Unit 1 Fluid Statics PDF

Unit 1 FLUID STATICS CONTENTS GENERAL PROPERTIES PASCAL’S PRINCIPLE HYDROSTATICS’ FUNDAMENTAL EQUATION ARCHIMEDES’ PRINCIPLE COMPRESIBLE FLUIDS: GASES • Equation of State • Boyle-Mariotte’s y Gay-Lussac’s Laws. • Gas Mixtures: Dalton’s Law of partial pressures GAS EXCHANGE IN BLOOD • Dilution o...

Unit 1 FLUID STATICS CONTENTS GENERAL PROPERTIES PASCAL’S PRINCIPLE HYDROSTATICS’ FUNDAMENTAL EQUATION ARCHIMEDES’ PRINCIPLE COMPRESIBLE FLUIDS: GASES • Equation of State • Boyle-Mariotte’s y Gay-Lussac’s Laws. • Gas Mixtures: Dalton’s Law of partial pressures GAS EXCHANGE IN BLOOD • Dilution of Gases in Liquids. Henry’s Law. • Partial Pressure of Gases in Blooden sangre. GAS TRANSPORT IN BLOOD PHYSIOLOGICAL EFFECTS OF HIGH AND LOW PRESSURES MEASUREMENT INSTRUMENTS GENERAL PROPERTIES FLUID  State of matter that does not have a definite shape (Liquid and gases) Ability to compress  Can be classified according to… Viscosity COMPRESSIBILITY. Kinetic molecular theory Matter is made up of particles in continuous motion. The differences between the different states of matter is determined by the distance between molecules. GASES SOLIDS The distance between their molecules is large and there is no interaction between molecules at ordinary 𝑇 and 𝑝.  They take on the volume and shape of the container.  Highly compressible. (particles are very separated)  Freedom of movement. LIQUIDS Small distance between molecules, in normal conditions of 𝑇 and 𝑝 they are denserFixed than gases  Defined volume, but take the shape of not-defined shape the container.  Slightly compressible. Almost incompressible  Freedom of movement. Molecules/atoms occupy a rigid position. Distribution with a three-dimensional regular configuration  Well-defined shape and volume.  Incompressible.  Molecules/atoms are not free to move. Vibrations.or rotations. fixed in a grid GENERAL PROPERTIES Intermolecular forces     Important in condensed matter. Sttractive forces between molecules. They are considerably weaker than ionic, covalent, and metallic bonds. The main intermolecular forces are: • The hydrogen bond (formerly known as hydrogen bond) • Van der Waals forces: Dipole - Dipole. Dipole - Induced Dipole. • London dispersion forces.  In fluids there are a series of effects and characteristics related to molecular forces Temporary attractive force that results when the electrons in two adjacent atoms occupy positions that make the atoms form temporary dipoles. SURFACE TENSION CAPILARITY GENERAL PROPERTIES SURFACE TENSION At the microscopic level, surface tension is due to the fact that the forces that affect each molecule are different inside the liquid and on the surface. Thus, within a liquid, each molecule is subjected to attractive forces that, on average, cancel each other out. However, at