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.

Orifices and Nozzles on a Horizontal Plane Formula

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

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

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

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

Where:

\(\large{ A }\) = area

\(\large{ h }\) = fluid head

\(\large{ \Delta h }\) = change in fluid head

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

\(\large{ z }\) = elevation

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

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

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

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

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

\(\large{ P }\) = pressure  \(\large{ \left( P_d - P_u \right) }\)

\(\large{ P_u }\) = upstream pressure of orifice or nozzle

\(\large{ P_d }\) = downstream pressure of orifice or nozzle

\(\large{ \Delta P }\) = pressure differential

\(\large{ \beta }\)  (Greek symbol beta) = ratio of pipe diameter to orifice diameter  \(\large{ \left( \frac{d_o}{d_u}  \right) }\)

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

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

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

 

Tags: Equations for Orifice