In a closed box water can be uniaxially stressed (in compression and in tension).
What is the slope of the stress versus strain curve obtained this way? This would be the Young's modulus of water...
In my opinión this curve give us the Bulk modulus, the box produces hydrostatic stress state.
Yes, I know about the bulk-modulus as a result of elastic deformation by hydrostatic pressure. However, if you put water in a tube and close the tube with two movable end caps (plungers). You can exert (uniaxial?) tensile stress to the water. Also the tensile strength of water can be determined this way.
The elastic regime of the stress-strain curve would provide the Young's modulus of water. So, what value is this E-modulus for water?
What is the tube size ? If the force applied dirctely on the water, possible to get it !
If container / box / tube used depending on material / thickness, Definetely the stress and strain correlation is there for materials. but thats not unique ?
Pascal effect and Car lifting are focussed in one direction, instead that direction other direction also be considered, but thats not a deflection !
The BULK 's modulus of water is about 0.2 10^10 Pa . For steel the Young modulus is 20 10^10 Pa.
The Bulk modulus is the ratio of the volume stress over the volume strain:
B= -Delta P / (Delta V / V)
The Young's modulus is the ration of the tensile stress over the tensile strain.
I would advice you to use the bulk modulus : initial density times square sound speed.
This would be the effective Bulk modulus of water including your box elasticity not the Young's modulus of water.
for soilds and/or fluids K=E/3(1-2.nu),
for steel E st= 210 GPa, nust= 0.283,
then Kst= 160.6 GPa
Since for water measured Kw = 2.20 GPa and since water contains dissolved air then
nuw
Elastic properties of fluids specially water are difficult to measure and mostly are in no practical use :). atleast in my field of study (Geomechanics).
There is a method to measure shear modulus of water using a floating disk rotating on the surface of the liquid. Using this method, the shear modulus of water would be around 1.3*10^(-5) Pa. As you see it is too low to consider in most analyses. If you use a pure newtonian fluid your shear modulus would be zero, because if you apply a force F the liquid simply flows and the strain becomes arbitrarily large.
The same goes for Young's modulus. You can not apply a considerable force to water. Pay attention "Water", Not a combination of water and some container. The container will alwaysprovide force to keep water to gether. if you could make a cylinder of water (with no container ir what so ever) then you can ask bout its modulus.
Kind regards,
What you measure in your experiment (uniaxial stress applied to a material with fixed boundary condition = no perpendicular contraction) is called the "seismic modulus" (M=K+4/3G), which reduces to the bulk modulus for ideal fluids (G=0).
To measure Young's modulus you would have to allow for contraction/extension in the directions perpendicular to the stress (no walls). If you could do that, there'd be no resistance of the water, i.e. Youngs modulus is zero for an ideal fluid.
Zero.
K=E/3(1-2.nu)
So...
E = K * ( 1 - 2 * nu)
Thus...
if Kw = 2.2 GPa and nuw = 0.5
Ew = 2.2 * ( 1 - 2 * 0.5 ) = 0
Regards.
I thank all participants that contributed to this discussion.
My conclusion about the issue is that the method suggested (water in a closed cylinder) will not provide the Young's modulus of water.
For an ideal fluid the modulus is zero and measured values for (floating disk on liquid) come pretty close to this value (zero).
Hi Mohammed,
E = 2K(1-2v), with v the Poisson's ratio of a material. This was also suggested by Sief Khorshid about a year ago (see above).
If you assume E = 3K, then you suggest that v=0.5; which means that the material is incompressible in the elastic regime. But that would suggest that the sound velocity in water is infinite, while it is (only) 1500 m/s at standard conditions.....
Your Cs is not the sound velocity in water (hence not equal to 1500 m/s) as Cs is the shear wave velocity, which only occurs in media with strength. And as a liquid, water lacks shear strength.....so: Cs = 0 m/s and water is compressible v < 0.5
I see. I don't have it by now. I appreciante your comment Konstantin Leonov
Please, see the following helpful link:
https://www.chegg.com/learn/physics/introduction-to-physics/elastic-modulus-of-water
Why there is no Young's modulus/stress for fluids, behold the attached figure.
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