What is Bulk modulus: Definition and 62 Discussions

The bulk modulus (


{\displaystyle K}


{\displaystyle B}
) of a substance is a measure of how resistant to compression that substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume. Other moduli describe the material's response (strain) to other kinds of stress: the shear modulus describes the response to shear, and Young's modulus describes the response to linear stress. For a fluid, only the bulk modulus is meaningful. For a complex anisotropic solid such as wood or paper, these three moduli do not contain enough information to describe its behaviour, and one must use the full generalized Hooke's law. The reciprocal of the bulk modulus at fixed temperature is called the isothermal compressibility.

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  1. J

    What is the relationship between surface area and bulk modulus in a collision?

    there are two materials: Material A Material B surface area A/surface area B= 30 bulk modulus B/bulk modulus A= 11 How much more pressure is exerted through material B than material A in a collision, all else being equal?
  2. F

    B Exploring Bulk Modulus: Examining Caesium and Beyond

    Today, while studying about bulk Modulus, I encountered a doubt. Please consider this thought experiment. I'm considering Caesium as an example as it seems to have a quite low Bulk Modulus (comparatively) of 1.6 GPa. Let's say I apply a pressure of X GPa. Volume change ratio can be given by...
  3. Alexanddros81

    I want to understand this equation - Fluid Mechanics

    Hi all! I have started reading Fluid Mechanics at my own pace (no university study) and really I would like to grasp the ideas behind it. So I have Fluid Mechanics by Cengel - 4th edition. At page 45 the coefficient of compressibility or bulk modulus of elasticity (κ) is introduced. ##κ =...
  4. T

    Calculate the bulk modulus and Derive the mean standard deviation

    (apologies for re-posting, I am unable to find my original thread.) A material which has a Young's modulus of elasticity of 250 GN m-2 and a poisons ratio of 0.32, calculate: (a) the bulk modulus of the material 
 Relevant equation, K=E/3(1-2v) Inputting our known values...
  5. Q

    Inverse bulk modulus / compression or shear?

    Hi, I'm afraid I not very good at these questions just yet and would like a walk through a bit better than the one I was given by my tutors. Thank you, please refer to the inline image.
  6. J

    How can I show that the bulk modulus is about r^-4?

    Homework Statement Using the equations, show the bulk modulus is about r^-4. Homework Equations The Attempt at a Solution Tried to plug Uij but it is not same as U. To be honest, I don't know where to start.
  7. electr

    Determine the bulk modulus of the material

    Homework Statement A material is formed into a solid sphere and has a diameter of 100mm when at a pressure of 2MPa. If the diameter of the sphere reduces by 0.1mm when the pressure is increased to 6MPa, determine the bulk modulus of the material Homework Equations K=− Δp/ΔV/V0 (Δp is pressure...
  8. S

    Expansion and elasticity of brines

    Hello, I am currently looking at a way to calculate brine density using temperature, pressure and salinity. I found the following page which describes the change in fluid density with pressure and temperature : http://www.engineeringtoolbox.com/fluid-density-temperature-pressure-d_309.html...
  9. R

    Relationship of bulk modulus and fractional volume change

    So my question is, if the bulk modulus change by 5%, what is the fractional volume change value? is it times 0.05 or divided by 0.05? or the fractional volume change still the same?
  10. R

    Integrating Bulk Modulus to Find Pressure at Variable Depth

    Homework Statement See image. Homework Equations pressure = density*gravity*depth The Attempt at a Solution The pressure at 5000 ft according to the book is 322,000 psf. This makes sense because density*gravity*depth = 2*32.2*5000 = 322,000 psf. How do I apply the bulk modulus equation to...
  11. leafjerky

    Bulk modulus given, find change in P [Fluid Mechanics]

    Homework Statement If the bulk modulus for water at 70∘F is 319 kip/in^2, determine the change in pressure required to reduce its volume by 0.3%. Homework Equations E = dP/(dV/V) E - Bulk Modulus dP - change in pressure dV - change in volume V - volume The Attempt at a Solution Well I just...
  12. S

    Calculating Bulk modulus

    Hi Can any please help: My course work is asking for me to calculate the Bulk modulus and shear modulus for a material that has a Young's modulus of elasticity of 250GN m-2 and a Poisson's ratio of 0.32? Any help will be great thanks Simon
  13. P

