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Bulk Modulus: Definition, Formula, Examples, Compressibility, Application
Consider you have two balloons filled with two different gases. Now if I ask you to compress these balloons and tell me which gas is easier to compress than others. So to know which gas is easier to compress you will normal stress on it and see which balloon is getting shrinked. So the gas which gets compressed by applying a small amount of force will be considered as more compressible than the gas which requires a huge amount of force. Now what if I tell you that there is a quantity in physics known as Bulk Modulus which gives the information about the fluid regarding its compressibility. So in this article let’s learn about Bulk Modulus.
Table of Contents
- Bulk modulus
- Bulk Modulus of Different Materials
- Relation between density, pressure and bulk modulus
- Compressibility
- Practice problems
- FAQs
Bulk Modulus
The bulk modulus is the proportion of volumetric stress related to the volumetric strain of specified material, while the material deformation is within the elastic limit. To put in more simple words, the bulk modulus is nothing but a numerical constant that is used to measure and describe the elastic properties of a fluid when pressure is applied on all the surfaces. It is defined as the ratio of the normal stress to the volumetric strain. It is important to remember
that it has dominance only on the fluids (i.e., on liquids and gases).
Normal stress or longitudinal stress is given by the following equation,
Note: negative sign means volume is reduced.
Hence the bulk modulus is mathematically written as,
Bulk modulus has the same unit and dimension as pressure or stress.
Comparison of bulk modulus for solids, liquids and gases is as follow:
Bulk Modulus of Different Materials
| Material | Bulk Modulus (Pa) |
| Aluminium |  |
| Brass |  |
| Copper |  |
| Crown Glass |  |
| Iron |  |
| Lead |  |
| Nickel |  |
| Steel | |
Relation between Density, Pressure and Bulk Modulus
When a pressure 
is applied on a substance having density 
and bulk modulus 
, then its volume changes from 
to 
. Hence,
………..(1)
………..(2)
From above equations,
Therefore,
Compressibility
The reciprocal of bulk modulus of elasticity is called compressibility. It is detonated by the letter K.
So 
The SI unit of compressibility is 
or 
.
Dimension of compressibility K is 
Comparison of compressibility for solids, liquids and gases is as follow:
Note: It is difficult to compress the gases that have a higher value of bulk modulus. In other words, higher the value of compressibility, easier it is to compress the gases as 
.
Practice Problems
Q. Calculate the density of water near the bottom of ocean where the pressure is about 
and density of water is 
approximately. Take bulk modulus of water as 
.
A. The density of water at the ocean’s surface where the pressure is 
is about Thus, 
of water at the surface has a mass of 
. Let us calculate the change in volume 
of this water when it is ar a pressure of .
The pressure change 
, which is equivalent to 
. Thus the volume change is
The density of water is then,
Q. A hydraulic press contains 
of oil. Find the decrease in volume of the oil when it is subjected to a pressure increase 
. The bulk modulus of the oil is 
.
A. 
Q. Compressibility of water is 
. Find the decrease in volume of 
of water when subjected to a pressure of 
.
A. The compressibility K is the reciprocal of the bulk modulus.
The decrease in volume is thus 
.
Q. Bulk modulus of rubber is 
. To what depth should a rubber ball be taken in a lake so that its volume is decreased by 
?
A. 
Let h be the required depth and the density of water be then
FAQs
Q. What is the effect of pressure on the bulk modulus?
A. Bulk modulus is independent of pressure as it is material property.
Q. What is the product of bulk modulus and compressibility?
A. 
Q. Which state of matter has the highest bulk modulus?
A. Solid has the highest bulk modulus.
Q. What is the significance of negative sign in the formula for bulk modulus?
A. The negative sign is used in the formula of bulk modulus to compensate for the negative value of change in volume in case of compression of volume. Therefore the bulk modulus will never be negative.
