Orifice Permanent (Unrecovered) Pressure Loss (ISO 5167)
The permanent pressure loss across a square-edge orifice plate - the head the pump or fan actually pays.
Example
You enter
- Pipe inside diameter (in) 4
- Bore / orifice diameter (in) 2
- Differential pressure across taps (psi) 1
- Orifice discharge coefficient Cd (~0.61) 0.61
You get
- Loss fraction of dP 73.1% lost
- Permanent pressure loss 0.73073
- Permanent loss inwc 20.227
- Recovered downstream 0.26927
- Beta ratio (d/D) 0.5
Checked against published worked examples from: ISO 5167-1/2.
Details, formula, and sources
ScopeThe differential pressure measured across the taps is mostly recovered downstream as the jet re-expands; only a fraction stays lost. ISO 5167-1/2 gives that fraction as dW/dP = (sqrt(1 - beta^4 (1 - Cd^2)) - Cd beta^2) / (sqrt(1 - beta^4 (1 - Cd^2)) + Cd beta^2), with beta = bore/pipe ID and Cd the orifice discharge coefficient (~0.61). A 2 in orifice in a 4 in line (beta 0.5) with 1 psi differential loses about 73% (0.73 psi, 20.2 in w.c.) and recovers only 27%; shrink the bore to 1.2 in (beta 0.3) and the loss climbs to 90%, while opening it to 2.8 in (beta 0.7) drops it to 51% - so a small bore meters a wide flow range but wastes the most pump head, the central trade in sizing an orifice. Square-edge orifice plates only: a classical venturi recovers most of the differential (its loss, ~10-20% of dP, is a separate divergent-cone calculation), and a flow nozzle sits between. The flow itself comes from the DP flow-meter equation, liquid or gas. 1 psi = 27.68 in w.c. A sizing estimate; the manufacturer's or ISO 5167 loss data governs.
Formula or tabledW/dP = (sqrt(1 - beta^4 (1 - Cd^2)) - Cd beta^2) / (sqrt(1 - beta^4 (1 - Cd^2)) + Cd beta^2); permanent loss = (dW/dP) dP; recovered = dP - loss. beta = d/D; 1 psi = 27.68 in w.c.
Source and editionThe ISO 5167-1/2 permanent (unrecovered) pressure-loss ratio for a square-edge orifice plate, cited by name; the underlying loss physics is public and the manufacturer's or ISO 5167 loss data governs.
Free accessThe permanent pressure-loss ratio is the published ISO 5167-1/2 form; the orifice discharge coefficient (~0.61) is editable. Pipe diameter, bore, and differential pressure are the user's inputs.
What governsEstimate. AHJ and licensed professional govern.
API field namespipe_id_in, bore_in, dp_psi, cd, loss_fraction, permanent_loss_psi, permanent_loss_inwc, recovered_psi, beta_ratio
- Loss ratio dW/dP = (sqrt(1 - beta^4(1 - Cd^2)) - Cd beta^2)/(sqrt(1 - beta^4(1 - Cd^2)) + Cd beta^2)ISO 5167-1/2
- Beta effect smaller beta (bore) = more permanent loss; beta 0.5 ~73%, beta 0.3 ~90%, beta 0.7 ~51%ISO 5167-1/2
- Scope square-edge orifice only; a venturi recovers most of the dP (separate); Cd editable, ~0.61scope of this tile