Variable-mass system events. The following derivation is for a body that is gaining mass (accretion). A body of time-varying mass "m" moves at a velocity v at an initial time "t". In the same instant, a particle of mass dm moves with velocity u. The initial momentum can be written as Now at a time "t" + d"t", let both the main body and the particle accrete into a body of velocity v + dv. Thus the new momentum of the system can be written as Since d"m"dv is the product of two small values, it can be ignored, meaning during d"t"
Pulse wave velocity in the investigation of hypertension. The theory of the velocity of the transmission of the pulse through the circulation dates back to 1808 with the work of Thomas Young. The relationship between pulse wave velocity (PWV) and arterial wall stiffness can be derived from Newton's second law of motion (formula_1) applied to a small fluid element, where the force on the element equals the product of density (the mass per unit volume; formula_2) and the acceleration. The approach for calculating PWV is similar to the calculation of the speed of sound, formula_3, in a compressible fluid (e.g. air): formula_4, where