the surface there is a net force towards the interior of the liquid. Strictly speaking, if there is a gas outside the liquid, there will be a minimum attractive force towards the outside, although in reality this force is negligible due to the large density difference between the liquid and the gas. GENERAL PROPERTIES CAPILLARITY When a liquid rises through a capillary tube, it is due to the fact that the intermolecular force or intermolecular cohesion between its molecules is lower than the adhesion of the liquid with the material of the tube. The liquid continues to rise until the surface tension is balanced by the weight of the liquid filling the tube. This is the case of water, and this property is what partially regulates its ascent within plants, without spending energy to overcome gravity. However, when the cohesion between the molecules of a liquid is stronger than the adhesion to the capillary, as in the case of mercury, the surface tension causes the liquid to descend to a lower level and its surface is convex. Surface tension ↑y cohesion GENERAL PROPERTIES DENSITY Density of a homogeneous substance equals the mass per unit volume. 𝜌= Example: 𝜌 𝜌 = 1 · 10 kg/m = 1.29 kg/m 𝑚 𝑉 kg/m The density of a liquid and a gas tells us that the average molecular scattering in a gas is greater than in a liquid. PRESSURE If a force 𝐹⃗ (𝐹⃗ = 𝐹 𝚤⃗ + 𝐹 𝚥⃗) acts on a Surface 𝑆, the pressure that this force exerts on the surface is defined as the quotient between the modulus of the normal component of 𝐹⃗ over 𝑆. 𝐹 𝑝= Pa 𝑆 𝑝 = 1 Pa = 1 N = 10 m 𝐹 𝑚 · 𝑎 𝑀·𝐿·𝑇 = = 𝑆 𝑆 𝐿 bar = 9.8692 · 10 = atm = 7.5006 · 10 N = Pa m Torr = 7.5006 · 10 mmHg PASCAL’S PRINCIPLE STATEMENT The effects of gravity are not considered. The weight of the fluid is not considered. “A change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all points in the fluid.” • The pressure is the same in all directions in any point of a fluid at equilibrium. • Pressure changes are transmitted equally at all points. APPLICATION: HYDRAULIC PRESS • Consists of two communicating cylinders that are provided with pistons of sections A and B and these are filled with a fluid (water or oil). • If a force 𝐹 is applied to 𝑆 , a pressure 𝑝 is being exerted, which is transmitted completely and instantaneously to the surface 𝑆 . 𝑆 By what factor is the force 𝐹 = 𝐹 being multiplied? 𝑆 HYDROSTATICS’ FUNDAMENTAL EQUATION STATEMENT The effects of gravity are considered The fluid weight is considered F5 z • Equilibrium X F =0 <latexit sha1_base64="dzT6iY41oAd1uZUvWmvEQcO+VDI=">AAAB/XicbZBLSwMxFIXv1Fetr6pLN8EiuCozRa0uhKIgLivYB7RDyaS3bWgmMyQZoQzF/+BWt+7Erb/FnT/FtHahrWf15Z5zyeUEseDauO6nk1laXlldy67nNja3tnfyu3t1HSWKYY1FIlLNgGoUXGLNcCOwGSukYSCwEQyvJ37jAZXmkbw3oxj9kPYl73FGjR012zoJyc2l28kX3KJ7elE+KxELUxFvHgowU7WT/2p3I5aEKA0TVOuW58bGT6kynAkc59qJxpiyIe1jy6KkIWo/nd47Jke9SBEzQDJ9/86mNNR6FAY2E1Iz0PPeZPivx6hkKOb+Nb1zP+UyTgxKZtes10sEMRGZVEG6XCEzYmSBMsXt5YQNqKLM2MJytpKFAhahXip6btG7OylUrmblZOEADuEYPChDBW6hCjVgIOAJnuHFeXRenTfn/SeacWY7+/BHzsc3OgqVVg==</latexit> F2 