**Vectors** can only be added, subtracted or multiplied using mathematical procedures that take account of the co-ordinates.

**Vector spaces** are applied throughout mathematics, science and engineering. They are the linear-algebraic notion to deal with systems of linear equations; offer a framework for Fourier expansion or provide an environment that can be used for solution techniques for partial differential equations.

v = u + at where v = velocity, u = start velocity, a = acceleration in m/s

In the field of vibration acceleration a, velocity v, displacement and angular frequency ω = 2·π·f , are related.

Velocity v = a/ω

Displacement s = v/ω

It follows that 10 m/s

This works for all frequencies, we just chose 159 Hz to keep the numbers simple. We also have a vibration nomogram for downloading.

See also group velocity • particle velocity • volume velocity
**Velocity reference level** : vo = 1 nm/s ≡ 0 dB (defined in ISO 1683) *

An increase or decrease in velocity of 20 dB = a factor of 10

40 dB = a factor of 100

60 dB = a factor of 1000, etc.

* ISO 1683 also states 'in connection with structure-borne sound, a reference value of 50 nm/s is also in use. In this event, the vibratory velocity level takes values close to the associated sound pressure and sound intensity levels'

See also angular velocity. • particle velocity, used in acoustic wave theory • peak particle velocity • standard reference levels table • volume velocity and the IEC definition of level

Vibration is commonly expressed in terms of acceleration, velocity, displacement and frequency which are related.

Vibration Acceleration Level

Vibration Dose Value

Vibration Exposure Action Value

Vibration Exposure Limit Value

Vibration Nomogram for downloading.

Vibration Reference Levels

Vibration Regulations

Vibration Velocity

Vibration Weighting Networks

Vibration White Finger

Vibratory Acceleration Level

Vibratory Velocity Level

Viscous Damping Definition (IEC 801-24-22) damping that occurs when a particle in an oscillating system is resisted by a force that has a magnitude proportional to the magnitude of the velocity of the particle and direction opposite to the direction of the particle

See also other damping topics.

Voice Simulator Definition (IEC 801-28-07) complex sound, usually emitted by an artificial mouth whose spectrum corresponds to that of the average human voice. Also known as an artificial voice

LV = 20 lg (V/Vo) dBV, the reference voltage : Vo = 1 volt ≡ 0 dB

**Volumetric Flow Rate (Q)** is the volume of fluid which passes through a given surface per unit time.

**Q = v·A,** where v = velocity, A = area/surface and the SI units are m^{3}/s.

**Volumetric flow rate** is also known as the *volume flow rate*, *rate of fluid flow* and *volume velocity*.

**Volumetric Flux (q)**, the volumetric flow rate across a unit area. SI units : m^{3}·s^{-1}·m^{-2}

**Volumetric Power Density**, volume based power density - watt/m^{3}

Volume Velocity Definition (IEC 801-21-31) integral, over a vibration surface, of the product of the component of particle velocity normal to the surface and the differential surface area.

Also known as *sound volume velocity*, *volumetric flow rate* and *volume flow rate*

See also velocity.

VWF : Vibration White Finger

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