# Pipeline Flow Calculator Documentation

For many pipeline applications, it is useful to estimate the velocity of the high pressure gas that flows through the line. Since pipeline flow rates are generally specified at standard temperature and pressure, the gas state at line temperature and pressure must be computed first before the gas velocity can be estimated.

## Equation for Gas Velocity

Consider a simple pipeline system comprised of some length of pipe with a compressor on one end and a control valve on the other to throttle flow. Let condition 1 represent the state of the gas as it enters the compressor inlet, assumed to be standard temperature and pressure. Let condition 2 represent the state of the gas at some point along the pipeline between the compressor outlet and the control valve at the far end.

The ideal gas law, corrected for compressibility, can be expressed as $$P\nu = ZRT$$ where $P$ is the absolute pressure, $\nu$ is the specific volume, $Z$ is the compressibility factor, $R$ is the gas constant, and $T$ is the absolute temperature. Writing the gas law for each condition above and applying conservation of mass yields an expression for $V_2$, the volume of gas at condition 2, as it relates to $V_1$, the volume of gas at condition 1. $$V_2 = \left(\frac{Z_2}{Z_1}\right) \left(\frac{P_1}{P_2}\right) \left(\frac{T_2}{T_1}\right) V_1$$ Rewriting in terms of volume flow rates $Q_2$ and $Q_1$, $$Q_2 = \left(\frac{Z_2}{Z_1}\right) \left(\frac{P_1}{P_2}\right) \left(\frac{T_2}{T_1}\right) Q_1$$ Average gas velocity $\vec{v}$ is related to volume flow rate and pipe cross sectional area $A$ by $$\vec{v} = \frac{Q}{A}$$ which can be used to obtain the final equation for gas velocity at condition 2 as $$\vec{v}_2 = \left(\frac{Z_2}{Z_1}\right) \left(\frac{P_1}{P_2}\right) \left(\frac{T_2}{T_1}\right) \left(\frac{4}{\pi d^2}\right) Q_1$$ where $d$ is the pipe inner diameter.

## Application

To apply the gas velocity equation above, the pipeline flow calculator accepts the following pipeline parameters as inputs from the user to establish the gas state at condition 2:

• pipeline product
• pipe outer diameter
• pipe wall thickness
• operating pressure
• product temperature

The remaining input is the volume flow rate at condition 1, specified at standard temperature and pressure, namely

• $T_1$ = 520 R
• $P_1$ = 14.7 psia

Various units are available for each input. The flow calculator handles all unit conversions so that the equation is always applied using a consistent set of units.

## Limitations

Compressibility factors for the various products are available for temperatures ranging from −10° F to 170° F and for pressures ranging from 15 psia to 2175 psia. The calculator does not extrapolate beyond the limits of these ranges. As such, temperature and pressure inputs that exceed these ranges are first clamped to be within the ranges before computing gas velocity.

## Disclaimer

The pipeline flow calculator is provided "as is" with no warranty, expressed or implied, concerning its accuracy, reliability, or suitability for a particular purpose. You assume the responsibility for selecting the calculator for your use and for the results you obtain from your use of the calculator.