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/s2 and t = time.
Velocity v = a/ω
Displacement s = v/ω
It follows that 10 m/s2 = 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.
Velocity Level also known as Vibratory Velocity Level (Lv) = 20 lg(v/vo) dB re 1 nm/s
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'
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 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.
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 (m3)
Volumetric Flow Rate (Q) is the volume of fluid which passes through a given surface per unit time.
Volumetric Flux (q) is the Volumetric Flow Rate across a unit area. SI units : m3·s-1·m-2
Volumetric Power Density volume based power density - watt/m3