Orifices and Nozzles on a Horizontal Plane

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 formulas

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

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