Orifice discharge calculator
Find how much liquid passes through a sharp-edged opening: 0.01 m² with a coefficient of 0.61 under 2 m of head lets through about 0.0382 m³/s. The ideal flow appears beside it, so you see what the coefficient takes away. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Area
- 0.01
- Discharge coefficient
- 0.61
- Head
- 2
- Gravity
- 9.80665
- Ideal velocity
- 6.2631142413
- Theoretical discharge
- 0.0626311424
- Discharge
- 0.0382049969
A sharp-edged orifice is a thin-plate opening used to meter or drain liquid under a known free-surface head. The textbook orifice flow equation gives volumetric discharge as Q equals the discharge coefficient Cd times the geometric opening area A times the square root of twice gravity times head. This orifice discharge flow calculator accepts those three quantities plus optional gravity, then returns the ideal jet speed, the theoretical discharge A·√(2gh), and the Cd-adjusted actual discharge in consistent volume-per-time units. Plant engineers size tank drains, calibration orifices, and emergency relief openings before they commit to a plate thickness or a piping schedule. Students check homework against the same identity used in fluid-mechanics laboratories.
The orifice flow equation and what Cd actually folds in
Discharge through a sharp-edged orifice is not the same problem as finding how fast the jet leaves the hole. Torricelli’s theorem still supplies the ideal speed v equals the square root of two g h, the speed a free-falling drop would reach after falling distance h. Volume flow, however, is that speed multiplied by the area the jet actually occupies, not the drilled hole.
Immediately downstream of a sharp plate the streamlines cannot turn the corner, so the jet contracts to a vena contracta smaller than the geometric opening. The coefficient of contraction Cc is the ratio of vena-contracta area to A; the coefficient of velocity Cv accounts for viscous and entrance losses that slightly reduce speed below √(2gh). Their product is the discharge coefficient Cd equals Cc times Cv, typically near 0.61 for a thin sharp-edged circular orifice discharging to atmosphere with a large upstream tank.
The working formula is therefore Q equals Cd A √(2gh). This calculator returns both the theoretical discharge Qt equals A √(2gh) (the Cd equals one ideal) and the actual discharge Q equals Cd times that value, plus the ideal velocity, so you can see how much the coefficient reduces volume flow without running a second tool. Head h is measured vertically from the free surface down to the orifice centreline.
Gravity must match the length unit of h: use about 9.80665 m/s² when h is in metres, or 32.174 ft/s² when h is in feet. Zero head correctly yields zero discharge. Negative head is rejected because it would not describe a free surface above the opening.
The model assumes an incompressible liquid, a free surface open to the same ambient pressure as the jet, and negligible approach velocity in a large tank; it does not integrate tank drawdown over time, model compressible gas orifices, or replace a calibrated meter factor from your own laboratory.
Where orifice flow estimates help
Process and water engineers estimate how much liquid leaves a tank bottom orifice, side plate, or calibration hole before specifying pipe size, drain time, or a relief path. University fluid-mechanics courses and exam generators need a deterministic oracle for Q equals Cd A √(2gh) that also returns the ideal velocity and the Cd-free theoretical discharge, without students re-implementing floating-point edge cases for zero head.
Content sites that rank for orifice discharge flow calculator, sharp-edged orifice calculator, Cd A sqrt 2gh, or tank orifice discharge benefit from a live free tool whose arithmetic matches the paid automation path byte-for-byte. This landing is not a nozzle-exit-velocity page: the search intent is volumetric discharge through an orifice, not jet speed alone. Invalid input is not billed.
Keep requests small, pin the rounded discharge field in tests, and you get reproducible orifice flow for LMS plugins, edge workers, and plant spreadsheets without standing up a full hydraulic solver.
What you can do with it
Tank drain and relief-orifice sizing
Compute volumetric discharge from measured free-surface head, plate area, and a sharp-edged Cd before choosing a drain diameter or emergency relief opening.
Calibration orifices and first-pass meters
Pin theoretical A·√(2gh) discharge, then apply a catalogue or measured Cd for thin-plate orifices in commissioning spreadsheets and CI checks.
FAQ
How do I calculate orifice discharge from area, Cd, and head?