    Calculating total bulk modulus of cylinder, piston and oil

    Hello, I have been thinking about following problem: I have some kind of piston and cylinder with oil. I know the pressure in oil. Let's say it is 500bar. I would want to know how much is displacement of piston. Let's say bulk modulus of oil is 3Gpa. Let's also say that bulk modulus of...
  14. M

    Fluid mechanics~ Bulk modulus

    Hey all, I am having trouble getting to the answer of the attached file below. It would be appreciated if anyone had some tips on getting to the answer.
  15. H

    Bulk Modulus and its derivative in a fcc lattice

    The bulk modulus B = - V (∂P/∂V). At constant temperature the pressure is given by P= -∂U/∂V, where U is the total energy. We can write B in terms of the energy per particle u = U/N and volume per particle v = V/N : B = v...
  16. T

    Density of water using bulk modulus

    Homework Statement Estimate the density of the water 5.3km deep in the sea. (bulk modulus for water is B=2.0×109N/m2.) Homework Equations P = F/A = Dgh The Attempt at a Solution I don't even know how to go about starting this one. Can someone point me in the right direction?
  17. C

    What is the the bulk modulus formula for anisotropic material?

    I can understand the derivation of bulk modulus (K) for isotropic material. However I have difficulty to do the same for anisotropic material. to start with we have the definition: mean_stress = K * (strain_xx+strain_yy+strain_zz) My question is for anisotropic material: Is mean_stress =...
  18. M

    Bulk Modulus Problem: Sphere of Brass Diameter Change

    Homework Statement A solid sphere of brass (bulk modulus of 14.0*10^10 N/m^2) with a diameter of 3.00 m is thrown into the ocean. By how much does the diameter of the sphere decrease as it sings to a depth of 1.0 km? Homework Equations Gauge pressure = density(water)*g*h Bulk...
  19. S

    First pressure derivative of bulk modulus at zero pressure

    what is the physical meaning of first pressure derivative of bulk modulus at zero pressure. if it is ∂k/∂p, i say how it change with pressure, if it is at zero pressure?
  20. ajayguhan

    Expression of bulk modulus of a cube in terms of strain

    In my text it's given when a cube underwents a uniform unit tensile force be applied in all six faces, bulk module=1/3(α-2β) Where α is longitudinal strain and β is lateral strain.is there a derviation for it..? And it states in x direction there will be increase in length and in y, z...
  21. Nemo's

    Calculate Pressure Increase of Frozen Water in Engine Block

    Homework Statement When water freezes it expands by about 9.00% What pressure increase would occur inside your automobile engine block if the water in it froze? ( The bulk modulus of ice is 2.00*10^9 N/m^2 Homework Equations Bulk modulus = ΔPressure/(ΔVolume/Initial Volume) The...
  22. J

    Young's Modulus, Bulk Modulus, and Shear

    I'm dealing with a cylinder. The equation for the stress of each is Force / Area. What are the different areas for the equation in regard to young's modulus, bulk modulus, and shear modulus? Is the area Young's Modulus stress the area of circle face? What about for shear stress? Would the...
  23. T

    Bulk modulus of water at 20000 psi

    Homework Statement For a university project I have to design a safety enclosure for hydrostatic testing at pressures up to (20000 psi) on equipment with maximum volume 8m3. I am having difficulty finding data to calculate the expansion energy of water in the event of a sudden brittle...
  24. W

    Bulk Modulus of unknown material

    Homework Statement A extremely strong wire of exotic material has a radius of 0.1 mm and a length of 5 m. A 1000 kg mass is hung vertically from the wire. The speed of sound in the wire is observed to be the same as the speed of a transverse wave on the wire. What is the Bulk Modulus of the...
  25. K

    Bulk Modulus, Expansion Coeff. and compression of a liquid in a piston

    Homework Statement A liquid is enclosed in a metal container that is provided with a piston of the same metal. The system is originally at a pressure of 1.00 atm (1.013*10^5 Pa) and at a temperature of 30.0 C. The piston is forced down until the pressure on the liquid is increased by 50.0 atm...
  26. A

