User:John R. Brews/Coriolis force: Difference between revisions
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==Coriolis Flowmeter== | ==Coriolis Flowmeter== | ||
{{Image|Coriolis flowmeter.PNG|right|250px|A fluid forced through a rocking tube experiences a Coriolis acceleration.}} | {{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. 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 | The Coriolis force is used to measure mass flows in fluid systems. 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>\mathbf{F_{Cor}} = 2m \mathbf{v \times \Omega} \ , </math> | :<math>\mathbf{F_{Cor}} = 2m \mathbf{v \times \Omega} \ , </math> | ||
where '''''Ω''''' 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 '''''Ω'''''. | where '''''Ω''''' 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 '''''Ω'''''. | ||
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. | 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. | ||
Revision as of 11:22, 18 March 2011
Coriolis Flowmeter
The Coriolis force is used to measure mass flows in fluid systems. 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:
where Ω 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 Ω.
As a result of the Coriolis force, the tube is subject to a 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.