Among five sets of identical twins, how many pairs are predicted to share the same hand preference?
Answers
In continuum mechanics, a hydrostatic stress is an isotropic stress that is given by the weight of water above a certain point. It is often used interchangeably with "pressure" and is also known as confining stress, particularly in the field of geomechanics. Its magnitude {\displaystyle \sigma _{h}} can be given by:
{\displaystyle \sigma _{h}=\displaystyle \sum _{i=1}^{n}\rho _{i}gh_{i}}
where {\displaystyle i} is an index denoting each distinct layer of material above the point of interest, {\displaystyle \rho _{i}} is the densityof each layer, {\displaystyle g} is the gravitational acceleration(assumed constant here; this can be substituted with any acceleration that is important in defining weight), and {\displaystyle h_{i}} is the height (or thickness) of each given layer of material. For example, the magnitude of the hydrostatic stress felt at a point under ten meters of fresh water would be
{\displaystyle \sigma _{h}=\rho _{w}gh_{w}=1000\,{\text{kg m}}^{-3}\cdot 9.8\,{\text{m s}}^{-2}\cdot 10\,{\text{m}}=9.8\cdot {10^{4}}{\text{ kg m}}^{-1}{\text{s}}^{-2}=9.8\cdot 10^{4}{\text{ N m}}^{-2}}
where the index {\displaystyle w} indicates "water".
Because the hydrostatic stress is isotropic, it acts equally in all directions. In tensor form, the hydrostatic stress is equal to
{\displaystyle \sigma _{h}\cdot I_{3}=\sigma _{h}\left[{\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}}\right]=\left[{\begin{array}{ccc}\sigma _{h}&0&0\\0&\sigma _{h}&0\\0&0&\sigma _{h}\end{array}}\right]}
where {\displaystyle I_{3}} is the 3-by-3 identity matrix.