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Linear Differential Equations
Inverse Cosine
Comparing Quantities using Percentage
Fractional Part Function Definition of Signum function Trigonometric Functions Ellipse Integration By Parts Sets Matrix Types of Sets Bijective Functions Algebra of Functions Composite Functions Binary Operations Domain Codomain & Range Functions Parametric Equation of a Circle Venn Diagram Tangent to a Circle Binomial Theorem L'Hospital Rule Relations Operation on Sets Particular Cases of a Circle Terms Related to an Ellipse Equality of Matrices Reflexive, Symmetric & Equivalence Relation Types of Functions Matrix Multiplication Tangents to an Ellipse Inverse Trigonometric FunctionsActive Transport Adaptive radiation evolution Aerobic and Anaerobic Respiration Agricultural Implements Algae Alimentary Canal Anatomy Angiosperms And Gymnosperms Difference Animal Cell Apiculture Beekeeping
Apoplast
Asexual Reproduction Animals Autotrophic Nutrition Biodiversity Biotic and AbioticBryophyta
Budding Camouflage Cattle Farming Animal Husbandry Cell Structure and Function Cell Wall and Cell Membrane Cells Chloroplasts Chromatin Classification of Animal Kingdom Composition of Lymph Conduction of Nerve Impulse Cyclic and Non Cyclic Cyclic Photophosphorylation Cytoplasm Structure Function Difference Between Active and Passive Transport Difference Between Archaea And Bacteria Difference Between Blood And Lymphth Difference Between Cerebellum And Cerebrum Difference Between Chromosome And Chromatid Difference Between Diffusion and Osmosis Difference Between DNA and RNA Difference Between Haploid And Diploid Difference Between Plant Cell and Animal Cell Difference between Renewable and Non Renewable Resources Difference Between Unicellular And Multicellular Organisms Difference Between Vertebrates and Invertebrates Difference between Voluntary and Involuntary Muscles Difference Between Xylem and Phloem Different Types Ecological Pyramids Diffusion - Means of Transport Disadvantages of Dams Ecology Endemic Species Endocrine System Ductless Glands Energy Flow In Ecosystem Excretion and Its Importance Food ProductionFood Web
Fragmentation
Gemmules
GibberellinsGrassland Adaptations
GuttationGymnosperms
Harmful Microorganisms
Homeostasis
Human Body Anatomy
Human HeartInvertebrates
Kingdom Monera Protista Fungi Law of Segregation and Law of DominanceLife process
Light-dependent Reactions
Lipids
Living Things
Macromolecule Meiosis 1 Stages and Process Mendelian Disorders Microbodies Modern Synthetic Theory of Evolution Monera Nephron Function Renal Tubules Nuclear Membrane Nucleolus Nucleus Our Environment Parasitism Parts of Plants Passive Transport Plant Cell Plant Kingdom Plantae Plant Respiration Plants Plastids Protista Red Data Book Reproductive System of Earthworm Ribosomes Scientific Names of Animals and Plants Seed germination Sensory Perception Snail Skeletal System Spermatogenesis Structure Of Eye Taxonomic Hierarchy Taxonomy Algae ThallophyteTypes of Soil
Vacuoles What Is Adaptation Agricultural Practices Animal Kingdom Alimentary Canal Coelenterata Conservation of Forest and Wildlife Difference between Endosmosis and Exosmosis Difference between Afforestation and Deforestation Difference between Algae and Fungi Difference between Cereals and Pulses Difference Between Fragmentation and Regeneration Difference Between Neurosis and Psychosis Difference Between Nucleotide and NucleosideDifference Between Sea and Ocean
Difference Between Turtles and Tortoises
Difference Between Wildlife Sanctuary and National Park
Modes of Plant Reproduction
Ecological Pyramid and Its Types
Double Fertilization in Angiosperms
Ecosystem EnzymesFertilisation in Plants
Five Kingdoms Classification
FlowerGanongs Potometer
Health and Hygiene
Herbivores and Carnivores
Heterotrophic Nutrition Human Digestive SystemVertebrates and Invertebrates
Morphology of Leaves
Modifications of Root
Phylum AschelminthesDiffusion
Osmosis
Prokaryotic Cells
Reproduction
Flora And Fauna
Overview of Food ChainDifference Between Rabi And Kharif Crops
Vegetative Propagation Angiosperms Characteristics Soil ProfileTypes of Pollution
Human Excretory System Sense Organs Rainwater HarvestingProkaryotic And Eukaryotic Cells
Living And Non Living Things
The Nucleus
Irrigation
Endoplasmic Reticulum
Between Data And Information
Mitochondria
Nitrogen Cycle
Diagram of Animal Cell
Meristematic TissueLaw of Segregation Law of Dominance
Eukaryotic CellsSources Animal Plant Products
Photosynthesis Respiration Ozone Layer Depletion Kingdom Fungi Aerobic Anaerobic Respiration Cell Organelles Peristalsis Bacteria OogenesisLeaves Morphology Types Modification
Mitosis and Meiosis
Dna StructureHow Do Organisms Reproduce
Diagram of Stomata
Monohybrid Cross Inheritance One Gene Mechanism of BreathingSoil Erosion
Plasmolysis
Urine Formation Osmoregulation
Porifera
Flagella
Amoeba
Aerobic Respiration
Pteridophyta
Arteries And Veins Difference
Reflex Action
Stomata
Cell Wall
Diagram of Neuron
A Guide To Composition And Function Of Lymph
Difference Between Ligaments And Tendons
Insectivorous Plants
Nutrition Modes Living Organisms
