# Orifice Flow Rate

Written by Jerry Ratzlaff on . Posted in Flow Instrument Orifice flow rate is the amount of fluid that flows in a given time.

## Orifice Flow Rate formula

 $$\large{ Q = C_d \; A_o \; \sqrt { 2 \; G \; h } }$$

### Where:

 Units English Metric $$\large{ Q }$$ = orifice flow rate $$\large{\frac{ft^3}{sec}}$$ $$\large{\frac{m^3}{s}}$$ $$\large{ A_o }$$ = orifice area $$\large{ in^2 }$$ $$\large{ mm^2 }$$ $$\large{ h }$$ = orifice center of head $$\large{ in }$$ $$\large{ mm }$$ $$\large{ C_d }$$ = orifice discharge coefficient $$\large{ dimensionless }$$ $$\large{ G }$$ = orifice gravitational constant $$\large{\frac{lbf-ft^2}{lbm^2}}$$ $$\large{\frac{N -m^2}{kg^2}}$$

## Related formulas

 $$\large{ Q = C_d \; A_o \; Y \;\sqrt { \frac{ 2 \; \Delta p }{ \rho \; \left( 1 \;-\; \beta^4 \right) } } }$$ (horizontal orifice and nozzle) $$\large{ Q = C_d \; A_o \; Y \;\sqrt { \frac{ 2 \; g \; \Delta h }{ \left( 1 \;-\; \beta^4 \right) } } }$$ (horizontal orifice and nozzle) $$\large{ Q = C_d \; A_o \; Y \;\sqrt { \frac{ 2 \; \left( \Delta p \;+\; \rho \; g \; \Delta y \right) }{ \rho \; \left( 1 \;-\; \beta^4 \right) } } }$$ (vertical orifice and nozzle) $$\large{ Q = C_d \; A_o \; Y \;\sqrt { \frac{ 2 \; g \; \left( \Delta h \;+\; \Delta y \right) }{ \left( 1 \;-\; \beta^4 \right) } } }$$ (vertical orifice and nozzle)

### Where:

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

$$\large{ h }$$ = center of head

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

$$\large{ \Delta y }$$ = elevation change

$$\large{ Y }$$ = expansion coefficient (Y = 1 for incompressible flow)

$$\large{ g }$$ = gravitational acceleration

$$\large{ \Delta h }$$ = head loss

$$\large{ A_o }$$ = orifice area

$$\large{ C_d }$$ = orifice discharge coefficient

$$\large{ G }$$ = orifice gravitational constant

$$\large{ p }$$ = pressure

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

$$\large{ \beta }$$  (Greek symbol beta) = ratio of pipe inside diameter to orifice diameter

$$\large{ d_o }$$ = orifice or nozzle diameter

$$\large{ d_u }$$ = upstream pipe inside diameter from orifice or nozzle

$$\large{ C_{d,c} }$$ = discharge coefficient compressible fluid

$$\large{ C_{d,i} }$$ = discharge coefficient incompressible fluid

### Solve For:

 $$\large{ \Delta y = y_1 - y_2 }$$ $$\large{ \Delta p = p_2 - p_1 }$$ $$\large{ Y = \frac{ C_{d,c} }{ C_{d,i} } }$$ $$\large{ \beta = \frac{d_o}{d_u} }$$ 