Orifices and Nozzles on a Vertical Plane
When orifices and nozzles are installed having the piping vertically and assuming that there is an elevation change, the following equations can be used.
Orifices and Nozzles on a Vertical Plane formulas |
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\( Q \;=\; C_d \; A_o \; Y \; \sqrt { 2 \; ( \Delta p + \rho \; g \; \Delta y ) \;/\; \rho \; ( 1 - \beta^4 ) } \) \( Q \;=\; C_d \; A_o \; Y \; \sqrt { 2g \; ( \Delta h + \Delta y) \;/\; \rho \; (1 - \beta^4 ) } \) \( Q \;=\; C_d \; A_o \; Y \; \sqrt { 2g \; ( \Delta h + \Delta y) \;/\; \rho \; ( 1 - \beta^4) } \) \( \Delta h \;=\; \frac{1}{2\;g} \; ( 1 - \beta^4 ) \; ( Q \;/\; C_d \; A_o \; Y )^2 - \Delta y \) |
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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) | \( dimensionless \) | |
| \( g \) = 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: |
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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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Tags: Orifice and Nozzle