DOCSLIB.ORG

Effects of Temperature and Molecular Weight on the Porous Structure Formation of Polymer Chemical Gels

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Effects of Temperature and Molecular Weight on the Porous Structure Formation of Polymer Chemical Gels Polymer Journal. Vol. 31, No.5, pp 447-451 (1999) Effects of Temperature and Molecular Weight on the Porous Structure Formation of Polymer Chemical Gels Toshiaki MIURA, Ryoichi KISHI, and Hisao lcHuo National Institute of' Materials and Chemical Research, Twkuha. Jharaki 305 8565. Japan (Received November 5, 1998) ABSTRACT: The e!Tects of temperature and molecular weight on the formation of inhomogeneous polymer gels, in which chemical gelation and phase separation take place simultaneously, were investigated. Slow chemical gelation by gamma ray irradiation was suitable for systematic analysis. In starting from ordinary polymer solutions, the characteristic wavenumber of the porous structure decreases very sharply with depth of temperature jump. However, with appropriate amount of pre-dose, the effects of temperature are almost taken over by those of the pre-dose. The shape of the phase boundary also contributes to this temperature insensitive region. Hence, pre-dose of polymer solutions. which induces the molecular weight build up, is an important factor that facilitates controlled preparations of inhomogeneous porous structures of chemical gel networks. KEYWORDS Poly(vinylmethylether) I Chemical Gels I Porous Structure I Pre-Dose I Polymer gels continue to attract considerable interest tempts.l. 2 bulk PVME gels of porous structures were from experimental and theoretical points of view. Some obtained without temperature control. In this case. the polymer gels show sharp transition in volume by temperature of the sample cells increased gradually from changing temperature or solvent. However, the slow the room temperature to around 500C. due to the heat dynamics of gels sometimes restricts applications. One transmitted from the radiation source as shown in Figure effective method to improve this slow dynamics is to use I. However. when we tried to prepare the same porous various higher order structures instead of homogeneous PVME gels with controlled stepwise temperature jump gels. The inhomogeneous gels that have interconnected above the phase separation point. we were not able to porous structure are examples. The volume relaxation obtain such porous gels. We only found that the dense times of inhomogeneous gels of appropriate porous homogeneous gels precipitated to the bottom of sample structures are several hundred times faster than homo­ cells in most cases. This seems strange and one question geneous gels. 1 - 4 For the preparation of gel networks arises. Is the gradual temperature increase the essential with large inhomogeneity in the order of hundred mi­ factor for the preparation of inhomogeneous polymer crometers. it is very effective to use phase separations. chemical gels? In order to clarify this problem and find The phase separation produces polymer rich and solvent suitable preparation conditions, quantitative analysis rich region. The competition of the phase separation and that systematically changes the experimental conditions gelation leads to inhomogeneous gels. We reported on in the porous structure formation of polymer chemical the rapid responsive porous poly(vinylmethylether) gels is necessary. This study investigates the effects of (PVME) gels that are prepared by }'-ray irradiation 1 . preparation temperature and molecular weight of the This corresponds to the simultaneous phase separation polymer solutions in detail and finds out the essential and chemical gelation. Preparations of porous gels have factors that determine the inhomogeneity of chemical gel also been reported on other gels as poly(N-isopropyl­ networks. acrylamide) gels 5 or some physical gels. 6 - 9 some of which were prepared by freezing and toughening. Polymer solutions from which chemical gels are produced 50 have strong concentrations or molecular weight de­ pendency in viscoelastic properties, which may add additional features that are different from polymer u 40 blends. Although the studies on competitive phase ....Cl> separation have been extensive for polymer blends, 1 0 - 14 ::I there is little detailed quantitative analysis on the -nl.... Cl> formation of porous chemical gels. This is partly because 0. E 30 the control of the gelation speed is usually difficult for the polymer chemical gels. However. by adopting the chemical gelation by }'-ray irradiation, the speed of gelation reaction is directly related to the exposure. 20 2 4 6 8 10 Hence, it becomes easy to control this experimental 0 Time (h) parameter. The size of porous structure depends on the balance Figure I. Without temperature control, the temperature of the irradiation cell increases gradually due to heat transmitted from the of the phase separation speed and gelation speed. radiation source. In our previous attempts, opaque gels with the However. the actual preparation of inhomogeneous inhomogeneous porous structures were obtained only at this condition. chemical gels has been very difficult. In previous at- Dashed line indicates the point where phase separation begins. 