Velocity

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

velocity 6Velocity, abbreviated as v or VEL, is the rate of change or displacement with time.  Velocity is a vector quantity having magnitude and direction.  The scalar absolute value of magnitude of the velocity vector is the speed of the motion.  Velocity is not speed, they do not mean the same thing.

Velocity is a vector quantity having magnitude and direction, some of these include acceleration, displacement, drag, force, lift, momentum, thrust, torque, and weight.

Velocity Formula

\(\large{ v = \frac{ d }{ t }   }\)

\(\large{ v = \frac{ x_f \;-\; x_i }{ t }   }\)

\(\large{ v = v_i + a \; t  }\)

\(\large{ v =  \sqrt { \frac {Ca \;  B}{\rho}  }  }\)     (Cauchy number)

\(\large{ v =  \sqrt {      \frac { 2\; \left (p \;-\;p_v \right)}  {Ca\; U^2}      }    }\)     (Cavitation number)

\(\large{ v = \sqrt{ a_c \; r }   }\)     (centripetal acceleration)

\(\large{ v = \sqrt{   \frac{ F_c \; r }{ m }   }   }\)     (centripetal force)

\(\large{ v = \sqrt { \frac { 2 \; h_l \; d_p \; g } { f_d \; l_p } } }\)     (Darcy-Weisbach equation)

\(\large{ v =  \sqrt  {  2  \;  Ec \; c \;  \triangle T     }    }\)     (Eckert number)

\(\large{ v =  \sqrt  {  \frac{\Delta p}{Eu \;  \rho}  }  }\)     (Euler number)

\(\large{ v =  Fr \; \sqrt{ g \; h_m  }  }\)     (Froude number)

\(\large{ v = \sqrt {  \frac{2 \; KE}{m} }  }\)     (kinetic energy)

\(\large{ v =   \sqrt{   2 \; g \; \left( NPSH - \frac{ p }{ \gamma } + \frac{ p_v }{ \gamma }  \right)   }  }\)     (net positive suction head)

\(\large{ v =  \frac {Pe \; k}{ \rho \; C \; l_c }    }\)     (Peclet number)

\(\large{ v = \frac{P}{F}  }\)     (power)

\(\large{ v = \frac{ Re \; \mu }{ \rho \; l_c  }  }\)     (Reynolds number)

\(\large{ v = Ma \; a_s }\)     (Mach number)

\(\large{ v = \frac{ Q }{ A  }  }\)     (volumetric flow rate)

\(\large{ v =  \sqrt{ \frac { We \; \sigma  }{ \rho \; l_c  }   }   }\)     (Weber number)

Where:

\(\large{ v  }\) = velocity

\(\large{ a  }\) = acceleration

\(\large{ A }\) = area

\(\large{ B }\) = bulk modulus elasticity

\(\large{ Ca  }\) = Cauchy number

\(\large{ a_c }\) = centripetal acceleration

\(\large{ F_c }\) = centripetal force

\(\large{ l_c }\) = characteristic length or diameter of fluid flow

\(\large{ U }\) = characteristic velocity

\(\large{ Ca }\) = Cavitation number

\(\large{ f_d }\) = Darcy friction factor

\(\large{ \rho }\)  (Greek symbol rho) = density

\(\large{ d  }\) = displacement

\(\large{ \mu }\)  (Greek symbol mu)  = dynamic viscosity

\(\large{ Ec }\) = Eckert number

\(\large{ Eu }\) = Euler number

\(\large{ Fr  }\) = Froude number

\(\large{ F }\) = force

\(\large{ x_f }\) = final position

\(\large{ x_i }\) = initial position

\(\large{ v_i  }\) = initial velocity

\(\large{ g }\) = gravitational acceleration

\(\large{ h_l }\) = head loss

\(\large{ C }\) = heat capacity

\(\large{ KE }\) = kinetic energy

\(\large{ Ma }\) = Mach number

\(\large{ m }\) = mass

\(\large{ h_m }\) = mean depth

\(\large{ NPSH }\) = net positive suction head

\(\large{ Pe  }\) = Peclet number

\(\large{ d_p }\) = pipe diameter (ID)

\(\large{ l_p }\) = pipe length

\(\large{ P }\) = power

\(\large{ p }\) = pressure

\(\large{ \Delta p }\) =  pressure differential

\(\large{ r }\) = radius of circular path

\(\large{ Re }\) = Reynolds number

\(\large{ \gamma }\)  (Greek symbol gamma) = specific weight

\(\large{ \Delta T }\) = temperature differential

\(\large{ k }\) = thermal conductivity

\(\large{ t  }\) = time

\(\large{ c }\) = specific heat

\(\large{ a_s }\) = speed of sound

\(\large{ \sigma }\)  (Greek symbol sigma) = surface tension

\(\large{ p_v }\) = vapor pressure

\(\large{ Q }\) = volumetric flow rate

\(\large{ We }\) = Weber number

 

Tags: Equations for Velocity