What Is Bulk Modulus Definition, Formulas, Examples

The bulk modulus is a constant the describes how resistant a substance is to compression. It is defined as the ratio between pressure increase and the resulting decrease in a materials volume. Together with Youngs modulus, the shear modulus, and Hookes law, the bulk modulus describes a materials response to stress or strain. Usually, bulk modulus is indicated by K or B in equations and tables. While it applies to uniform compression of any substance, it is most often used to describe the behavior of fluids. It can be used to predict compression, calculate density, and indirectly indicate the types of chemical bonding within a substance. The bulk modulus is considered a descriptor of elastic properties because a compressed material returns to its original volume once the pressure is released. The units for the bulk modulus are Pascals (Pa) or newtons per square meter (N/m2) in the metric system, or pounds per square inch (PSI) in the English system. Table of Fluid Bulk Modulus (K) Values There are bulk modulus values for solids (e.g., 160 GPa for steel; 443 GPa for diamond; 50 MPa for solid helium) and gases (e.g., 101 kPa for air at constant temperature), but the most common tables list values for liquids. Here are representative values, in both English and metric units: English Units(105 PSI) SI Units(109 Pa) Acetone 1.34 0.92 Benzene 1.5 1.05 Carbon Tetrachloride 1.91 1.32 Ethyl Alcohol 1.54 1.06 Gasoline 1.9 1.3 Glycerin 6.31 4.35 ISO 32 Mineral Oil 2.6 1.8 Kerosene 1.9 1.3 Mercury 41.4 28.5 Paraffin Oil 2.41 1.66 Petrol 1.55 - 2.16 1.07 - 1.49 Phosphate Ester 4.4 3 SAE 30 Oil 2.2 1.5 Seawater 3.39 2.34 Sulfuric Acid 4.3 3.0 Water 3.12 2.15 Water - Glycol 5 3.4 Water - Oil Emulsion 3.3 2.3 The K value varies, depending on the state of matter of a sample, and in some cases, on the temperature. In liquids, the amount of dissolved gas greatly impacts the value. A high value of K indicates a material resists compression, while a low value indicates volume appreciably  decreases under uniform pressure. The reciprocal of the bulk modulus is compressibility, so a substance with a low bulk modulus has high compressibility. Upon reviewing the table, you can see the liquid metal mercury is very nearly incompressible. This reflects the large atomic radius of mercury atoms compared with atoms in organic compounds and also the packing of the atoms. Because of hydrogen bonding, water also resists compression. Bulk Modulus Formulas The bulk modulus of a material may be measured by powder diffraction, using x-rays, neutrons, or electrons targeting a powdered or microcrystalline sample. It may be calculated using the formula: Bulk Modulus (K) Volumetric stress / Volumetric strain This is the same as saying it equals the change in pressure divided by the change in volume divided by initial volume: Bulk Modulus (K) (p1 - p0) / [(V1 - V0) / V0] Here,  p0 and V0 are the initial pressure and volume, respectively, and p1 and V1 are the pressure and volume measured upon compression. Bulk modulus elasticity may also be expressed in terms of pressure and density: K (p1 - p0) / [(Ï 1 - Ï 0) / Ï 0] Here, Ï 0 and Ï 1 are the initial and final density values. Example Calculation The bulk modulus may be used to calculate hydrostatic pressure and density of a liquid. For example, consider seawater in the deepest point of the ocean, the Mariana Trench. The base of the trench is 10994 m below sea level. The hydrostatic pressure in the Mariana Trench may be calculated as: p1 Ï *g*h Where p1 is the pressure, Ï  is the density of seawater at sea level, g is the acceleration of gravity, and h is the height (or depth) of the water column. p1 (1022 kg/m3)(9.81 m/s2)(10994 m) p1 110 x 106 Pa or 110 MPa Knowing the pressure at sea level is 105 Pa, the density of the water at the bottom of the trench may be calculated: Ï 1 [(p1 - p)Ï  K*Ï ) / K Ï 1 [[(110 x 106 Pa) - (1 x 105 Pa)](1022 kg/m3)] (2.34 x 109 Pa)(1022 kg/m3)/(2.34 x 109 Pa) Ï 1 1070 kg/m3 What can you see from this? Despite the immense pressure on water at the bottom of the Mariana Trench, it isnt compressed very much! Sources De Jong, Maarten; Chen, Wei (2015). Charting the complete elastic properties of inorganic crystalline compounds. Scientific Data. 2: 150009. doi:10.1038/sdata.2015.9Gilman, J.J. (1969).  Micromechanics of Flow in Solids. New York: McGraw-Hill.Kittel, Charles (2005). Introduction to Solid State Physics  (8th edition). ISBN 0-471-41526-X.Thomas, Courtney H. (2013). Mechanical Behavior of Materials (2nd edition). New Delhi: McGraw Hill Education (India). ISBN 1259027511.

