A constant pressure flowmeter for extremely high vacuum.

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 volume changes ($\approx 70$ $\mu$L). We outline the present flowmeter's construction, detail its operation, and quantify its uncertainty, which is $<1$ % over the entire operating range and better than 0.3 % over a majority. In particular, we present an analysis of its hydraulic system, and quantify the shift and uncertainty due to the slightly compressible oil. Finally, we compare our flowmeter against a NIST standard flowmeter, and find agreement to within 0.61 % ($k=2$). Future modifications could achieve a $k=2$ uncertainty of 0.2 %.