g F3 • Gravity on z-axis: F4 F1 x-axis: F1 = F2 y-axis: F3 = F4 <latexit sha1_base64="9DcPUw08eVYGV8UZIr5lCkY+92c=">AAAB/nicbZBLSwMxFIUz9VXrq+rSTbAIrspMUasLoSgUlxXsQ9phyKS3bWiSGZKMUIaC/8Gtbt2JW/+KO3+Kae1CW8/qyz3nkssJY860cd1PJ7O0vLK6ll3PbWxube/kd/caOkoUhTqNeKRaIdHAmYS6YYZDK1ZARMihGQ6vJ37zAZRmkbwzoxh8QfqS9Rglxo7uq4GHL3E1KAX5glt0Ty/KZyVsYSrszUMBzVQL8l+dbkQTAdJQTrRue25s/JQowyiHca6TaIgJHZI+tC1KIkD76fTgMT7qRQqbAeDp+3c2JULrkQhtRhAz0PPeZPivR4mkwOf+Nb1zP2UyTgxIates10s4NhGedIG7TAE1fGSBUMXs5ZgOiCLU2MZytpKFAhahUSp6btG7PSlUrmblZNEBOkTHyENlVEE3qIbqiCKBntAzenEenVfnzXn/iWac2c4++iPn4xvQGZUG</latexit> <latexit sha1_base64="18BEt4bl2CZ+0Yn4noC79pputaI=">AAAB/nicbZBLSwMxFIUz9VXrq+rSTbAIrspMrVYXQlEoLivYh7TDkEnvtKGZzJBkhDIU/A9udetO3PpX3PlTTGsX2npWX+45l1yOH3OmtG1/Wpml5ZXVtex6bmNza3snv7vXVFEiKTRoxCPZ9okCzgQ0NNMc2rEEEvocWv7weuK3HkAqFok7PYrBDUlfsIBRos3ovuad4Etc88pevmAX7dOLylkJG5gKO/NQQDPVvfxXtxfRJAShKSdKdRw71m5KpGaUwzjXTRTEhA5JHzoGBQlBuen04DE+CiKJ9QDw9P07m5JQqVHom0xI9EDNe5Phvx4lggKf+1cH527KRJxoENSsGS9IONYRnnSBe0wC1XxkgFDJzOWYDogkVJvGcqaShQIWoVkqOnbRuS0XqlezcrLoAB2iY+SgCqqiG1RHDURRiJ7QM3qxHq1X6816/4lmrNnOPvoj6+Mb1m2VCg==</latexit> Same weight of the solid F6 y x z-axis: M F⑯5 = F·6 + mg <latexit sha1_base64="tygYfd4YbIr6rnR2wHIyZ2z+ONg=">AAACBnicbZBLSwMxFIUzPmt9dNSlm2ARBKHMFNvqQigKxWUF+4B2GDLpnTY0mRmSjFBK9/4Ht7p1J279G+78Kaa1C209qy/3nEsuJ0g4U9pxPq2V1bX1jc3MVnZ7Z3cvZ+8fNFWcSgoNGvNYtgOigLMIGpppDu1EAhEBh1YwvJn6rQeQisXRvR4l4AnSj1jIKNFm5Nu5ml/CV7jml/EZFrjv23mn4JQuK+UiNjATdhchj+aq+/ZXtxfTVECkKSdKdVwn0d6YSM0oh0m2mypICB2SPnQMRkSA8sazwyf4JIwl1gPAs/fv7JgIpUYiMBlB9EAtetPhvx4lEQW+8K8OL7wxi5JUQ0TNmvHClGMd42knuMckUM1HBgiVzFyO6YBIQrVpLmsqWSpgGZrFgusU3LvzfPV6Xk4GHaFjdIpcVEFVdIvqqIEoStETekYv1qP1ar1Z7z/RFWu+c4j+yPr4BmuOlto=</latexit> V= S h . 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sha1_base64="rkQgvGaFX45Ala1aSMqSbIDP2zc=">AAAB/3icbZA7T8MwFIWd8irlVWBksaiQmKqkAgoDUgULY5HoQ7RR5bg3jVXbiWwHqYo68B9YYWVDrPwUNn4KbukALWf6fM+58tUJEs60cd1PJ7e0vLK6ll8vbGxube8Ud/eaOk4VhQaNeazaAdHAmYSGYYZDO1FARMChFQyvJ37rAZRmsbwzowR8QQaShYwSY0f3Al/iropi3OwVS27ZPb2onlWwhamwNw8lNFO9V/zq9mOaCpCGcqJ1x3MT42dEGUY5jAvdVENC6JAMoGNREgHaz6YXj/FRGCtsIsDT9+9sRoTWIxHYjCAm0vPeZPivR4mkwOf+NeG5nzGZpAYktWvWC1OOTYwnZeA+U0ANH1kgVDF7OaYRUYQaW1nBVrJQwCI0K2XPLXu3J6Xa1aycPDpAh+gYeaiKaugG1VEDUSTRE3pGL86j8+q8Oe8/0Zwz29lHf+R8fANRW5Xr</latexit> V =Sh <latexit 