Oval (Obround) Tank Volume from Dipstick

The partial liquid volume of a horizontal OVAL (obround) tank from a dipstick depth - the residential 275-gallon heating-oil tank shape. The cross-section is a rectangle of width W and straight height s = H - W capped by two semicircles of radius r = W/2 (full area pi r^2 + W s). The wetted area is piecewise - a circular segment through the bottom rounded end, then the half-round plus a rectangle, then the full area minus the empty top segment - times the length. A 27 x 44 x 60 in tank holds 268 gallons full (the nominal '275'); by symmetry the half-height mark is exactly half. Enter inside dimensions in inches. A vertical oval with flat ends; a round tank is gauged separately, and the tank's own chart governs custody. Reported in gallons, cubic feet, and cubic inches with the percent full.

r = W/2, s = H - W; wetted area = seg(h) for h<=r, pi r^2/2 + W(h-r) for h<=r+s, else (pi r^2 + W s) - seg(H-h); volume = area x length. seg(t) = r^2 acos((r-t)/r) - (r-t) sqrt(2 r t - t^2).

Horizontal oval (obround) tank partial gauging - the cross-section is a stadium (rectangle capped by two semicircles) and the wetted area is a piecewise circular-segment build-up; standard plane/solid geometry with the circular-segment relation as in Machinery's Handbook (Industrial Press), by name; public domain.

Public-domain geometry; the tank width, height, length, and dipstick depth are user-supplied.

Estimate. AHJ and licensed professional govern.

Field names used by the API: width_in, height_in, length_in, depth_in, volume_gal, percent_full

• Cross-section stadium: rectangle W x (H-W) capped by two semicircles r = W/2 (rounded top and bottom)plane geometry
• Wetted area piecewise circular segment -> half-round + rectangle -> full minus empty top segmentcircular-segment relation
• Scope vertical oval with flat ends; a round tank is the tank-volume tile; the tank chart governs custodyscope of this tile