Discharge is Q = Cd·A·√(2gh). Optional gravity defaults to 9.80665.
What units should I use for area, head, and gravity?
Any consistent set: square metres with metres and m/s², or square feet with feet and ft/s². Discharge is then volume per time in that system.
What is a typical discharge coefficient for a sharp-edged orifice?
About 0.61 for a thin sharp-edged circular orifice discharging to air from a large tank. It is the product of the contraction coefficient and the velocity coefficient; rounded or short-tube openings have higher values.
Why is the actual flow lower than the theoretical flow?
Because the jet narrows just past the plate into a vena contracta smaller than the hole, and friction slows it slightly. In the example, the coefficient of 0.61 cuts the ideal flow down to about 0.0382 m³/s.
Can it tell me how long a tank takes to drain?
No, it solves the orifice flow at one head only. For a drain time, combine this flow with the plan area of your tank as the level falls. It also does not cover gas orifices or replace a calibrated meter.
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/orifice-flow \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"area":0.01,"discharge_coefficient":0.61,"head":2}'const res = await fetch("https://api.kit.forhosting.com/eng/orifice-flow", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"area": 0.01,
"discharge_coefficient": 0.61,
"head": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/eng/orifice-flow",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"area": 0.01,
"discharge_coefficient": 0.61,
"head": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/eng/orifice-flow", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"area":0.01,"discharge_coefficient":0.61,"head":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"area":0.01,"discharge_coefficient":0.61,"head":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/eng/orifice-flow", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"area": 0.01,
"discharge_coefficient": 0.61,
"head": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "eng.orifice_flow",
"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
Invalid input—missing area, a non-positive coefficient, negative head, or non-positive gravity—fails with invalid_input and is not billed.
Input contract, response fields, units, and error behaviour
Cd must be positive and not greater than two, covering ordinary engineering values from a sharp plate near 0.61 up to well-rounded or short-tube orifices without inviting absurd amplification. Numeric results are rounded to twelve decimal places for stable goldens and automation. Example: area 0.01, Cd 0.61, and head 2 with default g yield discharge near 0.0382 in cubic metres per second if area was in square metres and head in metres, because √(2 × 9.80665 × 2) is √39.2266 and 0.61 times 0.01 times that speed is the reported Q. Pair discharge with your own tank plan area if you later need a drawdown time; this capability solves the orifice flow equation only. POST a JSON body with three required finite numbers: area, the positive geometric opening of the orifice; discharge_coefficient, the dimensionless Cd; and head, the non-negative upstream liquid height above the orifice centreline. Area aliases include A, orifice_area, and opening_area. Discharge-coefficient aliases include cd, Cd, C_d, and coefficient_of_discharge. Head aliases include h, liquid_head, water_head, and orifice_head. Optional gravity (aliases g, g_accel, gravitational_acceleration) defaults to 9.80665 and must be strictly positive when supplied. Fields may arrive as JSON numbers or numeric strings. Missing area, missing discharge_coefficient, missing head, non-finite values, non-positive area or Cd, negative head, or non-positive gravity fail with invalid_input naming the problem; those failures are not billed. On success the body echoes area, discharge_coefficient, head, and gravity (rounded), and returns ideal_velocity as √(2gh), theoretical_discharge as A times that speed, discharge as Cd times theoretical_discharge, a formula string, method set to orifice_flow, and a short human-readable message.
Where an orifice discharge API earns its keep
Instrumentation groups that still use thin-plate orifice meters as a first check can pin theoretical_discharge and then apply a measured Cd instead of hand-coding √(2gh) in every spreadsheet.
Integration use cases
Homework and fluid-mechanics labs
Check Q = Cd·A·√(2gh) against textbook problems and weigh-tank labs using the same pure module as the free browser widget.
Technical questions
What is a typical discharge coefficient for a sharp-edged orifice?
A thin sharp-edged circular orifice discharging to atmosphere from a large tank is commonly taken near Cd = 0.61. Rounded or short-tube openings have higher Cd.
How is this different from a nozzle exit velocity calculator?
Torricelli gives jet speed √(2gh). This tool multiplies that speed by area and Cd to return volumetric discharge Q, plus the theoretical Cd = 1 discharge.
What does the orifice discharge flow calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.