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sha1_base64="8WPCkXetEWAR1XFx+k52Rd6dJco=">AAACEHicbVDLSgMxFM34rPU16krcBIsgCGWm2FYFoejGZQX7gM4wZNI7ndDMgyQjlFL8B//BrW7diVv/wJ2fYlq70NYDuZzccy7JPX7KmVSW9WksLC4tr6zm1vLrG5tb2+bOblMmmaDQoAlPRNsnEjiLoaGY4tBOBZDI59Dy+9djvXUPQrIkvlODFNyI9GIWMEqUbnnmPq57ZXypawWfYEeEiXOBe/qEnlmwilb5vFopYU0mwPYsKaAp6p755XQTmkUQK8qJlB3bSpU7JEIxymGUdzIJKaF90oOOpjGJQLrDyQojfBQkAqsQ8OT+2zskkZSDyNeeiKhQzmrj5r8aJTEFPvOuCs7cIYvTTEFM9ZjWgoxjleBxOrjLBFDFB5oQKpj+OaYhEYQqnWFeRzIXwDxploq2VbRvTwu1q2k4OXSADtExslEV1dANqqMGougBPaFn9GI8Gq/Gm/H+Y10wpjN76A+Mj2/6q5pe</latexit> . <latexit sha1_base64="xgX5VlEEqzwPlFijp7hPNWDad1c=">AAACGnicbZDLSgMxFIYz9VbrrerSTbAIbiwzxbYqCEVduBzB1kJnKJn0TCc0cyHJCGXoA/gOvoNb3boTt27c+SimtQttPZDw5fz/IcnvJZxJZZqfRm5hcWl5Jb9aWFvf2Nwqbu+0ZJwKCk0a81i0PSKBswiaiikO7UQACT0Od97gcqzf3YOQLI5u1TABNyT9iPmMEqVb3WLJuQKuCLbxOba7VXyk95pmRwSxc4b7egXaZZbN6mm9VsEaJoWtWSihadnd4pfTi2kaQqQoJ1J2LDNRbkaEYpTDqOCkEhJCB6QPHY0RCUG62eQzI3zgxwKrAPDk/NubkVDKYehpT0hUIGe1cfNfjZKIAp+5V/knbsaiJFUQUT2mNT/lWMV4nBPuMQFU8aEGQgXTL8c0IIJQpdMs6EjmApiHVqVsmWXr5rjUuJiGk0d7aB8dIgvVUQNdIxs1EUUP6Ak9oxfj0Xg13oz3H2vOmM7soj9lfHwDoxad1w==</latexit> m = ⇢V P65 = P⑤ 6+⇢gh zbottom F =PS <latexit sha1_base64="Q0fTJ+4mdHx5gqjTxeyucAWgoOg=">AAAB/HicbZA7SwNBFIXvxleMr6ilzWAQrMJuUKOCEBTEMqJ5QLKE2cndZMjsg5lZISzxP9hqaye2/hc7f4qTmEITT/XNPecyl+PFgitt259WZmFxaXklu5pbW9/Y3Mpv79RVlEiGNRaJSDY9qlDwEGuaa4HNWCINPIENb3A19hsPKBWPwns9jNENaC/kPmdUm1Hj+qLaPid3nXzBLtrHZ+WTEjEwEXFmoQBTVTv5r3Y3YkmAoWaCKtVy7Fi7KZWaM4GjXDtRGFM2oD1sGQxpgMpNJ+eOyIEfSaL7SCbv39mUBkoNA89kAqr7atYbD//1GA0Zipl/tX/qpjyME40hM2vG8xNBdETGTZAul8i0GBqgTHJzOWF9KinTpq+cqWSugHmol4qOXXRujwqVy2k5WdiDfTgEB8pQgRuoQg0YDOAJnuHFerRerTfr/SeasaY7u/BH1sc3CI6UpA==</latexit> • Considering constant density, independent of the position HYDROSTATICS’ FUNDAMENTAL EQUATION Pressure difference between two points of a fluid at rest 𝑝 =𝑝 +𝜌𝑔ℎ Manometric Pressure • Difference in high between the points where pressure is measured • Pressure increases with Depth in the fluid • Difference of pressures between the two points depends only in the heigh distance between them. • Pressure at the free surface of the liquid (atmosphere) 𝑝 = 𝑝 • 𝑝−𝑝 =𝜌𝑔ℎ Communicating Vessels • Containers connected by a homogeneous liquid. • When the liquid is at rest, it reaches the same level in all vessels, regardless of shape or volume. • Atmospheric pressure and gravity are constant so hydrostatic pressure is always the same The pressure at each point is due to the weight of the column of fluid and air that it regardless of the geometry. supports. ARCHIMEDES’ PRINCIPLE STATEMENT • Real weight: 𝑃 = 𝑚 𝑔 • Apparent weight (𝑃 ): Weight of the object submerged in a fluid (𝑃 > 𝑃 ) ↳ Empuje Pap = PE Normal weight minus a force • Buoyancy (𝐸): • Upward force acting in the sense contrary to gravity 𝐸 =𝑃−𝑃 • Archimedes’ Principle: “Any object, totally or partially immersed in a fluid or liquid, is buoyed up by a force equal to the weight of the fluid displaced by the object.” The object The space 𝐸=𝜌 𝑔𝑉 the occupies in water 𝑃 (Weight) The volume will go up The volume of the rock Equal Volume 𝑃 (Apparent weight) ARCHIMEDES’ PRINCIPLE 𝐸=𝜌 𝑃=𝜌 𝑔𝑉 𝑔𝑉 It's the same in as occupies is The came 𝑃 =𝑃−𝐸 = 𝜌 fe 𝑃>𝐸 Sinks 𝑃=𝐸 Equilibrium 𝑃<𝐸 Ascends = m ,. 