Added mass - Citizendia

In fluid mechanics, added mass is the inertia added to a system because an accelerating or decelerating body must move some volume of surrounding fluid as it moves through it, since the object and fluid cannot occupy the same physical space simultaneously. Fluid mechanics is the study of how Fluids move and the Forces on them The vis insita or innate force of matter is a power of resisting by which every body as much as in it lies endeavors to preserve in its present state whether it be of rest or of moving For simplicity this can be modeled as some volume of fluid moving with the object, though in reality "all" the fluid will be accelerated, to various degrees.

The concept of added mass can be thought of as a classical physics analogue of the quantum mechanical concept of quasiparticles. In Physics, a quasiparticle refers to a particle -like entity arising in certain systems of interacting particles It is, however, not to be confused with relativistic mass increase. The term Mass in Special relativity usually refers to the Rest mass of the object which is the Newtonian mass as measured by an observer moving along with

1 History
2 Applications
3 See also
4 References

History

Friedrich Bessel proposed the concept of added mass in 1828 to describe the motion of a pendulum in a fluid. Friedrich Wilhelm Bessel (22 July 1784 &ndash 17 March 1846 was a German Mathematician, Astronomer, and systematizer of the Bessel functions The period of such a pendulum increased relative to its period in a vacuum (even after accounting for buoyancy effects), indicating that the surrounding fluid increased the effective mass of the system. (See: G. G. Stokes, Trans. Camb. Philos. Soc. 9, 8, 1851. )

Applications

The added mass can be incorporated into most physics equations by considering an effective mass as the sum of the mass and added mass. This sum is commonly known as the "virtual mass".

A simple formulation of the added mass for a spherical body permits Newton's classical second law to be written in the form

F = m a

becomes

F = (m + m added) a

One can show that the added mass for a sphere (of radius $r$ ) is $2 / 3π r 3 ρ f l u i d$ . For a general body, the added mass becomes a tensor (referred to as the induced mass tensor), with components depending on the direction of motion of the body. History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually It should be noted that not all elements in the added mass tensor will have dimension mass, some will be mass*length and some will be mass*length².

All bodies accelerating in a fluid will be affected by added mass, but since the added mass is dependent on the density of the fluid, the effect is often neglected for dense bodies falling in much less dense fluids. For situations where the density of the fluid is comparable to or greater than the density of the body, the added mass can often be greater than the mass of the body and neglecting it can introduce significant errors into a calculation.

For example, a spherical air bubble rising in water has a mass of $4 / 3π r 3 ρ a i r$ but an added mass of $2 / 3π r 3 ρ w a t e r$ . Since water is approximately 800 times denser than air (at RTP), the added mass in this case is approximately 400 times the mass of the bubble. In Physical sciences standard conditions for temperature and pressure are Standard sets of conditions for experimental measurements to allow comparisons to be made

References

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Contents

History

Applications

See also

References