Abstract
We demonstrate operation of a constant-pressure flowmeter capable of generating and accurately measuring flows as low as $1\times10^-13}$mol/s. Generation of such small flows is accomplished by using a small conductance element with $C\approx 25$nL/s. Accurate measurement then requires both low outgassing materials ($<10^-15}$mol/s) and small displacements ($\approx 70$$\mu$L). We discuss the theoretical background for all flowmeters, and introduce new corrections due to the van der Waals interactions within the gas. We detail the present flowmeter's operation, and quantify its uncertainty, which is $<1$\% over the entire operating range and better than 0.3\% over a majority. Finally, we compare our flowmeter against a NIST standard flowmeter, and find agreement to within 0.55\% ($k=2$). Several future modifications can be made to achieve higher accuracy, with an ultimate goal of achieving a total $k=1$ uncertainty of $\approx 0.1$\%.