User:John R. Brews/Coriolis force: Difference between revisions

From Citizendium
Jump to navigation Jump to search
imported>John R. Brews
No edit summary
 
(5 intermediate revisions by one other user not shown)
Line 1: Line 1:
{{AccountNotLive}}
===Quarks===


[http://books.google.com/books?id=h5JelZ9EgRUC&pg=PA265&dq=coriolis+effect+inpublisher:wiley&hl=en&ei=rDt1TeiwHIOosAOjob2_Cw&sa=X&oi=book_result&ct=result&resnum=9&ved=0CFkQ6AEwCA#v=onepage&q=coriolis%20effect%20inpublisher%3Awiley&f=false Tides]
The quarks that may engage one another in reactions are determined by the [[Cabbibo-Kobayashi-Maskawa matrix]]:[http://books.google.com/books?id=f89yg8a1t-EC&pg=PA23&dq=Cabibbo+angle&hl=en&ei=XYZvToTqN7PZiAKM55juBg&sa=X&oi=book_result&ct=result&resnum=2&ved=0CDIQ6AEwATgK#v=onepage&q=Cabibbo%20angle&f=false Morii]
:<math>\begin{pmatrix}
d'\\
s'\\
b'\\
\end{pmatrix} = \begin{pmatrix}
U_{ud}&U_{us}&U_{ub}\\
U_{cd}&U_{cs}&U_{cb}\\
U_{td}&U_{ts}&U_{tb}\\
\end{pmatrix}=\begin{pmatrix}
d\\
s\\
b\\
\end{pmatrix} </math>


The quarks can be arranged to exhibit right- and left-handedness, subscripts ''L'' and ''R'', to resemble the leptons. The right-handed quarks do not couple to the weak interaction, and are labeled with subscript ''R''. The left-handed quarks corresponding to these right-handed quarks are mixtures of quarks. Thus, the up and down quarks are assembled as:


==Coriolis Flowmeter==
:<math> \tbinom {u}{d}_L \ ; \ \ u_R,\ d_R \ .</math>
{{Image|Coriolis flowmeter.PNG|right|250px|A fluid forced through a rocking tube experiences a Coriolis acceleration.}}
The Coriolis force is used to measure mass flows in fluid systems.<ref name= DeSá>


For an analysis, see for example {{cite book |title=Instrumentation fundamentals for process control |url=http://books.google.com/books?id=TUc6kZEe7s4C&pg=PA21 |pages=pp. 20 ''ff'' |chapter=The Coriolis mass flowmeter |isbn=1560329017 |year=2001 |publisher=Taylor & Francis |author=Douglas O. J. DeSá}}
The other generations are arranged similarly:


</ref> As shown in the figure, the fluid flows into a U-shaped tube with velocity '''''v''''' and exits with equal but oppositely directed velocity. The tube is rocked, and at a particular moment appears to be rotating along a line joining its openings, as shown. From the viewpoint of the fluid, it experiences a Coriolis acceleration normal to the plane of the tube, which has opposite signs on the two legs of the tube. An element of fluid with mass ''m'' experiences a Coriolis force:
:<math> \tbinom {c}{s}_L \ ; \ \ c_R,\ s_R \ , </math>
:<math>\mathbf{F_{Cor}} = 2m \mathbf{v \times \Omega} \ , </math>
:<math> \tbinom {t}{b}_L \ ; \ \ t_R,\ b_R \ . </math>
where '''''&Omega;''''' is the vector angular rate of rotation as found using the [[right-hand rule]] and '''''v''''' is the fluid velocity. Idealizing the tube as having right-angle corners at its base, the Coriolis force is the same along the entire leg of the tube, and is zero at the base where the velocity is parallel to the rotation '''''&Omega;'''''.
{| class="wikitable" style="margin: 0 auto; text-align:center"
|+'''Right- and left-handed quarks'''
! Symbol
! Electric charge, ''Q''
! Weak isospin, (''I<sub>W</sub>, I<sub>W3</sub>'')
! Weak hypercharge, (''Y<sub>W</sub>'')
|-
| ''u<sub>L</sub>, c<sub>L</sub>, t<sub>L</sub>''
| +2/3
| (1/2, +1/2)
| +1/3
|-
| ''d<sub>L</sub>, s<sub>L</sub>, b<sub>L</sub>''
| −1/3
| (1/2, −1/2)
| +1/3
|-
| ''u<sub>R</sub>, c<sub>R</sub>, t<sub>R</sub>''
| +2/3
| 0
| +4/3
|-
| ''d<sub>R</sub>, s<sub>R</sub>, b<sub>R</sub>''
| −1/3
| 0
| −2/3
|-
|}


As a result of the Coriolis force, the tube is subject to a [[Torque#Equivalence_of_a_force_to_a_displaced_force_and_couple|force couple]] twisting it about its vertical axis of symmetry. By detecting this [[torque]], the speed of mass flow in the tube can be measured. For example, the torque can be measured by observing the angle of twist of the tube which, like a spring, resists turning due to its mechanical properties.
 
{{Reflist}}

Latest revision as of 03:07, 22 November 2023


The account of this former contributor was not re-activated after the server upgrade of March 2022.


Quarks

The quarks that may engage one another in reactions are determined by the Cabbibo-Kobayashi-Maskawa matrix:Morii

The quarks can be arranged to exhibit right- and left-handedness, subscripts L and R, to resemble the leptons. The right-handed quarks do not couple to the weak interaction, and are labeled with subscript R. The left-handed quarks corresponding to these right-handed quarks are mixtures of quarks. Thus, the up and down quarks are assembled as:

The other generations are arranged similarly:

Right- and left-handed quarks
Symbol Electric charge, Q Weak isospin, (IW, IW3) Weak hypercharge, (YW)
uL, cL, tL +2/3 (1/2, +1/2) +1/3
dL, sL, bL −1/3 (1/2, −1/2) +1/3
uR, cR, tR +2/3 0 +4/3
dR, sR, bR −1/3 0 −2/3