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The Chézy formula describes mean flow velocity in turbulent open channel flow and is used broadly in fields related to fluid mechanics and fluid dynamics. Open channels refer to any open conduit, such as rivers, ditches, canals, or partially full pipes. The Chézy formula is defined for uniform equilibrium and non-uniform, gradually varied flows.
The Chézy equation is a pioneering formula in the field of fluid mechanics, and was expanded and modified by Irish engineer Robert Manning in 1889 [1] as the Manning formula. The Chézy formula concerns the velocity of water flowing through conduits and is widely celebrated for its use in open channel flow calculations. [ 2 ]
Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.
For a constant mass m, acceleration a is directly proportional to force F according to Newton's second law of motion: = In classical mechanics of rigid bodies, there are no forces associated with the derivatives of acceleration; however, physical systems experience oscillations and deformations as a result of jerk.
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
Unprimed quantities refer to position, velocity and acceleration in one frame F; primed quantities refer to position, velocity and acceleration in another frame F' moving at translational velocity V or angular velocity Ω relative to F. Conversely F moves at velocity (—V or —Ω) relative to F'. The situation is similar for relative ...
In classical mechanics, for a body with constant mass, the (vector) acceleration of the body's center of mass is proportional to the net force vector (i.e. sum of all forces) acting on it (Newton's second law): = =, where F is the net force acting on the body, m is the mass of the body, and a is the center-of-mass acceleration.
The linear motion can be of two types: uniform linear motion, with constant velocity (zero acceleration); and non-uniform linear motion, with variable velocity (non-zero acceleration). The motion of a particle (a point-like object) along a line can be described by its position x {\displaystyle x} , which varies with t {\displaystyle t} (time).