447 T. MIURA, R. KISHI, and H. !CHIJO Temperature r -ray Cross-linking Temperature u Jump __T_.' +-C---------1--------J 35 e::I 41 Time c.. E 30 1-phase region {! Gelation Time Molecular Weight 25 0 20 40 60 80 100 Concentration(%) Figure 3. A phase diagram of PVME solutions. Filled circles indicate the boundary of one-phase region and two-phase region. Above the open circles, phase separation takes place very rapidly. Inhomogeneous gels thus obtained were cooled and immersed in water at 25oC for observation. Porous A structures of thin gel films were observed using a phase contrast optical microscope. Microscopic images were Time recorded on videotape. Characteristic length of these porous gels was calculated by image analysis using a personal computer. Two-dimensional Fourier transfor­ Gelation Time mation of a real space image gives us the wave space information, equivalent to the results that can be Gelation Threshold obtained by light scattering. Since the microscopic images are not periodic, the procedure to reduce the edge effect Figure 2. Experimental scheme to change chemical gelation speed. is necessary. We cut the original images whose sizes are 640 x 480 pixels to those of 400 x 400 pixels. These images EXPERIMENTAL were extrapolated to 512 x 512 by zero padding. The fast Fourier transformation (FFT) was applied using the Aqueous solution of PVME (Tokyo Kasei Co., Ltd.) hamming window function. Since these gels are isotropic, was used without further purification. Weight-averaged we calculated the radial distribution of FFT intensity by molecular weight was 92000 (M,) Mn = 3.3) measured averaging the two-dimensional FFT results for all from GPC. We prepared narrowly distributed PVME directions. The scattering functions were averaged over samples by GPC fractionation. Fractionated PVME many snapshots of gels. was weight-averaged molecular weight of 83000 with polydispersity of 1.24. The phase diagram of PVME RESULTS AND DISCUSSION solutions was determined by phase contrast microscope (Olympus BH-2) and differential scanning calorimeter Since the phase separation temperature is the baseline (Seiko Instruments SSC5200). to determine the depth of the temperature jump, we first PVME solution of 30wt% becomes gel with irradia­ determined the phase diagram of our PVME samples tion of 21.4 kGy (21.4 kJ kg -l) of the y-ray from the with narrow molecular weight distribution. As shown 6 °Co source (IIOTBq). The dose rate was 8.56kGyh- 1 . in Figure 3, the PVME solution becomes two-phase in the The gelation threshold of PVME solution depends on high temperature region. Although the phase boundary the concentrations of polymers as reported elsewhere. 15 between the mixed region and two-phase region has Temperature jump was carried out by circulating the unique dependency on the polymer concentration, phase temperature-controlled water around the sample cells. separation becomes very fast over 35°C, from which Experimental conditions of the temperature jump and endothermic also showed a sharp increase. Opaque irradiation are illustrated in Figure 2. In addition to the inhomogeneous gels were not obtained below 35°C. The temperature factor. we changed the molecular weight of shape of the phase diagram of PVME does not come polymer solution by pre-dose. By inducing the molecular from the polydispersity effect of the polymer samples, weight build up of polymer sample, the gelation time since we used fractionated samples. It may be ascribed decreases. Specifically, when the original polymer to the specific hydrophobic interaction of PVME. There solution becomes gel with the irradiation of time tgei• we was no significant difference in the transition points prepare samples that are irradiated for 0.2tgei• 0.4tgei• between fractionated samples and original ones. Hence, 0.6! gel· and 0.8/ gel at room temperature before simul­ we used the original PVME samples hereafter. taneous phase separation and chemical gelation. As Figure 4 shows typical results of image analysis for shown in Figure 2, pre-dosed polymer solutions form the inhomogeneous gel samples. The temperature of gels with irradiation of 0.8/gei• 0.6tgei• 0.4tgeb 0.2/gel re­ the preparation was 39oC and pre-dose amount was spectively, which are faster than the original polymer 17.1 kGy. As with ordinary phase separation of binary solution. solutions, the scattering function of inhomogeneous gels 448 Polym. J., Vol. 31, No. 5, 1999 Porous Structure Formation of Polymer Chemical Gels 0.2 48 46 Ill VI 544 c: 0.1 Ill 'Iii c: lii 42 - 0. E40 38 0 104 105 10' 107 Wavenumber (m.') 5 10 15 Pre-dose (kGy) Figure 4. Typical example of the scattering functions of the in­ homogeneous chemical gels. Figure 5. Structure mapping of inhomogeneous PVME gels obtained from 30 wt% solutions. The darkness represents the characteristic showed a broad peak. Hereafter, we use this peak porous size of gels. This chart is painted with seven ranges in the darkness, in which the brighter part indicates the larger porous wavenumber as the convenient characteristic length of structure. The length range is from 25 .urn to 210 .urn. Boundaries of the porous structure.
