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.

 

Formulas that use Orifice Flow Rate

\(\large{ Q =  C_d \; A_o \; \sqrt { 2 \; G \; h } }\)  
\(\large{ Q =  C_d \; A_o \; Y \;\sqrt {  \frac{ 2 \; \Delta p }{ \rho \; \left( 1 \;-\; \beta^4   \right)    }   } }\) (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

\(\large{ C_d }\) = discharge coefficient

\(\large{ \Delta y }\) = elevation change ( \(\Delta y = y_1 - y_2\) )

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

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

\(\large{ G }\) = gravitational constant

\(\large{ \Delta h }\) = head loss

\(\large{ A_o }\) = orifice area (GOA)

\(\large{ p }\) = pressure

\(\large{ \Delta p }\) = pressure differential ( \(\Delta p = p_2 - p_1\) )

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

Solve for:

\(\large{ Y =  \frac{ C_{d,c} }{ C_{d,i} }  }\)

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

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

\(\large{ \beta }\)  (Greek symbol beta) = \(\frac{d_0}{d_u}\)

\(\large{ d_o }\) = orifice or nozzle diameter

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

 

Tags: Equations for Flow Equations for Orifice and Nozzle