One psi per hundred feet, and a constant nobody can derive
There are two numbers that size most of the pipe in a chemical plant. About one psi of pressure drop per hundred feet of liquid line, and about twenty metres a second for gas. Neither is a law. Both are ceilings, and they exist because the cost of going faster is not linear, it is quadratic and cubic and in one case it is a hole in an elbow.
What follows is where those numbers bite, what the arithmetic underneath them actually says, and the uncomfortable history of the one constant that the oil and gas industry has been typing into its pipe sizing for fifty years without being able to derive it.
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The two numbers, and what they are really saying
The liquid rule is a pressure gradient, not a velocity: hold the friction loss to roughly one psi for every hundred feet of straight run. The gas rule is a velocity, because for a compressible fluid the thing that hurts first is usually not the pump bill, it is the noise, the shaking and the metal loss.
They are the same rule wearing different clothes. Both are asking you to keep the kinetic energy of the stream small compared with the value of the pipe carrying it. And both are ceilings, which matters, because a rule with only an upper bound reads as permission to go as slow as you like. It is not. There is a floor underneath.
Put a real line through it. Water at 20°C, commercial steel, 4-inch schedule 40, which has an inside diameter of 102.3 mm. At 1.5 m/s the Reynolds number is about 153,000, the relative roughness is 0.00044, the Colebrook friction factor comes out at 0.0191, and the gradient is 0.93 psi per 100 ft. The rule has just told you that a 4-inch water line wants to run at about a metre and a half a second, which is also the bottom of the liquid velocity band. The two heuristics agree, because they are the same physics seen from two directions.
Go faster and you pay three ways
Friction climbs with the square of velocity. That is the
v² in Darcy-Weisbach, and it is the part everyone quotes. The part that
is worse, and that people miss, is what it does to the pump. Pumping power is pressure
drop times flow. In a pipe of fixed diameter, pressure drop goes as
v² and flow goes as v, so the power goes as
v³. Run a line 25 percent faster than it needs to and
you are paying about double the friction power for the rest of the plant's life.
Turn that around and it becomes the most useful single fact in line sizing. At a fixed
flow rate, velocity goes as 1/D², so the gradient goes as
1/D⁵. Going up one commercial pipe size, 4-inch to
6-inch, is a diameter ratio of 1.51 and cuts the pressure drop by a factor of
7.7. Computed properly, with the friction factor re-evaluated at the new
Reynolds number, that 4-inch line carrying its 2 m/s duty at 1.61 psi per 100 ft falls to
0.21 psi per 100 ft in 6-inch. One size up is almost never the wrong
answer on a line that runs continuously.
The pipe starts to sing and shake. Flow-induced noise and vibration
scale steeply with velocity too, and there is a nastier cousin: surge. Stop a moving
column of liquid suddenly and the Joukowsky equation prices it at
ΔP = ρ a Δv, where a is the pressure wave speed,
roughly 1200 m/s in a steel water line. A valve slammed on a 3 m/s line generates
about 520 psi of surge on top of the operating pressure. At 1 m/s the
same slam is 174 psi. The velocity cap is a mechanical rating decision disguised as a
hydraulics one.
Anything with grit in it sandblasts the elbows from the inside. Solid
particle erosion of ductile steel goes as roughly v to the power 2.4 to 3,
and it does not attack the straight run. It attacks wherever the fluid has to change
direction and the particles, being heavier, cannot. The outer radius of the first elbow
downstream of anything that makes solids is the thinnest metal in the system.
The floor, which is the half people forget
Go too slow and the solids settle and the line silts up. For an ordinary process liquid carrying a bit of grit, about 1 m/s is the working floor. For a real slurry that number is not good enough, and the honest calculation is Durand's deposition velocity.
Sand at s = 2.65 in that same 4-inch line, with FL = 1.2, gives 2.2 m/s. That is above the whole liquid design band, which is exactly the point: a slurry line is not a liquid line with solids in it, it is a different sizing problem, and the generic rule of thumb will quietly put the bed in for you. The 1 m/s figure is a floor for ordinary service, not a slurry answer.
