Orifice Pressure Loss

Written by Jerry Ratzlaff on . Posted in Flow Instrument

Orifice Pressure Loss formulas

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

Where:

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

\(\large{ \rho }\)  (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)

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

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

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

\(\large{ \beta }\)  (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 Pressure Equations for Orifice and Nozzle