokes equation for hydrostatics is a vector equation, which can be split into three components. The convention will be adopted that gravity always acts in the negative z direction. Thus, and the three components of the hydrostatics equation reduce to Since pressure is now only a function of z, total derivatives can be used for the z-component instead of partial derivatives. In fact, this equation can be integrated directly from some point 1 to some point 2. Assuming both density and gravity remain nearly constant from 1 to 2 (a reasonable approximation unless there is a huge elevation difference between points 1 and 2), the z- component becomes Another form of this equation, which is much easier to remember is This is the only hydrostatics equation needed. It is easily remembered by thinking about scuba diving. As a diver goes down, the pressure on his ears increases. So, the pressure "below" is greater than the pressure "above." Some "rules" to remember about hydrostatics Recall, for hydrostatics, pressure can be found from the simple equation, There are several "rules" or comments which directly result from the above equation: If you can draw a continuous line through the same fluid from point 1 to point 2, then p1 = p2 if z1 = z2. For example, consider the oddly shaped container below: By this rule, p1 = p2 and p4 = p5 since these points are at the same elevation in the same fluid. However, p2 does not equal p3 even though they are at the same elevation, because one cannot draw a line connecting these points through the same fluid. -
Density Altitude
Federal Aviation Administration Density Altitude FAA–P–8740–2 • AFS–8 (2008) HQ-08561 Density Altitude Note: This document was adapted from the original Pamphlet P-8740-2 on density altitude. Introduction Although density altitude is not a common subject for “hangar flying” discussions, pilots need to understand this topic. Density altitude has a significant (and inescapable) influence on aircraft and engine performance, so every pilot needs to thoroughly understand its effects. Hot, high, and humid weather conditions can cause a routine takeoff or landing to become an accident in less time than it takes to tell about it. Density Altitude Defined Types of Altitude Pilots sometimes confuse the term “density altitude” with other definitions of altitude. To review, here are some types of altitude: • Indicated Altitude is the altitude shown on the altimeter. • True Altitude is height above mean sea level (MSL). • Absolute Altitude is height above ground level (AGL). • Pressure Altitude is the indicated altitude when an altimeter is set to 29.92 in Hg (1013 hPa in other parts of the world). It is primarily used in aircraft performance calculations and in high-altitude flight. • Density Altitude is formally defined as “pressure altitude corrected for nonstandard temperature variations.” Why Does Density Altitude Matter? High Density Altitude = Decreased Performance The formal definition of density altitude is certainly correct, but the important thing to understand is that density altitude is an indicator of aircraft performance. The term comes from the fact that the density of the air decreases with altitude. A “high” density altitude means that air density is reduced, which has an adverse impact on aircraft performance. -
Module 2: Hydrostatics
Module 2: Hydrostatics . Hydrostatic pressure and devices: 2 lectures . Forces on surfaces: 2.5 lectures . Buoyancy, Archimedes, stability: 1.5 lectures Mech 280: Frigaard Lectures 1-2: Hydrostatic pressure . Should be able to: . Use common pressure terminology . Derive the general form for the pressure distribution in static fluid . Calculate the pressure within a constant density fluids . Calculate forces in a hydraulic press . Analyze manometers and barometers . Calculate pressure distribution in varying density fluid . Calculate pressure in fluids in rigid body motion in non-inertial frames of reference Mech 280: Frigaard Pressure . Pressure is defined as a normal force exerted by a fluid per unit area . SI Unit of pressure is N/m2, called a pascal (Pa). Since the unit Pa is too small for many pressures encountered in engineering practice, kilopascal (1 kPa = 103 Pa) and mega-pascal (1 MPa = 106 Pa) are commonly used . Other units include bar, atm, kgf/cm2, lbf/in2=psi . 1 psi = 6.695 x 103 Pa . 1 atm = 101.325 kPa = 14.696 psi . 1 bar = 100 kPa (close to atmospheric pressure) Mech 280: Frigaard Absolute, gage, and vacuum pressures . Actual pressure at a give point is called the absolute pressure . Most pressure-measuring devices are calibrated to read zero in the atmosphere. Pressure above atmospheric is called gage pressure: Pgage=Pabs - Patm . Pressure below atmospheric pressure is called vacuum pressure: Pvac=Patm - Pabs. Mech 280: Frigaard Pressure at a Point . Pressure at any point in a fluid is the same in all directions . Pressure has a magnitude, but not a specific direction, and thus it is a scalar quantity . -
