The application of fast-scan linear sweep voltammetry methods to a high-speed wall-tube electrode (HWTE) is reported. Experiments are reported for the oxidation of N,N,N′,N′-tetramethyl-p-phenylenediamine (TMPD) in propylene carbonate solution containing 0.10 M tetrabutylammonium perchlorate for a 24 μm radius platinum microdisk electrode housed within the HWTE using a range of scan rates from 200 to 3000 V s and average flow jet velocities from 0.24 to 9.4 m s (corresponding to volume flow rates of 0.003-0.12 cm s, and centre-line jet velocities from 0.5 to 18.9 m s). Linear sweep voltammograms (LSVs) are analysed for a simple electron transfer under high volume flow rates, by curve fitting. Analysis of the transient LSVs yielded values for k, α, and E for TMPD of (5.9±2.4)×10 cm s, 0.46±0.08 and 0.217±0.019 V (vs. Ag), respectively. This is in good agreement with independent experiments conducted using the high-speed channel electrode which yielded the results: k=(6.3±0.4)×10 cm s, α=0.52±0.01, and E=0.234±0.005 V (vs. Ag). The range of applicability of this method for measuring k was also investigated and compared with existing channel electrode techniques.