Orifices and Nozzles on a Vertical Plane formulas |
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\( Q \;=\; C_d \cdot A_o \cdot Y \cdot \sqrt { \dfrac{ 2 \cdot ( \Delta p + \rho \cdot g \cdot \Delta y ) }{ \rho \cdot ( 1 - \beta^4 ) } } \) \( Q \;=\; C_d \cdot A_o \cdot Y \cdot \sqrt { \dfrac{ 2 \cdot g \cdot ( \Delta h + \Delta y) }{ \rho \cdot (1 - \beta^4 ) } } \) \( Q \;=\; C_d \cdot A_o \cdot Y \cdot \sqrt { \dfrac{ 2 \cdot g \cdot ( \Delta h + \Delta y) }{ \rho \cdot ( 1 - \beta^4) } } \) \( \Delta h \;=\; \dfrac{1}{2 \cdot g} \cdot ( 1 - \beta^4 ) \cdot \left( \dfrac{ Q }{ C_d \cdot A_o \cdot Y } \right)^2 - \Delta y \) |
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| 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) | \( dimensionless \) | \( dimensionless \) |
| \( g \) = Gravitational Acceleration | \(ft\;/\;sec^2\) | \(m\;/\;s^2\) |
| \( A_o \) = Orifice Area | \( in^3 \) | \( mm^2 \) |
| \( C_d \) = Orifice Discharge Coefficient | \( dimensionless \) | \( dimensionless \) |
| \( G \) = 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 | \( dimensionless \) | \( dimensionless \) |
Solve for: |
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\( Y = C_{d,c} \;/\; C_{d,i} \) \( C_{d,c} \) = discharge coefficient compressible fluid \( C_{d,i} \) = discharge coefficient incompressible fluid \( \beta \) (Greek symbol beta) = \(d_0\;/\;d_u\) \( d_o \) = orifice or nozzle diameter \( d_u \) = upstream pipe inside diameter from orifice or nozzle |
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When orifices and nozzles are installed having the piping vertically and assuming that there is an elevation change, the following equations can be used.
