Orifices and Nozzles on a Horizontal Plane

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 formulas

$$Q \;=\; C_d \; A_o \; Y \; \sqrt { 2 \; \Delta p \;/\; \rho \; ( 1 - \beta^4 ) }$$

$$Q \;=\; C_d \; A_o \; Y \; \sqrt { 2 \; g \; \Delta h \;/\; \rho \; ( 1 - \beta^4 ) }$$

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

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

Symbol English Metric
$$Q$$ = flow rate $$ft^3\;/\;sec$$  $$m^3\;/\;s$$
$$\rho$$  (Greek symbol rho) = density $$lbm\;/\;ft^3$$ $$kg\;/\;m^3$$
$$\Delta y$$ = elevation change ( $$\Delta y = y_1 - y_2$$ ) $$ft$$ $$m$$
$$Y$$ = expansion coefficient (Y = 1 for incompressible flow) $$dimensionless$$
$$g$$ = gravitational acceleration $$ft\;/\;sec^2$$ $$m\;/\;s^2$$
$$A_o$$ = orifice area $$in^3$$ $$mm^2$$
$$C_d$$ = orifice discharge coefficient $$dimensionless$$
$$G$$ = orifice gravitational constant $$lbf-ft^2\;/\;lbm^2$$  $$N - m^2\;/\;kg^2$$
$$\Delta h$$ = orifice head loss $$ft$$ $$m$$
$$p$$ = pressure $$lbf\;/\;in^2$$ $$Pa$$
$$\Delta p$$ = pressure differential ( $$\Delta p = p_2 - p_1$$ ) $$lbf\;/\;in^2$$ $$Pa$$
$$\beta$$  (Greek symbol beta) = ratio of pipe inside diameter to orifice diameter $$dimensionless$$

Solve for:

$$Y = C_{d,c} \;/\; C_{d,i}$$

$$C_{d,c}$$ = discharge coefficient compressible fluid

$$C_{d,i}$$ = discharge coefficient incompressible fluid

$$\beta$$  (Greek symbol beta) = $$\frac{d_0}{d_u}$$

$$d_o$$ = orifice or nozzle diameter

$$d_u$$ = upstream pipe inside diameter from orifice or nozzle

Tags: Orifice and Nozzle