𝑃=𝐸 Floats g - my g . = −𝜌 pjVsy P Ve - - . g = both , the volume the object the same as the displaced volume 𝑔𝑉 (p pe)Vs - , • If 𝜌 >𝜌 →𝑃>𝐸→𝑃 > 0 → 𝑎 > 0 →The solid SINKS. • If 𝜌 =𝜌 →𝑃=𝐸→𝑃 = 0 → 𝑎 = 0 →The solid is SUBMERGED, but at rest. • If 𝜌 <𝜌 →𝑃<𝐸→𝑃 < 0 → 𝑎 < 0 →The solid ASCENDS until FLOATING - g • In flotation, part of the volumen of the solid (𝑉 ∗ ) is suberged in the fluid in such way that an equilibrium between weight and buayancy exists: The inmerse part compensates the outside part 𝜌 ∗ 𝑔𝑉 =𝜌 𝑔𝑉 𝜌 𝑉 = 𝜌 ∗ 𝑉 𝑚 = 𝜌 COMPRESSIBLE FLUIDS: GASES • Gases normally occupy the entire container in which they are contained.. • As the temperature of a gas contained in a container increases, the pressure increases. • If the gas expands at constant temperature, its pressure decreases. BOYLE’S LAW: • At constant temperature, the volume of a given mass of gas is inversely proportional to the pressure. • The product of pressure times the volume of a gas is constant at constant temperature. 𝑝𝑉 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 ⇒ 𝑝 𝑉 = 𝑝 𝑉 CHARLES’ LAW: • At constant pressure, the volume of a given mass of gas is directly proportional to the temperature. • The ratio of volume to temperature of a gas is constant at constant pressure. 𝑉 𝑉 𝑉 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 ⇒ = 𝑇 𝑇 𝑇 COMPRESSIBLE FLUIDS: GASES GAY LUSSAC’S LAW: • At constant volume, the pressure of a given mass of gas is directly proportional to the temperature. • The ratio of pressure to temperature of a gas is constant at constant volume. 𝑝 𝑝 𝑝 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 ⇒ = 𝑇 𝑇 𝑇 • When the pressure and temperature of a gas vary simultaneously, the Boyle and Charles equations can be combined and the following equation is obtained: 𝑝 𝑉 𝑝 𝑉 = 𝑇 𝑇 IDEAL GAS AND IDEAL GAS LAW • Gases diluted far from their liquefaction point Atoms/molecules do not interact with each other 𝑝𝑉 = 𝑛𝑅𝑇 State equation of ideal gases COMPRESSIBLE FLUIDS: GASES IDEAL GAS LAW • • • • 𝑝𝑉 = 𝑛𝑅𝑇 n, is the number of moles of the gas R, is the ideal gas constant. 𝑅 = 8.314 J/(K · mol) = 0.08205 (atm · L)/(K · mol) p (pressure), V (volume) y T (temperature) are the three state variables Under normal conditions of pressure (1 atm) and temperature (20 ℃), most real gases behave qualitatively as an ideal gas. COMPRESSIBLE FLUIDS: GASES DALTON’S LAW • In a mixture of gases, each constituent of the mixture exerts a partial pressure equal to that which it would exert if it only occupied a volume equal to that of the mixture at the same temperature. ni is the number of moles of the i-th gas 𝑛 𝑅𝑇 T is the temperatura of the mixture 𝑃 = V is the volume occupied by the mixture 𝑉 • The total pressure of the mixture is equal to the sum of the partial pressures of all the components. 