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The Womersley number, usually denoted , is defined by the relation = = = =, where is an appropriate length scale (for example the radius of a pipe), is the angular frequency of the oscillations, and , , are the kinematic viscosity, density, and dynamic viscosity of the fluid, respectively. [2]
A correct description of such an object requires the application of Newton's second law to the entire, constant-mass system consisting of both the object and its ejected mass. [7] Mass flow rate can be used to calculate the energy flow rate of a fluid: [8] ˙ = ˙, where is the unit mass energy of a system.
Once again, the molar volume is used to calculate the mass concentration, or mass density, but the reference fluid is a single component fluid, and the reduced density is independent of the relative molar mass. In mathematical terms this is
Mass continuity (conservation of mass) The rate of change of fluid mass inside a control volume must be equal to the net rate of fluid flow into the volume. Physically, this statement requires that mass is neither created nor destroyed in the control volume, [2] and can be translated into the integral form of the continuity equation:
The area required to calculate the volumetric flow rate is real or imaginary, flat or curved, either as a cross-sectional area or a surface. The vector area is a combination of the magnitude of the area through which the volume passes through, A , and a unit vector normal to the area, n ^ {\displaystyle {\hat {\mathbf {n} }}} .
Rotational viscosity is a property of a fluid which determines the rate at which local angular momentum differences are equilibrated. In the classical case, by the equipartition theorem , at equilibrium, if particle collisions can transfer angular momentum as well as linear momentum, then these degrees of freedom will have the same average energy.
The weight of the displaced fluid can be found mathematically. The mass of the displaced fluid can be expressed in terms of the density and its volume, m = ρV. The fluid displaced has a weight W = mg, where g is acceleration due to gravity. Therefore, the weight of the displaced fluid can be expressed as W = ρVg.
Mass transfer coefficients can be estimated from many different theoretical equations, correlations, and analogies that are functions of material properties, intensive properties and flow regime (laminar or turbulent flow). Selection of the most applicable model is dependent on the materials and the system, or environment, being studied.