Weld metal volume and filler consumption

Weld metal volume is a pure geometry problem plus two losses. The geometry is the groove cross-section: for a single-V preparation with included angle α, root face f and root gap g in plate of thickness t, the bevelled part is two right triangles of height (t − f) and base (t − f)·tan(α/2), giving (t − f)²·tan(α/2), and the root gap adds a rectangle g·t. A double-V preparation halves the bevel depth on each side and so needs roughly half the bevel volume of a single-V — which is exactly why double-V is chosen for thick sections despite the extra handling.

To that must be added the cap. A weld cap is close to a parabolic segment, so its area is about two thirds of width times height, and the width is the groove opening at the surface plus the toe extension each side. On thin plate with a wide gap the cap can be a third of the total volume, so ignoring it under-orders consumables significantly.

The two losses are separate and often confused. Deposition efficiency is the fraction of the consumable purchased that ends up as weld metal: for covered electrodes it is around 60 to 65 % because of the stub end and the flux coating, for solid wire around 90 to 95 %, for flux-cored around 75 to 85 % depending on whether it is gas shielded, and for submerged arc close to 100 % for the wire alone (flux is bought and consumed separately, typically at about 1 kg flux per kg of wire). Deposition rate in kg/h is a different quantity and drives arc time, not consumable quantity.

Two practical cautions. Real preparations are never exactly to drawing — root gaps open up under tacking and fit-up, and a 1 mm gap increase on a 20 mm butt adds 20 mm² of cross-section — 20 cm³ of weld metal per metre of joint, around 7 % of a typical single-V section. And the figure this calculation produces is deposited metal for the joint alone; it excludes tacks, run-on and run-off plates, repairs and the material lost to any back-gouging, which together commonly add 10 to 20 % on real fabrication.

Single-V:  A_groove = (t − f)²·tan(α/2) + g·t
Double-V:  A_groove = (t − f)²·tan(α/2)/2 + g·t
Fillet:    A_groove = z²/2   (z = leg length)
Cap:       A_cap = (2/3)·w_cap·h_cap ,  doubled for a double-V
Volume = A_total × L ;  Deposited mass = Volume × ρ
Filler purchased = deposited mass / deposition efficiency