In this paper, we derive scaling relations between photometric observable quantities and disk galaxy rotation velocity V_rot, or Tully-Fisher relations (TFRs). Our methodology is dictated by our purpose of obtaining purely photometric, minimal-scatter estimators of V_rot applicable to large galaxy samples from imaging surveys. To achieve this goal, we have constructed a sample of 189 disk galaxies at redshifts z<0.1 with long-slit H-alpha spectroscopy from Pizagno et al. (2007) and new observations. By construction, this sample is a fair subsample of a large, well-defined parent disk sample of ~170 000 galaxies selected from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7). The optimal photometric estimator of V_rot we find is stellar mass M_* from Bell et al. (2003), based on the linear combination of a luminosity and a colour. Assuming a Kroupa IMF, we find: log [V_{80}/(km s^-1)] = (2.142 +/- 0.004)+(0.278 +/- 0.010)[log (M_*/M_sun)-10.10], where V_{80} is the rotation velocity measured at the radius R_{80} containing 80 per cent of the i-band galaxy light. This relation has an intrinsic Gaussian scatter of 0.036 +/- 0.005 dex and a measured scatter of 0.056 dex in log V_{80}. For a fixed IMF, we find that the dynamical-to-stellar mass ratios within R_{80}, (M_dyn/M_*)(R_{80}), decrease from approximately 10 to 3, as stellar mass increases from M_* ~ 10^9 to 10^{11} M_sun. At a fixed stellar mass, (M_dyn/M_*)(R_{80}) increases with disk size, so that it correlates more tightly with stellar surface density than with stellar mass or disk size alone. In future work, we will use these results to study disk galaxy formation and evolution, and perform a fair, statistical analysis of the dynamics and masses of a photometrically-selected sample of disk galaxies. [Abridged]
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