# 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