Load more

Recommended publications
  • Simple Experiment Confirming the Negative Temperature Dependence of Gravity Force
    SIMPLE EXPERIMENT CONFIRMING THE NEGATIVE TEMPERATURE DEPENDENCE OF GRAVITY FORCE Alexander L. Dmitriev St-Petersburg National Research University of Information Technologies, Mechanics and Optics, 49 Kronverksky Prospect, St-Petersburg, 197101, Russia Results of weighing of the tight vessel containing a thermo-isolated copper sample heated by a tungstic spiral are submitted. The increase of temperature of a sample with masse of 28 g for about 10 0 С causes a reduction of its apparent weight for 0.7 mg. The basic sources of measurement errors are briefly considered, the expediency of researches of temperature dependence of gravity is recognized. Key words: gravity force, weight, temperature, gravity mass. PACS: 04.80-y. Introduction The question on influence of temperature of bodies on the force of their gravitational interaction was already raised from the times when the law of gravitation was formulated. The first exact experiments in this area were carried out at the end of XIXth - the beginning of XXth century with the purpose of checking the consequences of various electromagnetic theories of gravitation (Mi, Weber, Morozov) according to which the force of a gravitational attraction of bodies is increased with the growth of their absolute temperature [1-3]. That period of experimental researches was completed in 1923 by the publication of Shaw and Davy’s work who concluded that the temperature dependence of gravitation forces does not exceed relative value of 2⋅10 −6 K −1 and can be is equal to zero [4]. Actually, as shown in [5], those authors confidently registered the negative temperature dependence of gravitation force.
    [Show full text]
  • Weight and Lifestyle Inventory (Wali)
    WEIGHT AND LIFESTYLE INVENTORY (Bariatric Surgery Version) © 2015 Thomas A. Wadden, Ph.D. and Gary D. Foster, Ph.D. 1 The Weight and Lifestyle Inventory (WALI) is designed to obtain information about your weight and dieting histories, your eating and exercise habits, and your relationships with family and friends. Please complete the questionnaire carefully and make your best guess when unsure of the answer. You will have an opportunity to review your answers with a member of our professional staff. Please allow 30-60 minutes to complete this questionnaire. Your answers will help us better identify problem areas and plan your treatment accordingly. The information you provide will become part of your medical record at Penn Medicine and may be shared with members of our treatment team. Thank you for taking the time to complete this questionnaire. SECTION A: IDENTIFYING INFORMATION ______________________________________________________________________________ 1 Name _________________________ __________ _______lbs. ________ft. ______inches 2 Date of Birth 3 Age 4 Weight 5 Height ______________________________________________________________________________ 6 Address ____________________ ________________________ ______________________/_______ yrs. 7 Phone: Cell 8 Phone: Home 9 Occupation/# of yrs. at job __________________________ 10 Today’s Date 11 Highest year of school completed: (Check one.) □ 6 □ 7 □ 8 □ 9 □ 10 □ 11 □ 12 □ 13 □ 14 □ 15 □ 16 □ Masters □ Doctorate Middle School High School College 12 Race (Check all that apply): □ American Indian □ Asian □ African American/Black □ Pacific Islander □White □ Other: ______________ 13 Are you Latino, Hispanic, or of Spanish origin? □ Yes □ No SECTION B: WEIGHT HISTORY 1. At what age were you first overweight by 10 lbs. or more? _______ yrs. old 2. What has been your highest weight after age 21? _______ lbs.
