In
fluid mechanicsFluid mechanics is the study of how fluids move and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest, and fluid dynamics, the study of fluids in motion. It is a branch of continuum mechanics, a subject which models matter without using the...
, the
force density has the physical dimensions of force per unit volume. Force density is a
vector fieldIn mathematics a vector field is a construction in vector calculus which associates a vector to every point in a subset of Euclidean space.Vector fields are often used in physics to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of...
representing the
fluxIn the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.* In the study of transport phenomena , flux is defined as the amount that flows through a unit area per unit time...
density of the hydrostatic force within the bulk of a
fluidA fluid is a substance that continually deforms under an applied shear stress. All gases are fluids, but not all liquids are fluids. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
. Force density is represented by the symbol
f, and given by the following equation, where
P is the
pressurePressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
:
Discussion
Ask a question about 'Force density' Start a new discussion about 'Force density' Answer questions from other users |
In
fluid mechanicsFluid mechanics is the study of how fluids move and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest, and fluid dynamics, the study of fluids in motion. It is a branch of continuum mechanics, a subject which models matter without using the...
, the
force density has the physical dimensions of force per unit volume. Force density is a
vector fieldIn mathematics a vector field is a construction in vector calculus which associates a vector to every point in a subset of Euclidean space.Vector fields are often used in physics to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of...
representing the
fluxIn the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.* In the study of transport phenomena , flux is defined as the amount that flows through a unit area per unit time...
density of the hydrostatic force within the bulk of a
fluidA fluid is a substance that continually deforms under an applied shear stress. All gases are fluids, but not all liquids are fluids. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
. Force density is represented by the symbol
f, and given by the following equation, where
P is the
pressurePressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
:
.
The net force on a differental volume element
dV of the fluid is:
Thus, the force density at a point in a fluid, divided by the
densityThe density of a material is defined as its mass per unit volume. The symbol of density is ρ .- Formula :Mathematically:where: is the density, is the mass, is the volume....
, is the
accelerationIn physics, and more specifically kinematics, acceleration is the change in velocity over time. Because velocity is a vector, it can change in two ways: a change in magnitude and/or a change in direction. In one dimension, i.e. a line, acceleration is the rate at which something speeds up or slows...
of the fluid at that point.