Summary
The pressure drop or flow rate through a valve or orifice plate is typically calculated using the a flow coefficient, Cv or orifice diameter. This article demonstrates how to convert between these two parameters when performing functions such as selecting a valve with an equivalent pressure drop to a given orifice plate.
Definitions
| $D$ | : | Orifice Diameter (m) |
| $C_{v}$ | : | Flow coefficient, US imperial units |
| $C_{d}$ | : | Discharge coefficient, dimensionless |
| $\beta$ | : | Ratio of orifice to pipe size $ \beta = D_{o}/D_{1}$ , dimensionless |
Subscripts
| $1$ | : | Upstream of orifice or nozzle |
| $2$ | : | Downstream of orifice or nozzle |
| $o$ | : | Orifice or nozzle |
Orifice Diameter as a function of Cv
The formula for equating the orifice diameter to the flow coefficient is as follows:
$$ \displaystyle D_o = \frac{0.00464986 \left( \left(1 - \beta^4 \right) C_v^2 \right)^{1/4}}{\sqrt{C_d}} $$
Where the diameter $D$ is in meters, and the $C_{v}$ is in US units USGPM and PSI.
The above equation permits the specification of a $\beta $ ratio, which is the ratio of the orifice diameter to the upstream pipe diameter. This equation can be simplified by assuming that the orifice diameter is small compared to the upstream pipe diameter, i.e. ( $ \beta = 0 $ ), as follows:
$$ \displaystyle D_o = \frac{0.00464986 \sqrt{C_v}}{\sqrt{C_d}} $$
Cv as a Function of Orifice Diameter
Alternatively an orifice diameter can be converted to an equivalent Cv using the equation below:
$$ \displaystyle C_v = \frac{46250.9 C_d D_o^2}{\sqrt{1 - \beta^4}} $$
Again we can simplify the equation by assuming that ( $ \beta = 0 $ ) to get the following:
$$ \displaystyle C_v = 46250.9 C_d D_{o}^{2} $$
Conversion Values
The table below provides a quick reference for the conversion between $C_{v}$ and $D$ assuming that $\beta = 0$ and $C_{d} = 0.61$ .
| Cv | D (mm) |
|---|---|
| 0.001 | 0.188 |
| 0.005 | 0.421 |
| 0.01 | 0.595 |
| 0.05 | 1.33 |
| 0.1 | 1.88 |
| 0.5 | 4.21 |
| 1 | 5.95 |
| 5 | 13.3 |
| 10 | 18.8 |
| 50 | 42.1 |
| 100 | 59.5 |
| 500 | 133 |
Further Reading
- Flow Measurement Engineering Handbook, R. W. Miller
- Albright's Chemical Engineering Handbook, L. Albright
- Instrument Engineers' Handbook, Vol. 1: Process Measurement and Analysis
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