    [Show full text]
  • Ideal Gasses Is Known As the Ideal Gas Law
    ESCI 341 – Atmospheric Thermodynamics Lesson 4 –Ideal Gases References: An Introduction to Atmospheric Thermodynamics, Tsonis Introduction to Theoretical Meteorology, Hess Physical Chemistry (4th edition), Levine Thermodynamics and an Introduction to Thermostatistics, Callen IDEAL GASES An ideal gas is a gas with the following properties: There are no intermolecular forces, except during collisions. All collisions are elastic. The individual gas molecules have no volume (they behave like point masses). The equation of state for ideal gasses is known as the ideal gas law. The ideal gas law was discovered empirically, but can also be derived theoretically. The form we are most familiar with, pV nRT . Ideal Gas Law (1) R has a value of 8.3145 J-mol1-K1, and n is the number of moles (not molecules). A true ideal gas would be monatomic, meaning each molecule is comprised of a single atom. Real gasses in the atmosphere, such as O2 and N2, are diatomic, and some gasses such as CO2 and O3 are triatomic. Real atmospheric gasses have rotational and vibrational kinetic energy, in addition to translational kinetic energy. Even though the gasses that make up the atmosphere aren’t monatomic, they still closely obey the ideal gas law at the pressures and temperatures encountered in the atmosphere, so we can still use the ideal gas law. FORM OF IDEAL GAS LAW MOST USED BY METEOROLOGISTS In meteorology we use a modified form of the ideal gas law. We first divide (1) by volume to get n p RT . V we then multiply the RHS top and bottom by the molecular weight of the gas, M, to get Mn R p T .
    [Show full text]
  • MAXIMUM METABOLISM FOOD METABOLISM PLAN the MAXIMUM Hreshold Spinach Salad: 1 Cup Spinach, 1/2 Cup Mixed 6 Oz
    THE MAXIMUM METABOLISM FOOD PLAN™ WEEK ONE SUNDAY MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY Breakfast 3/4 oz. multi-grain cereal 1/2 cup oatmeal 2 lite pancakes (4” diameter); use non-stick 1 slice of wheat toast; top with 1/2 cup 1 1/2 oz. low fat granola Apple cinnamon crepe: 1 wheat tortilla, Omelet: 3 egg whites, 1 cup mixed zucchini, 1/2 sliced banana or 3/4 cup sliced 1/2 tbs. raisins pan; top with 1/2 cup peaches or 1/2 banana nonfat cottage cheese and 1/2 sliced 1 cup nonfat milk 1/3 cup nonfat ricotta cheese, 1 apple green peppers, onions, and tomatoes, 12 oz. of water before breakfast strawberries 1/2 cup nonfat milk 1 tbs. reduced calorie syrup apple; sprinkle with 1 tsp. cinnamon 1/2 medium banana (sliced), 1 tsp. cinnamon, 1/2 tsp. vanilla 2 oz. reduced calorie cheese, and salsa 1/2 cup nonfat milk 1 medium apple 1/2 cup low fat maple yogurt extract; heat in skillet over low flame 1 slice wheat toast 1/2 cup nonfat milk 1 tsp. butter Mid-Morning Snack 12 oz. water 12 oz. water 12 oz. water 12 oz. water 12 oz. water 12 oz. water 12 oz. water 1/2 bagel 1/2 cup nonfat yogurt 1/2 cup low fat cottage cheese 1 cup nonfat flavored yogurt with 1 tsp. 1 cup flavored nonfat yogurt 1 cup flavored nonfat yogurt 1 cup flavored nonfat yogurt 1 tbs. nonfat cream cheese 1/2 cup pineapple chunks sliced almonds 1 tbs.
