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James F. Price's Draining a Tank, an appendix to Dimensional Analysis of Models and Data Sets, describes an actual tabletop experiment in sections 2.1–2.3. Tap water filled a semitransparent polypropylene beaker with a marked volume scale and drilled side openings. Some trials added horizontal outlet tubes. Temperature was measured, and dye checked that the water had settled before uncovering the outlet. The readout was elapsed time at successive volume marks. Opening diameter and tube length varied between trials. Reported repeatability was checked; tube bores were measured with feeler gauges rather than accepted from nominal sizes.^[ref]

For tank area $A$ and volume $W_o$ at outlet level, the observations give $h_i=(W_i-W_o)/A$ and interval volumetric flow rate $Q_i\simeq (W_i-W_{i+1})/(t_{i+1}-t_i)$. Price compared $Q/(a\sqrt{2gh})$ across heads to infer a discharge coefficient where that ratio was nearly constant. At small head, drainage could stop with a protruding water cap; surface tension mattered. Outlet tubes introduced viscosity effects. This experiment tests a useful operating range, rather than proving ideal drainage down to zero head.^[ref]

A useful independent test of the constant-coefficient model avoids numerical derivatives of noisy head readings. Its exact square root relation predictsFit a straight line to $\sqrt{h_i}$ against time over a chosen positive-head interval; the negative slope determines $b$. Repeat from the same initial head and compare slopes, then vary the head interval to test constancy of $C_d$. This is a proposed diagnostic derived from the draining tank with constant cross-sectional area, not an additional procedure or measured fit attributed to Price. Startup transients, uncertain outlet level, a changing jet shape and terminal low-head data can spoil the straight line. Independent collection of discharged volume provides a check on the tank-scale readout.

By James F. Price. An appendix to Essay 2: Dimensional Analysis of Models and Data Sets. Section 8 credits the experiments, models, code, text and technical figures to the author. Woods Hole Oceanographic Institution is his affiliation and provides administrative support; MIT OpenCourseWare hosts the appendix in its Topics in Fluid Dynamics resource collection.

Online text: ocw.mit.edu/courses/res-12-001-topics-in-fluid-dynamics-fall-2024/mitres_12_001_f24_appendix.pdf

Inspected version: 9 February 2026, printed on the PDF cover. This version date is distinct from the Fall 2024 resource-collection label; no original publication date is asserted.

Cited passages: PDF cover p. 1, author and February 9, 2026 date; §§2.1–2.3, printed pp. 9–12: parameter control, semitransparent beaker, temperature and dye preparation, volume/time readout, repeatability and bore uncertainty; equations (1)–(2), printed pp. 10–11: head from measured volume, flow from volume/time differences; Fig. 2, printed p. 12: head trajectories and incomplete low-head drainage; §§2.5 and 3.1, printed pp. 15–18, equations (10)–(14) and Fig. 3: ideal speed and empirical discharge normalization; §4 introductory discussion, printed pp. 19–20: protruding cap and surface tension; §5 introduction and §2 apparatus description: viscous outlet-tube effects; §8, printed p. 51: attribution of experiments and technical figures.