Orifice Head Loss

Written by Jerry Ratzlaff on . Posted in Flow Instrument

Orifice Head Loss formulas

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

Where:

 Units English SI
\(\large{ \Delta h }\) = head loss \(\large{ ft }\) \(\large{ m }\)
\(\large{ \Delta y }\) = elevation change (\(\Delta y = y_1 - y_2\)) \(\large{ ft }\) \(\large{ m }\)
\(\large{ Y }\) = expansion coefficient (Y = 1 for incompressible flow) \(\large{ dimensionless }\)
\(\large{ g }\) = gravitational acceleration  \(\large{\frac{ft}{sec^2}}\) \(\large{\frac{m}{s^2}}\)
\(\large{ A_o }\) = orifice area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ C_d }\) = orifice discharge coefficient \(\large{ dimensionless }\)
\(\large{ Q }\) = orifice flow rate \(\large{\frac{ft^3}{sec}}\) \(\large{\frac{m^3}{s}}\)
\(\large{ \beta }\)  (Greek symbol beta) = ratio of pipe inside diameter to orifice diameter \(\large{ dimensionless }\)

 

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 Head Equations for Orifice and Nozzle