    [Show full text]
  • The Relation of Metabolic Rate to Body Weight and Organ Size
    Pediat.Res. 1: 185-195 (1967) Metabolism basal metabolic rate growth REVIEW kidney glomerular filtration rate body surface area body weight oxygen consumption organ growth The Relation of Metabolic Rate to Body Weight and Organ Size A Review M.A. HOLLIDAY[54J, D. POTTER, A.JARRAH and S.BEARG Department of Pediatrics, University of California, San Francisco Medical Center, San Francisco, California, and the Children's Hospital Medical Center, Oakland, California, USA Introduction Historical Background The relation of metabolic rate to body size has been a The measurement of metabolic rate was first achieved subject of continuing interest to physicians, especially by LAVOISIER in 1780. By 1839 enough measurements pediatricians. It has been learned that many quanti- had been accumulated among subjects of different tative functions vary during growth in relation to sizes that it was suggested in a paper read before the metabolic rate, rather than body size. Examples of Royal Academy of France (co-authored by a professor these are cardiac output, glomerular filtration rate, of mathematics and a professor of medicine and oxygen consumption and drug dose. This phenomenon science) that BMR did not increase as body weight may reflect a direct cause and effect relation or may be increased but, rather, as surface area increased [42]. a fortuitous parallel between the relatively slower in- In 1889, RICHET [38] observed that BMR/kg in rab- crease in metabolic rate compared to body size and the bits of varying size decreased as body weight increased; function in question. RUBNER [41] made a similar observation in dogs. Both The fact that a decrease in metabolism and many noted that relating BMR to surface area provided re- other measures of physiological function in relation to a sults that did not vary significantly with size.
    [Show full text]
  • Chapter 28 Pressure in Fluids
    CHAPTER 28 PRESSURE IN FLUIDS EXERCISE 128, Page 281 1. A force of 280 N is applied to a piston of a hydraulic system of cross-sectional area 0.010 m 2 . Determine the pressure produced by the piston in the hydraulic fluid. force 280 N Pressure, p = = 28000Pa = 28 kPa area 0.010m2 That is, the pressure produced by the piston is 28 kPa 2. Find the force on the piston of question 1 to produce a pressure of 450 kPa. Pressure, p = 450 kPa = 450000 Pa force Pressure p = hence, force = pressure × area area = 4540000 × 0.010 = 4500 N = 4.5 kN 3. If the area of the piston in question 1 is halved and the force applied is 280 N, determine the new pressure in the hydraulic fluid. 0.010 New area = 0.005m2 2 force 280 N New pressure, p = = 56000Pa = 56 kPa area 0.005m2 331 © John Bird Published by Taylor and Francis EXERCISE 129, Page 283 1. Determine the pressure acting at the base of a dam, when the surface of the water is 35 m above base level. Take the density of water as 1000 kg/m 3 . Take the gravitational acceleration as 9.8 m/s 2 . Pressure at base of dam, p = gh = 1000 kg/m 3 9.8 m/s2 0.35 m = 343000 Pa = 343 kPa 2. An uncorked bottle is full of sea water of density 1030 kg/m 3 . Calculate, correct to 3 significant figures, the pressures on the side wall of the bottle at depths of (a) 30 mm, and (b) 70 mm below the top of the bottle.