    (Thermodynamics) Express adiabatic bulk modulus in terms of

    Homework Statement The adiabatic bulk modulus is defined as: \beta_s=-V(\frac{∂P}{∂V})_sExpress it in terms of experimental variables: C_p, C_v, \alpha, \beta Homework Equations Heat capacity at constant pressure:C_P=(\frac{∂Q}{∂T})_P Heat capacity at constant volume:C_V=(\frac{∂Q}{∂T})_V...
  27. N

    Pressure in Tube, Bulk Modulus

    A straight tube, 1m long, of radius 10mm and wall thickness, is closed at both ends. It is found that when the pressure inside is increased from 10^5 Pa to 10^6 Pa the tube lengthens by 100um. What is the bulk modulus of the material of the tube? Well know that P = -Bdv/V and also that for a...
  28. AakashPandita

    Bulk Modulus formula help

    bulk modulus = Δp/ΔV/V Why do we need to divide change in volume by the original volume? why is it important?
  29. I

    Calculate Bulk Modulus: Solve Rock Density Problem

    Homework Statement A rock at the surface has a density of 2600kg(m^(-3) 90000m down its density is 3100kg(m^(-3) Change in pressure at the depth is due to hydrostatic pressure. Whats the bulk modulus of the rock? Homework Equations Δp=p + ƿgh Δp=-B(ΔV/V) The Attempt at a...
  30. O

    Understanding Sound and Bulk Modulus: Formula, Interplay, and Phase Dependence

    I am trying to understand what the formula v=sq rt( Bulk Modulus/density). I understand that Bulk Modulus is indicative of a Pressure force and shows how much an object resists being compressed. So if we take a solid, it will have a greater Bulk Modulus than a liquid and so sound will travel...
  31. C

    Bulk Modulus and the speed of sound

    Why is it that materials with a higher bulk modulus value allow for sound waves to propagate through them faster? A material with a high bulk modulus requires a relative greater increase in pressure to contract by the same volume as a material with a lower bulk modulus, and as such sound waves...
  32. N

    Bulk Modulus Problem - Two solutions?

    Homework Statement Question: When water freezes it expands about 9%. What pressure increase would occur inside your automobile engine if the water froze. The bulk modulus of the ice is 2x10⁹N/m². Homework Equations B = - Δp/(ΔV/V) The Attempt at a Solution My 1st solution: Volume...
  33. J

    Bulk Modulus of a Fermi Gas

    Homework Statement It is just a line of equation from my Stat Mech textbook, that says B = -V(dp)/(dV) = (10U)/(9V) = (2nEf)/3 where B is the bulk modulus, V is the volume, p is the pressure, U is the energy, n is the number per unit volume and Ef is the fermi energy. Homework...
  34. A

    Bulk modulus question

    Bulk modulus question...please help Homework Statement What is the change in density of water in a lake at a depth of 400 m below the surface? The density of water at the surface is 1030 kg/m3 and bulk modulus of water is 2*109 Nm2 Homework Equations For fluid New Density= Initial...
  35. L

    How to derive plane strain bulk modulus?

    This is a homework problem and I thought about putting it in the homework section bu since its very materials science specific I decided to put it here: For a transversely isotropic material, the “plane strain bulk modulus”, K23, is an engineering constant that is defined by the stress...
  36. T

    Calculating change in volume (bulk modulus)

    Homework Statement a hydraulic system operates at 3000 psi. Compute the percentage change in the volume of the oil in the system as the pressure is increased from zero to 3000 psi if the bulk modulus of the oil is 189000 psi.Homework Equations E=∆p/(∆V)/V The Attempt at a Solution 189 000 psi...
  37. T

    Is this the way to calculate the bulk modulus using V. d. Waals-equation?

