Weymouth Gas Pipeline Flow (Flow from the Pressure Drop)

The Weymouth equation answers a practical question about a gas line: given the pressure at the inlet and at the outlet, how much gas moves through the pipe? The flow $Q$ is stated at base conditions, a base temperature $T_b$ and a base pressure $P_b$, so it is the volume the gas would fill if it were brought to those conditions, not the volume passing a point in the pipe, where the gas is compressed and takes up less room. The pressures enter as $P_1^{2} - P_2^{2}$, and both must be absolute: a gauge reading gives the wrong answer.

The other terms each have a plain meaning. The flow falls with the gas gravity $G$, the flowing temperature $T$, the length $L$ and the compressibility factor $Z$: a heavier gas, a warmer gas, a longer pipe and a larger compressibility factor all reduce the flow for the same fall in pressure. It rises very steeply with the inside diameter, as $D^{2.667}$, so a small change in diameter changes the flow a great deal. The efficiency $E$, from 0.92 to 1.00, allows for a pipe rougher or dirtier than new. Weymouth has no friction factor of its own; it assumes one that falls with the diameter. In Menon's worked example it gives a larger pressure drop than the Panhandle equations for the same flow, so its answer is the more conservative.

The equation is T. R. Weymouth's of 1912, written for high-pressure gas gathering lines. This page follows E. S. Menon's Gas Pipeline Hydraulics and his course text, which print the constant as 433.5 in US customary units and as 3.7435e-3 in an SI form (cubic metres a day, kilopascals, kilometres, millimetres). The page accepts any unit and converts exactly, which leaves 137.34 in SI base units. The elevation term of the full equation is left out, so the pipe is taken as level.

The worked example is Menon's example 11: an NPS 18 line with 17.5 in inside diameter, 20 miles long, carrying 150 MMSCFD of gas of gravity 0.6 at 70 °F, with $Z = 0.85$, $E = 0.95$, base conditions of 60 °F and 14.7 psia, and an inlet pressure of 1 000 psig (1 014.7 psia). Menon finds an outlet pressure of 946.24 psia. The page's example enters the same case in his SI form and returns 6.5240 MPa out, within 1e-5 of the US form. Run backwards from the printed outlet pressure, it returns the diameter 17.5 in, the length 20 miles and the efficiency 0.95.