    [Show full text]
  • 11 Archimedes Principle
    Exp 11-1 P Experiment 11. Archimedes' Principle An application of Archimedes' principle - a piece of iron - sinks while a steel cup of the same weight floats on water. Objective: (a) To determine the specific gravity of a liquid by using a hydrometer. (b) the specific gravity of a solid heavier than water, the specific gravity of a liquid and the specific gravity of a solid lighter than water by· apj51yThg___Arcn1medes' principle: -- ····------···· --·-···- Apparatus: A balance, a solid heavier than water, a wooden cylinder, a hydrometer, alcohol and distilled water Theory: According to Archimedes' principle, when a body is immersed in a fluid (Fig. 1 ), either wholly or partially, the fluid exerts a buoyant force 8 on it. This buoyant force is equal to the weight of the fluid displaced by the body. Thus the apparent weight of the body is less than its actual weight, the loss of weight being equal to the buoyant force. - W = weight of the body B = buoyant force T = tension in the string supporting the body Fig. 1 Fig. 2 Consider the following problem: Weight of the body in air (actual weight of the body), w = 600 gm-wt Volume of the body, V = 80 cm3 Density of the liquid, p = 1.2 gm/cm 3 Volume of the liquid displaced = volume of the bodyVe = 80 cm3 Weight of the liquid displaced, we= Vex p = 96 gm-wt Buoyant force, B = 96 gm-wt Apparent weight of the body, wa = 600 - 96 gm-wt = 504 gm-wt Note that the apparent loss of weight of the body is equal to the - buoyant force of the fluid acting on the body, which, in turn, is equal to Exp 11-2P the weight of the flui9 displaced by the body.
    [Show full text]
  • View the August Table of Excluded Times Due to Low Tides
    WHATCOM COUNTY Ferry Department PUBLIC WORKS DEPARTMENT 322 N. Commercial Street, Suite 210 Bellingham, WA 98225-4042 JON HUTCHINGS Telephone: (360) 778-6200 DIRECTOR FAX: (360) 778-6201 www.whatcomcounty.us July 30, 2020 To Whom It May Concern: Re: Lummi Island Ferry Use Due to the damage we have incurred during low tides on the loading ramps at both Gooseberry Point and Lummi Island, we have had to find a solution to alleviate this problem. The ensuing policy was recommended by the Whatcom County Public Works Engineering Division, was reviewed by the County, and this policy was implemented effective May 22, 1995. NO TRUCK OVER 40,000 GVW WILL BE PERMITTED ON THE FERRY AT ANY TIDE UNDER ZERO The following timetable should assist you in scheduling deliveries to Lummi Island; however, should you have any questions regarding this timetable, please do not hesitate to contact the Whatcom Chief Ferry at (360) 815-5629. If you would like to be put on our Tide Table mailing list please contact Public Works Administration at (360) 778-6200 or email [email protected]. All times are acceptable, except as noted in the following tide timetable. AUGUST: 1 Between the hours of 8:10 a.m. - 12:15 p.m. excluded. 2 Between the hours of 8:55 a.m. - 1:00 p.m. excluded. 3 Between the hours of 9:45 a.m. - 1:30 p.m. excluded. 4 Between the hours of 10:30 a.m. - 1:55 p.m. excluded. 5 Between the hours of 11:30 a.m.
    [Show full text]
  • 12. Methods of Surface Tension Measurements
    12. Methods of surface tension measurements There are several methods of surface tension measurements: 1. Capillary rise method 2. Stallagmometer method – drop weight method 3. Wilhelmy plate or ring method 4. Maximum bulk pressure method. 5. Methods analyzing shape of the hanging liquid drop or gas bubble. 6. Dynamic methods. 1. Capillary rise method This is the oldest method used for surface tension determination. A consequence of the surface tension appearance at the liquid/gas interface is moving up of the liquid into a thin tube, that is capillary, which is usually made of glass. This phenomenon was applied for determination of the liquid surface tension. For this purpose, a thin circular capillary is dipped into the tested liquid. If the interaction forces of the liquid with the capillary walls (adhesion) are stronger than those between the liquid molecules (cohesion), the liquid wets the walls and rises in the capillary to a defined level and the meniscus is hemispherically concave. In the opposite situation the forces cause decrease of the liquid level in the capillary below that in the chamber and the meniscus is semispherically convex. Both cases are illustrated in Fig. 11.1 Fig. 12.1. Schematic representation of the capillary rise method. If the cross-section area of the capillary is circular and its radius is sufficiently small, then the meniscus is semispherical. Along the perimeter of the meniscus there acts a force due to the surface tension presence. (1) f1 = 2π r γ cos θ Where: r – the capillary radius, γγγ – the liquid surface tension, θθθ – the wetting contact angle.