Hydrostatic Leveling Systems 19
© 1965 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. 1965 PELISSIER: HYDROSTATIC LEVELING SYSTEMS 19 HYDROSTATIC LEVELING SYSTEMS” Pierre F. Pellissier Lawrence Radiation Laboratory University of California Berkeley, California March 5, 1965 Summarv is accurate to *0.002 in. in 50 ft when used with care. (It is worthy of note that “level” at the The 200-BeV proton synchrotron being pro- earth’s surface is in practice a fairly smooth posed by the Lawrence Radiation Laboratory is curve which deviates from a tangent by 0.003 in. about 1 mile in diameter. The tolerance for ac- in 100 ft. When leveling by any method one at- curacy in vertical placement of magnets is tempts to precisely locate this curved surface. ) *0.002 inches. Because conventional high-pre- cision optical leveling to this accuracy is very De sign time consuming, an alternative method using an extended mercury-filled system has been deve- The design of an extended hydrostatic level is loped at LRL. This permanently installed quite straightforward. The fundamental princi- reference system is expected to be accurate ple of hydrostatics which applies must be stated within +O.OOl in. across the l-mile diameter quite carefully at the outset: the free surface of machine, a liquid-or surfaces, if interconnected by liquid- filled tubes-will lie on a gravitational equipoten- Review of Commercial Devices tial if all forces and gradients except gravity are excluded from the system. -
Aircraft Performance: Atmospheric Pressure
Aircraft Performance: Atmospheric Pressure FAA Handbook of Aeronautical Knowledge Chap 10 Atmosphere • Envelope surrounds earth • Air has mass, weight, indefinite shape • Atmosphere – 78% Nitrogen – 21% Oxygen – 1% other gases (argon, helium, etc) • Most oxygen < 35,000 ft Atmospheric Pressure • Factors in: – Weather – Aerodynamic Lift – Flight Instrument • Altimeter • Vertical Speed Indicator • Airspeed Indicator • Manifold Pressure Guage Pressure • Air has mass – Affected by gravity • Air has weight Force • Under Standard Atmospheric conditions – at Sea Level weight of atmosphere = 14.7 psi • As air become less dense: – Reduces engine power (engine takes in less air) – Reduces thrust (propeller is less efficient in thin air) – Reduces Lift (thin air exerts less force on the airfoils) International Standard Atmosphere (ISA) • Standard atmosphere at Sea level: – Temperature 59 degrees F (15 degrees C) – Pressure 29.92 in Hg (1013.2 mb) • Standard Temp Lapse Rate – -3.5 degrees F (or 2 degrees C) per 1000 ft altitude gain • Upto 36,000 ft (then constant) • Standard Pressure Lapse Rate – -1 in Hg per 1000 ft altitude gain Non-standard Conditions • Correction factors must be applied • Note: aircraft performance is compared and evaluated with respect to standard conditions • Note: instruments calibrated for standard conditions Pressure Altitude • Height above Standard Datum Plane (SDP) • If the Barometric Reference Setting on the Altimeter is set to 29.92 in Hg, then the altitude is defined by the ISA standard pressure readings (see Figure 10-2, pg 10-3) Density Altitude • Used for correlating aerodynamic performance • Density altitude = pressure altitude corrected for non-standard temperature • Density Altitude is vertical distance above sea- level (in standard conditions) at which a given density is to be found • Aircraft performance increases as Density of air increases (lower density altitude) • Aircraft performance decreases as Density of air decreases (higher density altitude) Density Altitude 1. -
Pressure and Fluid Statics
