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where B is the bulk modulus (see [link] ), V 0 size 12{V rSub { size 8{0} } } {} is the original volume, and F A size 12{ { {F} over {A} } } {} is the force per unit area applied uniformly inward on all surfaces. Note that no bulk moduli are given for gases.

What are some examples of bulk compression of solids and liquids? One practical example is the manufacture of industrial-grade diamonds by compressing carbon with an extremely large force per unit area. The carbon atoms rearrange their crystalline structure into the more tightly packed pattern of diamonds. In nature, a similar process occurs deep underground, where extremely large forces result from the weight of overlying material. Another natural source of large compressive forces is the pressure created by the weight of water, especially in deep parts of the oceans. Water exerts an inward force on all surfaces of a submerged object, and even on the water itself. At great depths, water is measurably compressed, as the following example illustrates.

Calculating change in volume with deformation: how much is water compressed at great ocean depths?

Calculate the fractional decrease in volume ( Δ V V 0 size 12{ { {ΔV} over {V rSub { size 8{0} } } } } {} ) for seawater at 5.00 km depth, where the force per unit area is 5 . 00 × 10 7 N / m 2 size 12{5 "." "00" times "10" rSup { size 8{7} } N/m rSup { size 8{2} } } {} .


Equation Δ V = 1 B F A V 0 is the correct physical relationship. All quantities in the equation except Δ V V 0 are known.


Solving for the unknown Δ V V 0 gives

Δ V V 0 = 1 B F A . size 12{ { {ΔV} over {V rSub { size 8{0} } } } = { {1} over {B} } { {F} over {A} } } {}

Substituting known values with the value for the bulk modulus B from [link] ,

Δ V V 0 = 5.00 × 10 7 N/m 2 2 . 2 × 10 9 N/m 2 = 0.023 = 2.3%.


Although measurable, this is not a significant decrease in volume considering that the force per unit area is about 500 atmospheres (1 million pounds per square foot). Liquids and solids are extraordinarily difficult to compress.

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Conversely, very large forces are created by liquids and solids when they try to expand but are constrained from doing so—which is equivalent to compressing them to less than their normal volume. This often occurs when a contained material warms up, since most materials expand when their temperature increases. If the materials are tightly constrained, they deform or break their container. Another very common example occurs when water freezes. Water, unlike most materials, expands when it freezes, and it can easily fracture a boulder, rupture a biological cell, or crack an engine block that gets in its way.

Other types of deformations, such as torsion or twisting, behave analogously to the tension, shear, and bulk deformations considered here.

Section summary

  • Hooke’s law is given by
    F = k Δ L , size 12{F=kΔL} {}

    where Δ L size 12{ΔL} {} is the amount of deformation (the change in length), F size 12{F} {} is the applied force, and k size 12{k} {} is a proportionality constant that depends on the shape and composition of the object and the direction of the force. The relationship between the deformation and the applied force can also be written as

    Δ L = 1 Y F A L 0 , size 12{ΔL= { {1} over {Y} } { {F} over {A} } L rSub { size 8{0} } } {}

    where Y size 12{Y} {} is Young’s modulus , which depends on the substance, A size 12{A} {} is the cross-sectional area, and L 0 size 12{L rSub { size 8{0} } } {} is the original length.

  • The ratio of force to area, F A size 12{ { {F} over {A} } } {} , is defined as stress , measured in N/m 2 .
  • The ratio of the change in length to length, Δ L L 0 size 12{ { {ΔL} over {L rSub { size 8{0} } } } } {} , is defined as strain (a unitless quantity). In other words,
    stress = Y × strain . size 12{"stress"=Y times "strain"} {}
  • The expression for shear deformation is
    Δ x = 1 S F A L 0 , size 12{Δx= { {1} over {S} } { {F} over {A} } L rSub { size 8{0} } } {}

    where S is the shear modulus and F is the force applied perpendicular to L 0 and parallel to the cross-sectional area A .

  • The relationship of the change in volume to other physical quantities is given by
    Δ V = 1 B F A V 0 , size 12{ΔV= { {1} over {B} } { {F} over {A} } V rSub { size 8{0} } } {}

    where B is the bulk modulus, V 0 is the original volume, and F A size 12{ { {F} over {A} } } {} is the force per unit area applied uniformly inward on all surfaces.

