Orifices and Nozzles on a Horizontal Plane

Written by Jerry Ratzlaff on . Posted in Flow Instrument

When orifices and nozzles are installed having the piping horizontal and assuming that there is no elevation change, the following equations can be used.

 

Formulas that use Orifices and Nozzles on a Horizontal Plane

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

Where:

\(\large{ Q }\) = flow rate

\(\large{ \rho }\)  (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 Orifice and Nozzle