Orifice Flow Rate

Written by Jerry Ratzlaff on . Posted in Flow Instrument

orifice liquid 1Orifice 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:

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

 

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Tags: Flow Equations Orifice and Nozzle Equations