Questions & Answers

a car move 6m. what is the acceleration?
Umaru Reply
depends how long
What is the simplest explanation on the difference of principle, law and a theory
Kym Reply
how did the value of gravitational constant came give me the explanation
Varun Reply
how did the value of gravitational constant 6.67×10°-11Nm2kg-2
A steel ball is dropped onto a hard floor from a height of 1.50 m and rebounds to a height of 1.45 m. (a) Calculate its velocity just before it strikes the floor.
Kris Reply
0.5m* mate.
0.05 I meant.
Guess your solution is correct considering the ball fall from 1.5m height initially.
How can we compare different combinations of capacitors?
Prakash Reply
find the dimension of acceleration if it's unit is ms-2
Happiness Reply
b=-2 ,a =1
M^0 L^1T^-2
what is botany
it is a branch of science which deal with the study of plants animals and environment
what is work
Sunday Reply
a boy moving with an initial velocity of 2m\s and finally canes to rest with a velocity of 3m\s square at times 10se calculate it acceleration
6.6 lol 😁😁
show ur work
sorry..the answer is -10
your question is wrong
If the boy is coming to rest then how the hell will his final velocity be 3 it'll be zero
re-write the question
men i -10 isn't correct.
using v=u + at
ya..1/10 is very correct..
how did the value 6.67×10°-11Nm2kg2 came tell me please
Work is the product of force and distance
what is longitudinal wave
Badmus Reply
A longitudinal wave is wave which moves parallel or along the direction of propagation.
longitudinal wave in liquid is square root of bulk of modulus by density of liquid
Is British mathematical units the same as the United States units?(like inches, cm, ext.)
Nina Reply
We use SI units: kg, m etc but the US sometimes refer to inches etc as British units even though we no longer use them.
Thanks, just what I needed to know.
What is the advantage of a diffraction grating over a double slit in dispersing light into a spectrum?
Uditha Reply
can I ask questions?
Boniface Reply
hello guys
when you will ask the question
anybody can ask here
is free energy possible with magnets?
you could construct an aparatus that might have a slightly higher 'energy profit' than energy used, but you would havw to maintain the machine, and most likely keep it in a vacuum, for no air resistance, and cool it, so chances are quite slim.
calculate the force, p, required to just make a 6kg object move along the horizontal surface where the coefficient of friction is 0.25
Yes ask
if a man travel 7km 30degree east of North then 10km east find the resultant displacement
Ajali Reply
disagree. Displacement is the hypotenuse length of the final position to the starting position. Find x,y components of each leg of journey to determine final position, then use final components to calculate the displacement.
1.The giant star Betelgeuse emits radiant energy at a rate of 10exponent4 times greater than our sun, where as it surface temperature is only half (2900k) that of our sun. Estimate the radius of Betelgeuse assuming e=1, the sun's radius is s=7*10exponent8metres
James Reply
2. A ceramic teapot (e=0.20) and a shiny one (e=0.10), each hold 0.25 l of at 95degrees. A. Estimate the temperature rate of heat loss from each B. Estimate the temperature drop after 30mins for each. Consider only radiation and assume the surrounding at 20degrees
Is our blood not red
Aditya Reply
If yes than why when a beam of light is passing through our skin our skin is glowing in red colour
because in our blood veins more red colour is scattered due to low wavelength also because of that scattered portion comes on skin and our skin act as a thinscreen.
so you saying blood is not red?
blood is red that's why it is scattering red colour!
like if u pass light frm red colour solution then it will scatter red colour only.. so same it is with our skin..red colour blood is moving inside the veins bcz of thinkness of our fingers.. it appears to be red.
No I am not saying that blood is not red
then ur qtn is wrong buddy.. 😊
Blood is red. The reason our veins look blue under our skin, is because thats the only wavelength on light that can penetrate our skin.
Red light is reflected from our blood but because of its wavelength it is not seen. While in the other hand blue light has a longer wavelength allowing it to pass the our skin and to our eyes.
Thus, our veins appear blue while they are really red... THE MORE YOU KNOW...(;
So in conclusion our blood is red but we can only see blue spectrum because of our skin. The more longer a wavelength is the more durable it is to reflection, so blue light cant pass thew skin completely causing a reflection which causes veins to appear blue. While the red light is scatter around.
the reason why when we shine a light at our skin it appears red is because the red light is increased and more goes to your eyes. So in other words it increases the amount of red light vs it being scatterd around everywhere.
I think the blood is only a mixture of colors but red is predominant due to high level of haemoglobin.
As a side note, the heme part of hemoglobin is why blood is red
a car starts from rest acceleration and moves with a uniform acceleration a, in time t. the distance covered during the motion is expressed as?.
Ifetomide Reply
Practice Key Terms 6

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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