cen72367_ch03.qxd 10/29/04 2:21 PM Page 65 CHAPTER PRESSURE AND 3 FLUID STATICS his chapter deals with forces applied by fluids at rest or in rigid-body motion. The fluid property responsible for those forces is pressure, OBJECTIVES Twhich is a normal force exerted by a fluid per unit area. We start this When you finish reading this chapter, you chapter with a detailed discussion of pressure, including absolute and gage should be able to pressures, the pressure at a point, the variation of pressure with depth in a I Determine the variation of gravitational field, the manometer, the barometer, and pressure measure- pressure in a fluid at rest ment devices. This is followed by a discussion of the hydrostatic forces I Calculate the forces exerted by a applied on submerged bodies with plane or curved surfaces. We then con- fluid at rest on plane or curved submerged surfaces sider the buoyant force applied by fluids on submerged or floating bodies, and discuss the stability of such bodies. Finally, we apply Newton’s second I Analyze the rigid-body motion of fluids in containers during linear law of motion to a body of fluid in motion that acts as a rigid body and ana- acceleration or rotation lyze the variation of pressure in fluids that undergo linear acceleration and in rotating containers. This chapter makes extensive use of force balances for bodies in static equilibrium, and it will be helpful if the relevant topics from statics are first reviewed. 65 cen72367_ch03.qxd 10/29/04 2:21 PM Page 66 66 FLUID MECHANICS 3–1 I PRESSURE Pressure is defined as a normal force exerted by a fluid per unit area. -
Some Rules About Hydrostatics Author: John M
Some Rules about Hydrostatics Author: John M. Cimbala, Penn State University Latest revision: 31 August 2012 For hydrostatics, pressure can be found from the simple equation, PPbelow above gz Air There are several “rules” that directly result from the above equation: Water 1. If you can draw a continuous line through the same fluid from point 1 to point 2, then P1 = P2 if z1 = z2 . E.g., consider the oddly shaped container in the sketch. By this rule, P1 = P2 4 5 and P4 = P5 since these points are at the same elevation in the same fluid. However, P2 does not equal P3 even though they are at the same elevation, Mercury because one cannot draw a line connecting these points through the same 1 2 3 fluid. In fact, P2 is less than P3 since mercury is denser than water. 2. Any free surface open to the atmosphere has atmospheric pressure, Patm. 1 (This rule holds not only for hydrostatics, by the way, but for any free surface exposed to the atmosphere, whether that surface is moving, stationary, flat, or curved.) Consider the hydrostatics example of a container of water. The little upside-down triangle indicates a free surface, and means that the pressure there is atmospheric pressure, Patm. In other words, in this example, P1 = Patm. To find the pressure at point 2, our hydrostatics equation is used: h PPbelow above gz PPgh21 2 PP2atm gh (absolute pressure) Or, Pgh2, gage (gage pressure) 3. In most practical problems, atmospheric pressure is assumed to be 2 constant at all elevations (unless the change in elevation is large). -
Lecture 4 Hydrostatics and Time Scales
Assumptions – most of the time • Spherical symmetry Broken by e.g., convection, rotation, magnetic fields, explosion, instabilities Makes equations a lot easier. Also facilitates Lecture 4 the use of Lagrangian (mass shell) coordinates Hydrostatics and Time Scales • Homogeneous composition at birth • Isolation frequently assumed Glatzmaier and Krumholz 3 and 4 Prialnik 2 • Hydrostatic equilibrium Pols 2 When not forming or exploding Uniqueness Hydrostatic Equilibrium One of the basic tenets of stellar evolution is the Consider the forces acting upon a spherical mass shell Russell-Vogt Theorem, which states that the mass dm = 4π r 2 dr ρ and chemical composition of a star, and in particular The shell is attracted to the center of the star by a force how the chemical composition varies within the star, per unit area uniquely determine its radius, luminosity, and internal −Gm(r)dm −Gm(r) ρ Fgrav = = dr structure, as well as its subsequent evolution. (4πr 2 )r 2 r 2 where m(r) is the mass interior to the radius r M dm A consequence of the theorem is that it is possible It is supported by the pressure to uniquely describe all of the parameters for a star gradient. The pressure P+dP simply from its location in the Hertzsprung-Russell on its bottom is smaller P Diagram. There is no proof for the theorem, and in fact, than on its top. dP is negative it fails in some instances. For example if the star has rotation or if small changes in initial conditions cause m(r) FP = P(r) i area−P(r + dr) i area large variations in outcome (chaos). -
Ship Hydrostatics and Structures
