# 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 Formula

$$\large{ v = \frac{ d }{ t } }$$

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

$$\large{ v = v_i + a \; t }$$

$$\large{ v = \frac{P}{F} }$$

$$\large{ v = \frac{ Q }{ A } }$$

$$\large{ v = \sqrt { \frac{2 \; KE}{m} } }$$

$$\large{ v = \sqrt{ \frac{ F_c \; r }{ m } } }$$

$$\large{ v = \sqrt{ a_c \; r } }$$

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

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

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

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

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

Where:

$$\large{ v }$$ = velocity

$$\large{ a }$$ = acceleration

$$\large{ A }$$ = area

$$\large{ a_c }$$ = centripetal acceleration

$$\large{ F_c }$$ = centripetal force

$$\large{ f_d }$$ = Darcy friction factor

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

$$\large{ d }$$ = displacement

$$\large{ Ec }$$ = 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

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

$$\large{ m }$$ = mass

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

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

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

$$\large{ l }$$ = pipe length

$$\large{ P }$$ = power

$$\large{ p }$$ = pressure

$$\large{ \Delta p }$$ =  pressure differential

$$\large{ r }$$ = radius of circular path

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

$$\large{ \Delta T }$$ = temperature differential

$$\large{ t }$$ = time

$$\large{ c }$$ = specific heat

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

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