# Velocity

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Velocity, 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 formulas

 $$\large{ v = \frac{ \Delta d }{ t } }$$ $$\large{ v = \frac{ x_f \;-\; x_i }{ t } }$$ $$\large{ v = v_i + a \; t }$$ $$\large{ v = \frac{ Q }{ A_c } }$$

### Where:

 Units English Metric $$\large{ v }$$ = velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$ $$\large{ a }$$ = acceleration $$\large{\frac{ft}{sec^2}}$$ $$\large{\frac{m}{s^2}}$$ $$\large{ A_c }$$ = area cross-section $$\large{ft^2}$$ $$\large{m^2}$$ $$\large{ \Delta d }$$ = displacement change $$\large{ft}$$ $$\large{m}$$ $$\large{ Q }$$ = flow rate $$\large{\frac{ft^3}{sec}}$$ $$\large{\frac{m^3}{s}}$$ $$\large{ x_f }$$ = final position $$\large{ft}$$ $$\large{m}$$ $$\large{ x_i }$$ = initial position $$\large{ft}$$ $$\large{m}$$ $$\large{ t }$$ = time $$\large{sec}$$ $$\large{s}$$ $$\large{ v_i }$$ = initial velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$

## Related formulas

 $$\large{ v = \sqrt { \frac {Ca \; B}{\rho} } }$$ (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) $$\large{ v = \sqrt {\frac {2 \;q} {\rho} } }$$ (Dynamic Pressure) $$\large{ v = Fr \; \sqrt{ g \; h_m } }$$ (Froude number) $$\large{ v = \sqrt { \frac{2 \; KE}{m} } }$$ (Kinetic Energy) $$\large{ v = \sqrt { \frac{2 \; L}{ C_l \; \rho \; A} } }$$ (Lift Force) $$\large{ v = \sqrt{ 2 \; g \; \left( NPSH - \frac{ p }{ \gamma } + \frac{ p_v }{ \gamma } \right) } }$$ (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

$$\large{ q }$$ = dynamic pressure

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

$$\large{ Fr }$$ = 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

$$\large{ d_p }$$ = inside diameter of pipe

$$\large{ KE }$$ = kinetic energy

$$\large{ l_p }$$ = lenght of pipe

$$\large{ C_l }$$ = lift coefficient

$$\large{ L }$$ = lift force

$$\large{ Ma }$$ = Mach number

$$\large{ m }$$ = mass

$$\large{ h_m }$$ = mean depth

$$\large{ NPSH }$$ = net positive suction head

$$\large{ Pe }$$ = Peclet number

$$\large{ P }$$ = 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

$$\large{ k }$$ = thermal conductivity

$$\large{ t }$$ = time

$$\large{ a_s }$$ = speed of sound

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

$$\large{ p_v }$$ = vapor pressure

$$\large{ Q }$$ = volumetric flow rate

$$\large{ We }$$ = Weber number