The bands, in one table
These are the numbers people actually reach for. They are consistent with the pressure gradient rule in the ranges where both apply, and where they disagree the gradient rule wins for liquids and the velocity rule wins for gas.
| Service | Velocity | What sets it |
|---|---|---|
| Pump suction | 0.5 to 1.5 m/s | NPSH. Friction here comes straight off the margin against cavitation, so the gradient target drops to about 0.4 psi per 100 ft. |
| Pump discharge | 1 to 3 m/s | Capital against power. About 2 psi per 100 ft is the usual allowance. |
| General liquid line | 1 to 3 m/s | The 1 psi per 100 ft rule. |
| Gravity and drain lines | 0.5 to 1 m/s | Available head, and self-venting behaviour. |
| Gas and vapour | 10 to 30 m/s | Noise, vibration and erosion. About 20 m/s is the heuristic cap. |
| Saturated steam | 20 to 40 m/s | Erosion by entrained condensate, which is why it is capped below dry gas practice. |
| Superheated steam | 30 to 60 m/s | No condensate to throw, so the cap relaxes. |
| Slurry | above VD, often 2 to 4 m/s | Durand deposition velocity at the bottom, erosion at the top. A narrow band. |
Sources: CHE 480 design heuristics and Week 3 lecture notes; Hall, Rules of thumb: flow parameters, The Chemical Engineer, 2021; Couper, Penney, Fair and Walas, Chemical Process Equipment, rules of thumb.
The constant nobody can derive
Now the part that will make you distrust your own textbook.
API RP 14E, the recommended practice for offshore production platform piping, gives an erosional velocity above which you are told not to run:
That equation, and that constant, have been typed into pipe sizing for about fifty years. It is in spreadsheets, in company standards, in the sizing step of projects worth billions. And the 2019 review in Wear by Madani Sani and co-authors traces the number back to a US Navy figure of c = 160 for carbon steel from the Second World War era, which was subsequently trimmed, and concludes that the theoretical basis of the equation is unclear.
Read that again. A whole industry sizes pipe on a rule of thumb it cannot derive. Not a correlation fitted to bad data, not a conservative simplification of something harder: a number whose provenance is a wartime figure and whose derivation nobody can produce.
It is worth being precise about the blast radius, because the honest criticism is narrower than the internet version. RP 14E is a two-phase, solids-free oil and gas rule. It was never a general liquid rule, it contains no particle size, no sand rate, no geometry and no material, and the review's charge is that it gets used far outside the place it came from. Where it does apply it tends to be conservative at high density and meaningless at low.
What the constant actually costs you
The gap between 100 and 160 is not academic. It is a pipe size, sometimes two, on every gas line in the scope.
| Flowing density | Ve at c = 100 | Ve at c = 160 | Which rule binds |
|---|---|---|---|
| 0.075 lb/ft³ air, atmospheric | 365 ft/s · 111 m/s | 584 ft/s · 178 m/s | The 20 m/s heuristic, by a mile |
| 0.55 lb/ft³ gas, about 100 psig | 135 ft/s · 41 m/s | 216 ft/s · 66 m/s | The heuristic |
| 1.5 lb/ft³ gas, about 300 psig | 82 ft/s · 24.9 m/s | 131 ft/s · 39.8 m/s | The heuristic, just. The two cross at 2.3 lb/ft³ |
| 5.0 lb/ft³ gas, about 1000 psig | 45 ft/s · 13.6 m/s | 72 ft/s · 21.8 m/s | RP 14E, and it costs you a size |
Notice what the top row is telling you. Applied to atmospheric air the equation permits 111 m/s, which is a third of the speed of sound and would make a line unusable long before it eroded. That is not a criticism of the number, it is a demonstration that the equation has a domain, and that the domain is dense two-phase hydrocarbon service. Outside it the heuristic is doing all the work and the standard is decoration.
How to size a line without lying to yourself
- Start from the velocity band, land on the gradient. Pick a velocity in the band for the service, compute the diameter, round up to the nearest commercial size, then check the gradient with a real friction factor. Do not stop at the velocity.
- Price the size, do not just check it. Because the gradient goes as
1/D⁵, the next size up is nearly an order of magnitude cheaper to run. On a continuous line, run the comparison rather than accepting the first size that passes. - Separate the suction from the discharge. A suction line sized like a discharge line is where NPSH problems come from, and the pump will be blamed for it.
- If there are solids, do Durand. The 1 m/s floor is not a slurry answer.
- If it is dense two-phase hydrocarbon, apply RP 14E and know what you are applying. Cite it as the standard it is, and if the number is driving the design, say so in the basis. If it is not binding, note that too, so the next engineer does not think it was checked when it was not.
- Then check it in a simulator. Every number here is a starting point that the real fluid, the real fittings and the real elevation profile will move. Good rules, honestly held, and then checked.
The API RP 14E review is Madani Sani, Shirazi and Nesic, Review of the API RP 14E erosional velocity equation: origin, applications, misuses, limitations and alternatives, Wear 426-427 (2019) 620 to 636.