𝑝 = ∑𝑃 𝑃 = 𝑛 = 𝑝 𝑛 GAS EXCHANGE IN BLOOD GAS DILUTION IN LIQUIDS. HENRY’S LAW • Dilution of a gas in liquid: a certain number of gas molecules pass into the liquid when they come into contact. Independent chemical reaction. • Solubility: ratio between dissolved gas volume and liquid volume. • Henry’s Law: “The amount of gas that can be dissolved in the unit volume of the liquid is proportional to the pressure of the gas (𝑃 ) for a given temperature” 𝑉 𝑉 = 𝛼𝑃 𝑉 : diluted gas volume 𝑉 : liquid volume α: solubility coefficient 𝜶 depends on the nature of the gas and the liquid, as well as on the temperature ↑ 𝑻 ⇒↓ 𝜶 ⇒ lower amount of gas diluted in the liquid ↑ 𝑷𝒈𝒂𝒔 ⇒ larger amount of gas diluted in the liquid GAS MIXTURE: • Each gas behaves according to Dalton’s Law. 𝑃 is the partial pressure of each gas. GAS EXCHANGE IN BLOOD PARTIAL PRESSURE OF A GAS IN BLOOD 𝑉 = 𝛼𝑃 𝑉 𝑃 : partial pressure to fulfill Henry’s Law Oxygen Equilibrium 𝑃 = 𝑃 Partial pressure of oxygen outside blood 𝑃 Absorption 𝑃 < 𝑃 Emanation 𝑃 >𝑃 𝑃 Blood Partial pressure of oxygen inside blood CO2 H2O N2 O2 Otros Alveolar air 40 (5) 47 (6) 570 (75) 100 (13) 3 (0.5) Dry Air - - 593 (78) 160 (21) 7 (1) Partial pressureas (Torr) in alveolar air and dry air for a total pressure of 760 Torr. Percetage ratio shown in parenthesis. GAS EXCHANGE IN BLOOD Venous Blood Tissue 𝑃 = 30 𝑇𝑜𝑟𝑟 𝑃 = 50 𝑇𝑜𝑟𝑟 𝑃 𝑃 CO2 = 40 𝑇𝑜𝑟𝑟 = 46 𝑇𝑜𝑟𝑟 𝑃 = 100 𝑇𝑜𝑟𝑟 𝑃 = 40 𝑇𝑜𝑟𝑟 Arterial Blood O2 Alveoli 𝑃 = 100 𝑇𝑜𝑟𝑟 𝑃 = 40 𝑇𝑜𝑟𝑟 GAS TRANSPORT IN BLOOD • In general, the amount of a gas in the blood conforms well to Henry's law (eg, N2). • Existing amount of O2 and CO2 is due to: (1) diluted gas and (2) chemically combined DILUTED • O2 is transported in the blood by two mechanisms: DILUTION OF DE O2 IN BLOOD PLASMA • Conditioned by the solubility of O2 in the plasma. COMBINED WITH HEMOGLOBIN 𝑉 𝑉 = 𝛼𝑃 Henry’s Law In 1 L of blood plasma at 38°C with a partial pressure of O2 of 100 Torr, there are diluted 3.1 mL of O2. Knowing that the solubility at that temperature is equal to 𝛼 = 0.023 𝑎𝑡𝑚 COMBINED WITH HEMOGLOBIN IN RED BLOOD CELLS • Hemoglobin:  Captures O2 in alveoli and takes it to tissues. Captures CO in tissues and takes it to lungs for expulsion. 𝐻𝑏 + 𝑂 ⟷ 𝐻𝑏𝑂 (𝑜𝑥𝑖ℎ𝑒𝑚𝑜𝑔𝑙𝑜𝑏𝑖𝑛) Equilibrium: equilibrium constant  If hemoglobin is completely saturated (transport 4 O2 molecules) Hb + 4𝑂 ⟷ 𝐻𝑏𝑂 GAS TRANSPORT IN BLOOD COMBINED WITH HEMOGLOBINE IN RED BLOOD CELLS In 1 L of blood plasma at 38 ℃ with a partial pressure of 𝑂 of 100 Torr, there are diluted 3.1 mL of 𝑂 knowing that the solubility at that temperature is 𝛼 = 0.023 atm . Blood with a normal proportion of fully oxygenated