fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids ( liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and ...

, the force density is the negative

gradient In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gr ...

pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...

. It has the physical dimensions of force per unit

volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). Th ...

. Force density is a vector field representing the flux density of the

hydrostatic force Fluid statics or hydrostatics is the branch of fluid mechanics that studies the condition of the equilibrium of a floating body and submerged body "fluids at hydrostatic equilibrium and the pressure in a fluid, or exerted by a fluid, on an imme ...

within the bulk of a fluid. Force density is represented by the symbol f, and given by the following equation, where ''p'' is the

: :

\mathbf = - \nabla p

. The net force on a differential

volume element In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates. Thus a volume element is an expression of the form :dV ...

''dV'' of the fluid is: :

d\mathbf = \mathbfdV

Force density acts in different ways which is caused by the boundary conditions. There are stick-slip boundary conditions and stick boundary conditions which affect force density. In a sphere placed in an arbitrary non-stationary flow field of viscous incompressible fluid for stick boundary conditions where the force density's calculations leads to show the generalisation of Faxen's theorem to force multipole moments of arbitrary order. In a sphere moving in an incompressible fluid in a non-stationary flow with mixed stick-slip boundary condition where the force of density shows an expression of the Faxén type for the total force, but the total torque and the symmetric force-dipole moment. The force density at a point in a fluid, divided by the

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

, is the

acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by t ...

of the fluid at that point. The force density f is defined as the force per unit volume, so that the net force can be calculated by: :

\mathbf=\int f(\mathbf)d^3 \mathbf

. The force density in an electromagnetic field is given in CGS by: :

\mathbf=\rho \mathbf+ \frac \times \mathbf

, where

\rho

is the charge density, E is the electric field, J is the current density, c is the speed of light, and B is the magnetic field.Force Density
Eric Weisstein's World of Physics. Accessed 17 January 2015.

References

Density {{Fluiddynamics-stub

See also

References