    [Show full text]
  • Experiment 12 Archimedes' Principle
    Experiment 12 Archimedes’ Principle Fig. 12-1 Equipment Graduated cylinder Triple Beam balance Pipette Wood cylinder Vernier caliper 2 Metal cylinders Rod & Clamp String Overflow container Experiment 12 Archimedes’ Principle Advance Reading: Serway & Jewett - Chapter 14, Section 14-4 Objective: The objective of this lab is to measure the buoyant force on a number of objects. Theory: Archimedes’ principle states that a body wholly or partially submerged in a fluid is buoyed up by a force equal in magnitude to the weight of the fluid displaced by the body. It is important to remember that fluid includes liquids and gases. This force is given by: FB = ρVg (Eq 1) where ρ (rho) is the density of the fluid, V is the volume of fluid displaced and g is acceleration due to gravity. It is the buoyant force that keeps ships afloat in water and hot air balloons floating in air. In this experiment, the buoyant force will be measured three ways and the results compared. The first method is by the measurement of force. This method involves weighing an object first in air, then in water, and using the difference in weight as the buoyant force. Though the object's mass does not change, its apparent weight will change when measured while immersed in a fluid that is denser than air. The second method is the displaced volume method. The volume of fluid displaced by the object is measured and its weight calculated. The weight of the water displaced is equal to the buoyant force exerted on the object, by Archimedes' Principle.
    [Show full text]
  • Hydrostatic Force on a Curved Surfaces
    Hydrostatic Force on a Curved Surfaces Henryk Kudela 1 Hydrostatic Force on a Curved Surface On a curved surface the forces pδA on individual elements differ in direction, so a simple summation of them may not be made. Instead, the resultant forces in certain directions may be determined, and these forces may then be combined vectorially. It is simplest to calculate horizontal and vertical components of the total force. Horizontal component of hydrostatic force Any curved surface may be projected on to a vertical plane. Take, for example, the curved surface illustrated in Fig. 1. Figure 1: Hydrostatic force on a curved surface Its projection on to the vertical plane shown is represented by the trace AC. Let Fx represent the component in this direction of the total force exerted by the fluid on the curved surface. Fx must act through the center of pressure of the vertical projection and is equal in magnitude to the force F on the fluid at the vertical plane. In any given direction, therefore, the horizontal force on any surface equals the force on the projection of that surface on a vertical plane perpendicular to the given direction. 1 The line of action of the horizontal force on the curved surface is the same as that of the force on the vertical projection. Vertical component of hydrostatic force The vertical component of the force on a curved surface may be determined by considering the fluid enclosed by the curved surface and vertical projection lines extending to the free surface. Thus FH = F2 = ρgzs (1) FV = F1 = ρgV (2) where V is the volume of the liquid between the free surface liquid and solid curved surface.
    [Show full text]
  • What Is a Healthy Weight?
    What Is A Healthy Weight? Your weight can affect your health and the way you feel about yourself. How much you weigh mainly depends on your lifestyle and your genes. A healthy weight is a weight that does not create health or other problems for you. Many people think this means they need to be thin or skinny. But being as “skinny” as a fashion model may not be what is healthy for you. Not everyone can or should be thin. But with the right choices, everyone can be healthier. Is my weight healthy? Use the chart below to find the maximum weight that is healthy for your height. MAXIMUM HEALTHY WEIGHT CHART Height Maximum Healthy (ft, in) Weight (lb) 5’0” 125 5’1” 125 5’2” 130 5’3” 135 5’4” 140 5’5” 145 5’6” 150 5’7” 155 5’8” 160 5’9” 165 5’10” 170 5’11” 175 6’0” 180 F-1 What is Body Mass Index (BMI)? Body Mass Index (BMI) adjusts your weight for your height. The maximum healthy weights shown in the chart on page F-1 are based on BMI. The higher your BMI is, the greater your chances of heart disease, stroke, high blood pressure, diabetes, osteoarthritis, some cancers, and/or sudden death. Do I have a healthy BMI? With a calculator, it is easy to figure out your BMI. Use this simple formula (using pounds and inches). Your weight X 703 BMI = Your height X your height The example below shows the BMI for Sarah, who is 5’3” (63”) and weighs 150 pounds.
    [Show full text]