2.019 Design of Ocean Systems Lecture 2 February 11, 2011 Typical Offshore Structures Platforms: – Fixed platform –FPSO – SPAR – Semi-Submersible – TLP (Tension Leg Platform) Key Components: – Platform on surface (with production facility, gas/oil storage) –Risers – Mooring – Subsea system – Pipelines or transport tankers © Centre for Marine and Petroleum Technology. All rights reserved. This content isexcluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse. Semi‐Submersible Platform Photo courtesy of Erik Christensen, CC-BY. Tension‐Leg Platform (TLP) Gravity‐Based Platform © SBM Atlantia. All rights reserved. This content is excluded from our © source unknown. All rights reserved. This content is excluded Creative Commons license. For more information, see http://ocw.mit.edu/fairuse. from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse. FPSO (Floating, Production, Storage, Offloading) Movable Versatile for use in smaller reservoirs Relatively cheap in cost © Jackson Lane Pty Ltd. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse. – Topside –Hull – Mooring/riser system Courtesy of Linde AG. Used with permission. Design of FPSO vs. Tankers/Ships Tankers/ships: FPSO: Storage Storage Stability Stability Speed No Speed requirement Motion (seakeeping) Motion (seakeeping) Cost – Limited riser top-end displacement – Production – Offloading – Equipment installation Freeboard – Green -
Chapter 4: Principles of Flight
Chapter 4 Principles of Flight Introduction This chapter examines the fundamental physical laws governing the forces acting on an aircraft in flight, and what effect these natural laws and forces have on the performance characteristics of aircraft. To control an aircraft, be it an airplane, helicopter, glider, or balloon, the pilot must understand the principles involved and learn to use or counteract these natural forces. Structure of the Atmosphere The atmosphere is an envelope of air that surrounds the Earth and rests upon its surface. It is as much a part of the Earth as the seas or the land, but air differs from land and water as it is a mixture of gases. It has mass, weight, and indefinite shape. The atmosphere is composed of 78 percent nitrogen, 21 percent oxygen, and 1 percent other gases, such as argon or helium. Some of these elements are heavier than others. The heavier elements, such as oxygen, settle to the surface of the Earth, while the lighter elements are lifted up to the region of higher altitude. Most of the atmosphere’s oxygen is contained below 35,000 feet altitude. 4-1 Air is a Fluid the viscosity of air. However, since air is a fluid and has When most people hear the word “fluid,” they usually think viscosity properties, it resists flow around any object to of liquid. However, gasses, like air, are also fluids. Fluids some extent. take on the shape of their containers. Fluids generally do not resist deformation when even the smallest stress is applied, Friction or they resist it only slightly. -
Chapter 2 Hydrostatics
Title 210 – National Engineering Handbook Part 634 Hydraulics National Engineering Handbook Chapter 2 Hydrostatics D R A F T (210-634-H, 1st Ed., DRAFT, Mar 2021) Title 210 – National Engineering Handbook Issued __________ T In accordance with Federal civil rights law and U.S. Department of Agriculture (USDA) civil rights regulations and policies, the USDA, its Agencies, offices, and employees, and institutions participating in or administering USDA programs are prohibited from discriminating based on race, color, national origin, religion, sex, gender identity (including gender expression), sexual orientation, disability,F age, marital status, family/parental status, income derived from a public assistance program, political beliefs, or reprisal or retaliation for prior civil rights activity, in any program or activity conducted or funded by USDA (not all bases apply to all programs). Remedies and complaint filing deadlines vary by program or incident. Persons with disabilities who require alternative means of communication for programA information (e.g., Braille, large print, audiotape, American Sign Language, etc.) should contact the responsible Agency or USDA's TARGET Center at (202) 720-2600 (voice and TTY) or contact USDA through the Federal Relay Service at (800) 877-8339. Additionally, program information may be made available in languages other than English. To fileR a program dis crimination complaint, complete the USDA Program Discrimination Complaint Form, AD-3027, found online at How to File a Program Discrimination Complaint and at any USDA office or write a letter addressed to USDA and provide in the letter all of the information requested in the form. To request a copy of the complaint form, call (866) 632-9992.