    Hi, Is this right? (p+a(n/v)2)(V-nb)=nRT Just differentiate both sides with respect to P? If I do that I get 0=V+P*(dV/dP)t-nb-(an2)/V2*(dV/dP)t+2abn3/V3*(dV/dP)t (dV/dP)t=(nb-V) / (P-n2a/V+2an3ab/V3) And now to calculate the bulk modulus: kt=-1/V*(dV/dP)t = -1/V *...
  38. R

    Adiabatic bulk modulus of a free electron gas at T=0

    Homework Statement Show that the adiabatic bulk modulus of a free electron gas can be given by B= \frac{2nE_{F}}{3} where n-number density E_{F} -Fermi energy Homework Equations I started with the adiabatic bulk for an ideal gas K=\gamma P where...
  39. J

    Finding Bulk Modulus of Refinery Fluids

    We are studying the waterhammer in a Refinery. Since the bulk modulus is involved in this study, we will like to know where to find the bulk modulus at different temperatures and pressures for several refinery fluids such as kerosene, diesel, atmospheric and vacuum residue. We have found some...
  40. M

    Bulk modulus and density

    Homework Statement The deepest point in the ocean is in the Mariana Trench, about 11 km deep. The pressure at that point is huge, about 1.13 x108 N/m2. (a) The deepest point in the ocean is in the Mariana Trench, about 11 km deep. The pressure at that point is huge, about 1.13 x108 N/m2...
  41. T

    Exploring Young's vs Bulk Modulus of Tin

    1. The Young's modulus for tin is 4.5x10^10. If the speed of sound in tin is measured to be 2.73km/s , find its density in (kg/m^3) . a)6.05x10^3 b)23.8x10^3 c)6.35x10^3 d)24.5x10^3 e)6.65x10^3 , E(tin)=4.5x10^10 ,speed of sound in tin=2.73km/s 2. v=sqrt(B/density) -where...
  42. I

    Diesel - bulk modulus of elasticity

    Hi, I need the compressibility of diesel, depending on density, pressure(0-200bar) and temperatur. Do you know where to find these values? Thanks Inkog
  43. P

    How temperature effects bulk modulus?

    hi all. I am doing an experiment that's involvse measureing the speed of sound through fluids at different temperatures and i want to able to predict the speeds before the experiment using equations. what i have found so far is that the speed of sound in a fluid,c, is equal to the sqaure root...
  44. L

    Percentage Decrease in Specific Volume using Bulk Modulus from Table

    Homework Statement "Water in a hydraulic press is subjected to a pressure of 4500 psia at 68 F. If the initial pressure is 15 psia, approximately what will be the percentage decrease in specific volume. Use Table 2.1 (below)." Homework Equations...
  45. 2

    Volume Stress and Bulk Modulus

    Homework Statement A cylindrical steel pressure vessel with volume 1.31 m^3 is to be tested. The vessel is entirely filled with water, then a piston at one end of the cylinder is pushed in until the pressure inside the vessel has increased by 1000 kPa. Suddenly, a safety plug on the top...
  46. B

    Young's modulus and bulk modulus of cooked pasta

    Hi there, I am doing some simulation on the cooking process of pasta. Now I need the viscoelastic parameters of cooked pasta (plane sheet lasagna to :) ). To be more specific, i need the shear modulus and the initial bulk modulus. Right now I found a paper, in which a relaxation test was...
  47. A

    Solids Elasticity (Bulk Modulus)

    Homework Statement When the water freezes it expands by about 9.00%. What pressure increase would occur inside your automobile engine block if the water in it froze?(The bulk modulus of ice is 2.00 x 10^9 N/m^2).Homework Equations B=\frac{\Delta P}{\Delta V / V_i} The Attempt at a Solution If...
  48. A

    Bulk modulus and poisson's ratio

    Homework Statement derive the equation for the bulk modulus, K = E/3(1 - 2v), where v is poisson's ratio. Homework Equations E = stress/e, where e is strain The Attempt at a Solution e_v = e_x + e_y + e_z e_y = e_z = -v*e_x e_v = (1 - 2v)*e_x K = stress/e_v therefore K =...
  49. B

    Volume and Bulk Modulus

    Homework Statement Part A What is the pressure at a depth of 5000 in the ocean? Given rho_water=1,030 kg/m^3 pTotal=p_0 + rho*g*h=5.06×107 Part B What is the fractional volume change of seawater at this pressure? Given B=0.2*10^10 dV/v=p/-B =−2.53×10−2 Part...
  50. R

    Bulk Modulus from DFT results

    Homework Statement I have been asked to calculate the bulk modulus for a carbon dioxide solid from data I have calculated. I have made a quick plot of unit cell size vs pressure (sorry for no labels, unit cell is Y axis as square angstroms, and pressure is in GPa), which looks ok...