Pipe continuity velocity calculator
When the inlet area is twice the outlet area, a liquid entering at 2.5 m/s leaves at 5 m/s. Give the inlet velocity and the area ratio to check contractions and expansions in steady incompressible flow. Free in your browser.
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- Your data stays on your device
Run — free
Worked example
- Inlet velocity
- 2.5
- Area ratio
- 2
- Outlet velocity
- 5
This pipe continuity velocity calculator applies conservation of volumetric flow to find outlet velocity from an inlet velocity and a cross-sectional area ratio. For steady incompressible flow, the continuity equation states that area multiplied by mean velocity remains constant between two pipe sections. Enter the inlet velocity and the ratio of inlet area to outlet area, and the calculator returns the corresponding outlet velocity. It is a focused engineering check for contractions, expansions, classroom exercises, preliminary sizing, and repeatable automated calculations.
Understand the ratio form of the continuity equation
For steady incompressible flow through a pipe, the volumetric flow rate at the inlet equals the volumetric flow rate at the outlet. A ratio greater than one describes an outlet that is narrower than the inlet, so the calculated outlet velocity is higher. A ratio between zero and one describes an outlet that is wider, so the velocity is lower.
A ratio of exactly one describes equal areas and therefore equal velocities. The ratio is dimensionless, but both areas used to calculate it must have shared the same unit. The inlet and outlet velocities consequently share one speed unit, such as metres per second or feet per second.
This relationship is a conservation rule, not a complete pipe-system model: it does not calculate pressure, friction loss, pump performance, turbulence, density changes, or elevation effects. Use it when the assumptions of steady, one-dimensional, incompressible flow are appropriate. For compressible gases or streams with changing density, mass continuity requires density terms and this simplified ratio is not sufficient.
Enter valid values and interpret the result
The area ratio must be formed as inlet area divided by outlet area, not the reverse. For example, an inlet area of 0.04 square metres and an outlet area of 0.02 square metres produce an area ratio of 2. If the inlet mean velocity is 2.5 metres per second, the result is an outlet velocity of 5 metres per second.
The output echoes the validated inlet velocity and area ratio, reports the calculated outlet velocity, and includes the applied formula so the direction of the ratio remains explicit. Zero inlet velocity is allowed because a stationary ideal stream has zero outlet velocity. Zero or negative area ratios are rejected because physical cross-sectional areas must be positive and a zero outlet area would make the underlying equation undefined.
Keep the velocity unit consistent when reading the response: an input in metres per second yields an answer in metres per second, while an input in feet per second yields feet per second. The tool does not perform unit conversion, so calculate the dimensionless area ratio first and supply the desired inlet speed unit directly.
Use the calculation responsibly in engineering work
The ratio form is useful for quick checks of reducers, diffusers, nozzles, hoses, ducts, and idealized channels. A contraction with an area ratio of 3 predicts three times the inlet velocity; an expansion with a ratio of 0.4 predicts forty percent of it. Those proportional checks are also a convenient way to catch a reversed ratio before relying on the result.
Real systems require more context. Continuity alone says how mean velocity changes when the flow rate is conserved, but it does not say whether a pump can sustain that flow, how much pressure is lost, whether cavitation occurs, or whether the assumed velocity profile is valid. Add Bernoulli analysis, loss coefficients, Reynolds-number checks, material limits, and applicable engineering standards when making design or safety decisions.
Measurements should represent average velocity over the cross section rather than a single local reading unless that reading has been corrected appropriately. The browser calculation runs locally for convenient one-off checks.
What you can do with it
Check a pipe contraction
Estimate the higher outlet velocity produced when a pipe narrows and the inlet-to-outlet area ratio is known.
Verify fluid mechanics exercises
Confirm ratio-form continuity calculations for coursework, answer keys, laboratory preparation, or training material.
FAQ
How should I calculate the area ratio?
Divide the inlet cross-sectional area by the outlet cross-sectional area. Both areas must use the same unit.
What units does the outlet velocity use?
The outlet velocity uses the same speed unit as the inlet velocity because the area ratio is dimensionless.
Can I use this calculator for compressible gas flow?
Not when density changes materially. Compressible mass continuity requires density terms that this simplified calculator does not accept.
What does an area ratio below one mean?
It means the outlet is wider than the inlet, so the fluid slows down. A ratio above one describes a narrower outlet and a faster stream, and a ratio of exactly one keeps the velocity unchanged.
Does this calculator give pressure or friction loss?
No. It applies only the conservation of volumetric flow between two sections. Pressure, friction loss, pump performance, turbulence and elevation effects need a fuller pipe-system calculation.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/eng/continuity-velocity \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"inlet_velocity":2.5,"area_ratio":2}'const res = await fetch("https://api.kit.forhosting.com/eng/continuity-velocity", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"inlet_velocity": 2.5,
"area_ratio": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/eng/continuity-velocity",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"inlet_velocity": 2.5,
"area_ratio": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/eng/continuity-velocity", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"inlet_velocity":2.5,"area_ratio":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"inlet_velocity":2.5,"area_ratio":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/eng/continuity-velocity", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"inlet_velocity": 2.5,
"area_ratio": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "eng.continuity_velocity",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Understand the ratio form of the continuity equation
Writing that balance as A_in × v_in = A_out × v_out and dividing by A_out gives v_out = v_in × (A_in / A_out). This calculator accepts the quantity in parentheses directly as area_ratio.
Enter valid values and interpret the result
Provide inlet_velocity as a finite, non-negative number and area_ratio as a finite number greater than zero. Missing values, nonnumeric text, NaN, Infinity, and results beyond the finite numeric range also return invalid_input instead of misleading JSON.
Use the calculation responsibly in engineering work
Automated API calls cost $0.002 per successful item and use the same deterministic solver, so identical numeric inputs produce the same structured response without network-dependent data, randomness, or timestamps.
Integration use cases
Build repeatable engineering fixtures
Generate deterministic structured results for calculators, regression tests, and preliminary sizing workflows.
Technical questions
Which continuity formula does the calculator use?
It uses v_out = v_in × (A_in / A_out), derived from A_in × v_in = A_out × v_out for steady incompressible flow.
What does an API calculation cost?
Each successful API item costs $0.002. The browser calculator is free for one-off local calculations.