Creative Writing An Experience between Mother and Son

Running through the hospitals long white halls, he thought that his mom was going to die. The paramedics were right in front of him, but it felt as if they were a thousand miles away. Reaching his hand out, he began to holler: PLEASE STOP! PLEASE!, the words brittled from his mouth. He fell onto his knees, in front of him the white floor had droplets of blood that was coming out of his mother. Time passes, the boy laying on the floor, motionless, Just looking at the flickering light above. I’ve found the boy, over. Bring him to O.R. #3. Gotcha. The nurse stopped and felt sympathy for the boy, he is lying on the ground just waiting. No child should go through this. The nurse said to herself. The nurse continued to walk, she as the boy lies on the ground; Hey buddy. How’s it going?. There was no answer from the boy. Lying down the cold floor was an indescribable pain. Come with me, okay? Reaching out her hand the boy responded by grabbing it. He looked up at the nurse, tears running down his face. The nurse did not want to show fear--but before looking for the boy, the nurse saw how severe the mother was. It was past twelve now, everything in the hospital is empty. Walking through the halls the boy saw how much pain and death there was in each room; unable to watch the pain he began to run. He ran down the hall as fast as he can, in his sight was an elevator. The sounds of coughing, vomiting, crying and yelling were just too much. The boy arrives to the elevator, theShow MoreRelatedAnalysis Of The Book Carte Blanche Essay1479 Words   |  6 Pagesall elements I considered when drafting ‘Time to let go.’ This narrative is not a direct recollection of my personal experience. But, interprets a devastating chain of events that happened to my son’s friend, and the effect this tragic accident had on a mother. I wanted to tell this story with as much sentiment and compassion as possible. 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Voices free essay sample

Yossarian desperately screams to Aarfy mid-flight commands, hell bent on survival. Yet, every response is the unwavering and infuriating â€Å"What? I can’t hear you.† A peculiar experience occurs every time I pore over the words of those moments. The Yossarian shouting for sacred life transforms, morphing into a familiar someone, me. Every word, every emotion, every thought is mine. I am the one screaming at Aarfy to listen to me, pleading, groveling, begging for sanctuary amidst the veritable storm of a plane careening to a fiery death. I am the one plunging to imminent obliteration, wishing only for someone to listen, to simply acknowledge my voice. I’ve never been in a plane, but that feeling, that horrendous, indignant anger is identical. No other event, save for one, has ever mirrored that feeling so closely, and I abhor that feeling. In the novel Catch-22 by Joseph Heller, a story following WWII Air Force pilots stationed near Italy, Yossarian, the protago nist, is determined to stay alive. We will write a custom essay sample on Voices or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page The pivotal character of Yossarian deeply influenced my life’s attitude. In particular, the aforementioned interactions with Aarfy, a plane crewmate who pretends that he can’t hear Yossarian during life-threatening bombing runs. Yossarian and I possess some vast differences, most notably that I’m not as cavalier with women (nor as successful), and I’m definitely not a pilot in the army. I also don’t have a deceased comrade’s lover stalking me with intent to kill. However, Yossarian’s repeated airplane plights with Aarfy struck a chord so deep within it resonated through every crevice in my body, empathy so primal I nearly crushed the book in my fingers. This empathy stems from a pivotal moment during my sophomore year. â€Å"Why won’t you listen to me?!† I shrieked, slamming my fists into the table. Heat emanated off my cheeks, and I panted heavily through clenched teeth. Furrows riddled my forehead, and I frantically sh ifted my eyes back and forth at my peers. They stared at me coldly, some with hanging jaws, but all with bewildered faces. Slowly, my fists unclenched themselves, and I slinked back into my chair, head hanging in quiet solitude. Class resumed awkwardly, and the game continued on, as if I had never screamed. â€Å"Next time, they’ll listen,† I muttered under my breath, and my eyes flicked back up to the teacher. The aforementioned English class outburst stands out in my mind as my first realization of my abhorrence towards ignorance. The occasion was a simple game, a basic class-building exercise for a little extra credit. As fate would have it, I played this exact game a year previous. Consequently, I knew the rules and I knew the winning strategy. Unfortunately, no one seemed to care, and slowly as they ignored my comments and suggestions I grew more and more irritated, more and more disillusioned with those around me, eventually culminating in my overemotional outbur st. That moment reflected that same anger I experienced when reading through Yossarian’s situations with Aarfy. It was through the parallels between my experiences and Yossarian’s that I looked to his actions to guide my own. At the end of the novel, his commanding officers, due to the trouble Yossarian has caused them with his rebellious attitude, offered him indefinite leave in exchange for embracing them as friends and upholding what he regards as twisted ideals. He vehemently rejects it, deserting the tangled heap of bureaucratic idiocy and flees to tie up his own affairs. Yossarian’s embrace of free will triggered an epiphany, that I, and only I, can make my voice heard.

Reading Habits Questionnaire free essay sample

Yes ii. No 2. If so, how often do you read news paper in a week? i. 1 ii. 2-3 iii. 4-5 iv. 6-7 3. If not, why don’t you read newspaper? i. Because of internet ii. Because of TV iii. Because of radio iv. Please specify the other reason 4. Which newspaper do you read? i. English ii. Hindi iii. Punjabi iv. Please specify the other 5. In average how many minutes do you read newspapers per day? i. 0-10 ii. 10-30 iii. 30-60 6. Where do you read your newspaper? . Home ii. Office 7. What is the most important criteria when you choose newspaper? 8. Which part in the newspaper is the one you like the most? i. News ii. Sports iii. Entertainment iv. Business v. Please specify the other reason 9. Which part in do you dislike? i. News ii. Sports iii. Entertainment iv. Business v. Please specify the other reason 10. How many daily newspapers do you subscribe in your household? i. We will write a custom essay sample on Reading Habits Questionnaire or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page One ii. Two iii. Three or more 11. Do you get the desired information in the newspaper? . Yes ii. No 12. Do you understand the vocabulary contained in the newspaper? i. Yes ii. No 13. With the internet being widely used, will you read less newspaper than before? i. Yes ii. No 14. Why do you choose newspaper rather than other media? i. Informative ii. Better at improving language skills iii. Reliable iv. Please specify other reason 15. Do you feel confident with the future of the newspaper industry with the rapid increase in the usage of internet? i. Yes ii. No