= Pulmonary vein
A \b[pulmonary vein] returns <blood> from a <lung> to the <left atrium>. The <pulmonary veins> complete the return side of the <pulmonary circulation>, after <blood> has received <oxygen> in the <lungs>. They are <veins> because they carry <blood> toward the <heart>, even though their oxygen content is higher than that of the <blood> arriving through the <pulmonary artery>.<How Blood Flows through the Heart by NHLBI>[Adding oxygen to blood]{ref}
Following a parcel of <blood> makes the sequence clear: <right ventricle>, <pulmonary trunk>, vessels of the <lungs>, <pulmonary vein>, <left atrium>, then <left ventricle>. The <pulmonary vein> connects the lung circuit to the receiving chamber of the left heart; it does not drain directly into the <right atrium>.
A simple oxygen balance illustrates why both content and flow matter. Suppose two returning streams have <blood flow> rates $Q_1,Q_2$ and oxygen contents $C_1,C_2$. If they mix without further oxygen exchange, the <left atrium>'s inflow content is
$$
C_{\rm mix}=\frac{Q_1C_1+Q_2C_2}{Q_1+Q_2}.
$$
For constructed values $Q_1=3$ L/min, $Q_2=2$ L/min, $C_1=0.20$ and $C_2=0.15$ mL/mL, this gives $0.18$ mL/mL. An unweighted average would give $0.175$ mL/mL. A specimen's vessel connections establish where the streams meet; <conservation of mass> establishes how their transported <oxygen> combines.
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