Chris Collins

Tools · physics

Fluid flow and pipe pressure drop

Reynolds number and Darcy–Weisbach pressure drop with Colebrook, Swamee–Jain, or Haaland friction factors and fitting losses; Hagen–Poiseuille laminar flow with an r⁴ sensitivity plot; pipe sizing from flow and velocity; Bernoulli solver; hydrostatic pressure and buoyancy; pump power and orifice flow — with unit-aware inputs.

Added · updated 14 October 2026

Works with

How to use it

Inputs accept units: 15 mm, 0.75 in, 20 L/min, 5 gpm, 2 bar, 30 psi, 1 cP. A bare number uses the default unit.

  • Fluids — water density and viscosity are interpolated from tabulated values (0–100 °C); air uses the ideal-gas law and Sutherland’s formula; oils and glycol are typical values (check the datasheet for yours). PG25 — the 25 % propylene-glycol coolant of direct-to-chip liquid cooling — uses ρ ≈ 1,019 kg/m³ and μ ≈ 1.6 mPa·s at 30 °C (Dow DOWFROST engineering data, approximate).

  • Pipe flow — Re = ρvD/μ: laminar below 2300, turbulent above 4000. Laminar f = 64/Re; turbulent f is solved from the Colebrook–White equation 1/√f = −2 log₁₀(ε/3.7D + 2.51/(Re√f)), or the explicit Swamee–Jain and Haaland approximations. Δp = f·(L/D)·½ρv² + ΣK·½ρv², with roughness ε from typical published values.

  • Laminar (Poiseuille) — see below.

  • Flow, velocity, size — Q = v·πD²/4.

  • Bernoulli — p₁/ρg + v₁²/2g + z₁ = p₂/ρg + v₂²/2g + z₂ + hL: leave one value blank to solve for it.

  • Hydrostatics — p = p₀ + ρgh; buoyant force ρfluid·V·g; a floating body sinks to ρobject/ρfluid of its volume.

  • Pump and orifice — shaft power = ρgQH/η; orifice flow Q = Cd·A·√(2Δp/ρ(1 − β⁴)).

For learning and planning. Size real systems with manufacturer data and applicable codes.

Laminar flow: Hagen–Poiseuille

Companion to chapter 9 (circulation and breathing) of Human Biology for the Medical Maker, which uses Poiseuille’s law to explain why arterioles are the body’s flow-control valves.

Educational — not a medical device. Not for diagnosis, treatment, monitoring or dosing. Use the r⁴ relationship to understand sensitivity to radius; do not use the equation to compute a flow in a person.

  • Q = π·Δp·r⁴ / (8·μ·L) for steady laminar flow of a Newtonian fluid through a rigid round tube; the tab also gives the resistance R = Δp/Q (in mmHg·s/mL), mean and centre-line velocity, wall shear stress and the Reynolds number. If Re is above 2300 it says so: the law then does not apply, and the Pipe flow tab is the one to use.

  • The plot shows relative flow Q/Q₀ against relative radius r/r₀: halve the radius and flow falls to one sixteenth; a 10 % narrowing costs about a third of the flow. The dashed line is what a merely proportional law would give, for contrast. Set "Change radius to" to mark any point.

  • Where the law fails in the body (chapter 9): blood is not Newtonian, vessels are compliant, tapered and branched, flow is pulsatile and not always laminar, and the radius is actively regulated. The tool is for the sensitivity lesson.

Related: physics calculators, ODE solver, thermal design (heat flux, and the coolant flow a heat load needs).

Liquid cooling for AI racks

Companion to coolant chemistry, flow and ΔT in AI Acceleration. Pressure drop grows roughly with flow to the power 1.75–2 in turbulent pipes, so tripling a rack’s coolant flow (59 → 177 L/min, the GB300 NVL72 figures at 25 °C and 45 °C supply) multiplies the drop about eight times — the book’s 2.3 → 18.4 psi. The presets put PG25 through an illustrative 10 m of 32 mm stainless pipe (not a real rack’s plumbing) to show the ratio.

Sharing

Share link (under the title) copies a URL that reopens this tool exactly as you have it — every tab’s inputs, with the current tab selected. Opening such a link replaces the inputs this browser had saved for the tool.

Linking to an example

Write a link by hand with these parameters and add the tab after #: pipe, laminar, size, bern, static or pump. Values may carry units; in a URL a space is + or %20 (q=20+L/min).

Parameter Meaning Example

fluid

Pipe-flow fluid: water, air, seawater, glycol50, pg25, glycerol, hydraulic, sae30, diesel, petrol, custom

fluid=pg25

t

Its temperature, °C (water and air)

t=40

rho, mu

Custom density and viscosity

rho=1020+kg/m3&mu=1.6+cP

q, d, l

Flow rate, inside diameter, length

q=59+L/min&d=32+mm&l=10+m

eps

Roughness in mm (0.0015 drawn tubing, 0.015 stainless, 0.045 steel)

eps=0.015

k, method

Fittings ΣK; colebrook, swamee or haaland

k=2&method=haaland

sq, sd, sv

Flow, velocity, size tab: flow, diameter, target velocity

sq=177+L/min&sv=1.5

dp, r, pl, rk

Laminar tab: Δp, radius, length, radius change in %

dp=10+mmHg&r=0.5+mm

pq, head, eff

Pump: flow, total head, efficiency %

pq=30+L/min&head=25+m

example

One of the presets below; parameters written beside it override the preset’s

example=d2c-loop-59lpm

Presets (?example=…; the link opens on the right tab even without #):

example= Shows

d2c-loop-59lpm

59 L/min of PG25 through 10 m of 32 mm stainless pipe (open)

d2c-loop-177lpm

Three times the flow, 177 L/min: about 7–8 times the pressure drop (open)

d2c-pipe-size

The pipe size for 177 L/min at 1.5 m/s: about 50 mm (open)

Older links (?s=…) still open as before.

Runs entirely in your browser; nothing you type leaves this page.