**Vector** is a quantity having both magnitude and direction, for example
acceleration,
force and
velocity.

As opposed to scalar quantities like density, mass and speed which have magnitude but no direction.

Vectors can only be added, subtracted or multiplied using mathematical procedures that take account of the co-ordinates. A vector is defined as an element of a vector space.

**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.

**Velocity (v)** the rate of change of position and is a vector quantity as both speed and direction are required to define it.

The SI units are metres per second, (m/s).

v = u + at where v = velocity, u = start velocity, a = acceleration in m/s^{2} and t = time.

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^{2} = 0.01 m/s = 10 μm at 159 Hz

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 and volume velocity

**Velocity Level (Lv)** also known as **vibratory velocity level** = 20 lg(v/vo) dB re 1 nm/s

The 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

a 40 dB = a factor of 100

a 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

**Velocity of Sound** is usually taken to mean the Speed of Sound, not be confused with the sound particle velocity, which is the velocity of the individual particles. To add to the confusion the unit v is often included.

**Vibration** mechanical oscillations occur about an
equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random.

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

See also the table of dB Reference Levels and Vibration Dose

**Vibration at Work Regulations** - Control of Vibration at Work Regulations 2005 (the Vibration Regulations), came into force on 6 July 2005 and aim to protect workers from risks to health from vibration.

The Regulations introduce the action and limit Values for hand arm and whole body vibration.

For others details see the Government and/or HSE websites.

See also • acceleration equivalent value • hand arm vibration syndrome • whole body vibration • certified vibration at work instrumentation

Vibration Nomogram for downloading.

**Vibration Parameters**

Acceleration

Velocity

Displacement

Vibration Regulations, see Vibration at Work Regulations

**Volt (V)** the derived SI unit of electric potential; the potential difference between two points on a conductor carrying a current of 1 ampere, when the power dissipated between these points is 1 watt

**Voltage Level (LV)** dB (1 V RMS) : voltage relative to 1 volt, regardless of impedance.

Lv = 20 lg (V/Vo) dBV

The reference voltage : Vo = 1 volt ≡ 0 dB

**Volume (V)** the amount of space that an object or substance occupies, the SI unit is the cubic metre (m^{3})

**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* and the *rate of fluid flow*

See also • volume velocity

**Volumetric Flux (q)** is 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}

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