Mendel Laws Of Inheritance
Nutrition In Amoeba
Calorific Value
Air Pollution Control
Fertilization In Plants
Life ProcessesBinary Fission
Omnivores
Saprophytes
Asexual Reproduction
Deficiency Diseases
Light Reaction Vs Dark Reaction
Global Warming
Wildlife Sanctuary
Viviparous Oviparous Embryo Development
GlycolysisFood Preservation Methods Food Poisoning
Crops
Biofertilizers
Biodiversity Conservation
Difference Between Endocrine And Exocrine Glands
Greenhouse Effect GasesDiagram Of Digestive System
Crop Production And Management
Types Of Pollination
Introduction and Characteristics of Living Beings Meristematic Cells Taxonomical Aids _Flora, Manual, Monograph And Catalogues Types of leaves structure of skeletal muscle spirometry human respiratory system herbarium dinoflagellates general characters and structure of leaf halophiles and their features Exchange of Gases Simple Permanent tissue Morphology of root and its types Complex permanent tissues Regions of Root History of classification and its need Breathing And Exchange Of Gases Transport of Gases Regulation of Respiration Disorders of Respiratory System Interaction of Haemoglobin with Other Gases Amniocentesis Anatomy of flowering plants ASSISTED REPRODUCTIVE TECHNOLOGIES (ARTs) Meristematic Cells Phloems Population explosion Reproductive Health RCH (Reproductive and Child Health Care) Medical termination of Pregnancy (MTP) Plant kingdom Biological Systems of Classification & Branches of Taxonomy Pteridophytes Gymnosperms Angiosperms Life cycle Patterns Anatomy of Roots Contraceptives Anatomy of stem Algae Bryophytes Tissues and its types STDs (Sexually Transmitted Diseases) Cell - The Basic Unit of Life & its Historical background Cell theory and its modification An Overview of Cell Secondary growth in dicot stem Tissue system and types Prokaryotic (Bacterial) cell Ribosomes Eukaryotic cell Cell: The basic unit of life Cytoskeleton Centrosome and Centriole Cilia and flagella Nucleus Chromosomes Evolution Movement and Locomotion Human Reproduction Absorption and Translocation of Solutes Soil as a reservoir of Essential Elements LOCOMOTION AND MOVEMENT Mechanism of Muscle Contraction Morphology in Flowering Plants Contractile proteins Muscular System Thyroid Puberty Hormones Origin of Universe Hypothalamus Cell wall Mitochondria Special Chromosomes Microbodies Introduction, Hydroponics and the study of mineral requirements of the plants Criteria of essentiality and Categorisation of Essential elements Deficiency symptoms of essential elements and toxicity The Stem The Root Cytoplasm and cell membrane Mineral Nutrition Disorders Related To Reproductive System Phylum Ctenophora Role of Macronutrients Role of Micronutrients Phylum - Coelenterata / Cnidaria Reptilia Aves Mammalia Anatomy of the leaf Animal kingdom Phylum Annelida Phylum Mollusca Phylum Echinodermata Vertebrata Chordates Disorders of circulatory system Abiotic Factors Male Reproductive System Kingdom Animalia Responses to Abiotic Factors Female Reproductive System Mammary Glands Pregnancy and Embryonic Development Cell Cancer Disorders of the Digestive System Infertility Morphology of Cockroach Blood and Plasma Alternation of Generations and Classification Predation Phaeophyceae and Rhodophyceae Phylum Coelenterata Phylum Porifera Phylum Platyhelminthes Chromosomal Disorders Competition Taxonomic Aids Alternation of generation in Pteridophytes Disorders of muscular and skeletal system General Characteristics of Living Digestive Glands Stomach Testis Buccal cavity Seed Common Diseases in Humans Permanent Tissue Permanent Tissues Xylem Pteridophytes Characteristics Parasitism and Commensalism Water Pollution and Its Control Differentiation, Dedifferentiation and Redifferentiation Organism and its Environment Carbohydrates Greenhouse Effect Gases Amino Acids Dynamic State of Body Constituents Photosynthesis Chloroplast Features of Living Beings Blood Group Lipids Kingdom Protista dense connective tissue connective tissue cartilage connective tissue blood plant cell viruses the stem Connective Tissue Bone Viroids Prions Lichens Animal cell Prokaryotic Cell Taxonomic Aids Herbarium and Museum Sphygmomanometer and ECG Population Attributes Noise pollution Diaphragm Parts of a Plant Photoperiodism Poultry Farming Nucleic Acids Cell Cycle Principles of Biotechnology Antibiotics IVF Glands Kranz Anatomy Sexual Reproduction in Plants Cytokinin Plant Development Biofertilizers Photorespiration Auxin Nutrient Cycling Types of Flowers Taxonomic Hierarchy and Categories Epidermal Tissue System Calyx and Corolla Ethylene Fertilization and Implantation Types of Fruits Inflorescence Types of Growth Macronutrients Family Liliaceae ETC and Oxidative Phosphorylation Classification of Wood Ground Tissue System Secondary Growth in Stem Plant Vascular System Electron Transport System Transpiration Difference Between Types of Cells Ovary Structure Birth Control Epithelial Tissue Endomembrane System Cell Envelopes and Cell Membrane Muscle Types Axial Skeleton Acquired Immunity Lung Volumes and Capacities Suspension and Migration Prokaryotic Cells
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