red blood cells and in equilibrium with oxygen at 100 Torr in the alveoli contains 20 cm3 of O2 for every 100 cm3 of blood. ⁄ ⁄ = , , = 64,5 ⇒ Red blood cells are 60 times more efficient at storing O2 than blood plasma. • Saturation curve of hemoglobin (O2): The effective degree of saturation of hemoglobin depends on the partial pressure of oxygen: pH = 7.4 and T = 38 °C GAS TRANSPORT IN BLOOD COMBINED WITH HEMOGLOBINE IN RED BLOOD CELLS For 𝑃 < 40 Torr The greatest release of O2 occurs Any change in PO2 causes a change in the ability of Hb to combine with O2 Variation with height Immersion pH=7.4 y T= 38 °C PHYSIOLOGICAL EFFECTS PHYSIOLOGICAL EFFECTS OF LOW PRESSURE ALTITUDE SICKNESS: tachycardia, malaise, headache, nausea and vomiting, drowsiness... Linear region vs biological compensation mechanisms. Increase in height affects the acquisition of O2 by hemoglobin (see Hb figure) ↑ heart and respiratory rate O2 transport is impaired 600 m “critical hypoxia” rapid loss of neuromuscular control and consciousness Límite vital crítico (30 Torr) muerte O2 Alveolar pressures as a function of total atmospheric pressure and height PHYSIOLOGICAL EFFECTS PHYSIOLOGICAL EFFECTS OF LOW PRESSURE DECOMPRESSIONS: very rapid decrease in pressure caused by rapid ascent DIVER'S DISEASE Immersion: air breathed same pressure as outside. If there is a significant difference in pressure in the muscles, they do not favor aspiration. At shallow depths ↑ 𝑃 increased amount of gases dissolved in body fluids that can be harmful In rapid decompressions by ↓ 𝑃 suddenly, producing embolisms. the gases can be released Air dive depth limit is 90 m: 𝑃 = 𝑃 + 𝜌𝑔ℎ = 10 atm and 𝑃 2 atm = How have cetaceans adapted to descend at large depths? DENSITY MEASUREMENT PYCNOMETER  Density of solids and fluids  Density of solids 𝑚 −𝑚 𝜌 = 𝜌 𝑚 −𝑚 m1: mass of solid and pycnometer filled with water m2: mass pycnometer filled with water m3: mass of pycnometer with solid inside and having removed water displaced  Densidad de líquidos 𝜌 = 𝑚 −𝑚 𝜌 𝑚 −𝑚 m1: mass of empty pycnometer m2: mass pycnometer filled with water m3: mass of the pycnometer filled with the problem fluid DENSITY MEASUREMENT HYDROSTATIC BALANCE Archimedes Balance  Liquids Density  Using Archimedes Principle Mörh-Westphal Balance 𝐸 = 𝐸 PRESSURE MEASUREMENT FREE AIR MANOMETER (U TUBE).  Used to measure the pressure of fluids contained in a container  Consists of a tank with a fluid whose pressure we want to measure connected to a U-shaped tube containing a fluid (normally Hg) connected to the atmosphere 𝑝=𝑝 + 𝜌𝑔ℎ MERCURY BAROMETER. ATMOSPHERIC PRESSURE MEASUREMENT.  Used to measure atmospheric pressure.  The tube contains Hg. The height of the fluid in the tube tells us the atmospheric pressure.  At sea level, the height of mercury is 760 mmHg. 𝑃 = 𝜌𝑔ℎ