This calculator estimates how much water flows by gravity through a pipe that runs from a tank and discharges freely at the far end — no pump needed. It uses the Hazen-Williams equation for pipe friction plus the small losses where water enters the pipe and leaves it.
Enter the tank height (head)
Measure the vertical distance from the water surface in the tank down to the pipe outlet (or down to the tank base, and put the rest in Elevation Drop). This height is what drives gravity flow — more height, more flow.
Enter the pipe inside diameter (ID)
Use the internal diameter of the pipe, not the nominal or outside size. A 1-inch Schedule 40 PVC pipe has an ID of about 1.05 in (26.6 mm). Pipe diameter has the biggest effect on flow — in a long pipe, doubling it gives roughly six times the flow.
Enter the pipe length
Measure the total run length of the pipe from the tank outlet to the discharge point. Longer pipes have more friction loss and reduce flow.
Add elevation drop (optional)
If you measured the head only down to the tank base, enter the further drop from the tank base to the outlet here (for example, a tank on a 6 ft stand discharging at ground level). The calculator adds the two. Leave it at 0 if your head figure already reaches the outlet.
Select pipe material
Different pipe materials have different friction coefficients (Hazen-Williams C). PVC and PE are smoothest (C=150); old cast iron and concrete are roughest (C=100). Default is PVC.
Click Calculate
Results show flow rate in L/min, GPM, L/hr and m³/hr, plus the velocity, the head used by pipe friction, the Reynolds number and the static pressure at the outlet (with the tap shut). The note under the results gives the flow in US units.
Note: This calculator models a pipe that discharges freely, with no fittings beyond the tank outlet. Elbows, valves and tees add friction — add 10–20% to the pipe length to allow for them, or more for many fittings. A tap, shower head or float valve at the end restricts the flow much further, so treat the result as the most the pipe can carry.
📐 The Formula
Gravity Feed Flow Rate Formula Explained
This calculator uses the Hazen-Williams equation, the industry standard for water distribution pipe flow calculations:
Q = 0.2785 × C × D^2.63 × S^0.54
Where:
Q = flow rate (m³/s)
C = Hazen-Williams roughness coefficient
D = pipe inside diameter (m)
S = friction slope = friction head loss ÷ pipe length (m/m)
US units: Q (GPM) = 0.2813 × C × d (in)^2.63 × S^0.54
In a gravity pipe that discharges freely, the whole height of water is used up along the way: most of it by pipe friction, and a little to get water into the pipe and to give it its speed at the outlet. The calculator finds the flow at which H = hf + 1.5 × v² ÷ 2g — total head equals the Hazen-Williams friction loss plus the entrance loss (0.5) and the outlet velocity head (1.0). Because the friction and the velocity both depend on the flow, it solves this numerically.
Outlet Pressure
The static pressure at the outlet — what a gauge reads with the tap shut — comes from the hydrostatic equation. Once water flows freely, almost all of it is used up by friction and velocity, which is why an open pipe end has no pressure to speak of.
P = ρ × g × h
P = pressure (Pa)
ρ = water density (1000 kg/m³)
g = gravitational acceleration (9.81 m/s²)
h = head height (m)
1 m of head ≈ 9.81 kPa ≈ 0.098 bar ≈ 1.42 PSI
1 ft of head ≈ 0.433 PSI
Hazen-Williams C Coefficients by Pipe Material
Pipe Material
C Value
Typical Use
PVC / HDPE / PE
150
Modern water supply, irrigation
Copper
140
Domestic plumbing
Galvanised Steel
120
Industrial, aged plumbing
Ductile Iron (lined)
140
Water mains
Cast Iron (unlined)
100
Old infrastructure
Concrete
100–120
Large-diameter mains
Asbestos Cement
140
Legacy infrastructure
Quick Reference: 1 m Head by Pipe Size (PVC, 10 m pipe)
Pipe ID
L/min
GPM
Velocity (m/s)
13 mm (½")
~7.6
~2.0
~0.96
19 mm (¾")
~20.2
~5.3
~1.19
25 mm (1")
~40.6
~10.7
~1.38
32 mm (1¼")
~75.6
~20.0
~1.57
50 mm (2")
~228
~60.3
~1.94
75 mm (3")
~605
~160
~2.28
100 mm (4")
~1,185
~313
~2.52
Free discharge from an open pipe end, 1 m (3.3 ft) of head, 10 m (33 ft) of straight PVC pipe, no fittings. A longer pipe, fittings, or a tap or shower head at the end all cut these figures — run your own numbers above.
🔧 When to Use This
Gravity Feed Flow Use Cases
🏠
Rooftop Tank Supply
Check that the supply pipe from a rooftop tank can carry enough flow for the household; use the minimum tank height calculator for the pressure side.
🌾
Drip Irrigation
Design gravity-fed drip lines from a header tank — confirm flow rate meets emitter requirements without a pump.
🏕️
Off-Grid Water Systems
Plan spring-fed or elevated tank systems for cabins, remote properties, and off-grid homesteads.
⚗️
Industrial Gravity Feed
Calculate gravity drain rates for process tanks, cooling systems, and gravity-fed chemical dosing lines.
💧
Rainwater Harvesting
Check how fast a raised rain tank or barrel can fill cans, troughs or a drip header by gravity.
🔥
Fire Suppression
Get a first estimate of how much a gravity tank could supply to a fire hose or standpipe. Sprinkler and fire systems must be designed to the local fire code (for example NFPA 13 or 22 in the US, EN 12845 in Europe) by a specialist.
Improving Gravity Flow Rate
If calculated flow is insufficient, consider these options in order of effectiveness:
Increase pipe diameter — the most effective change; in a long pipe, flow scales with about D^2.63, so one size up often roughly doubles it
Raise the tank higher — flow rises with about the square root of the head, so doubling the head gives roughly 45% more flow
Shorten the pipe run — route more directly to reduce friction losses
Use smoother pipe material — switch from galvanised to PVC for lower friction
Eliminate unnecessary fittings — each elbow adds equivalent pipe length
🧮 Worked Example
Worked example: filling a stock tank from a raised water tank
A storage tank's water surface is 10 ft (3.05 m) above the end of a 60 ft (18.3 m) run of 1-inch Schedule 40 PVC (inside diameter 1.049 in, 26.6 mm) that fills a livestock trough.
Flow: about 17.2 GPM (65 L/min, 1,034 gallons an hour) with the pipe end open.
Where the head goes: about 9.0 ft of the 10 ft is used by pipe friction; the rest gets the water into the pipe and moving at 6.4 ft/s (1.95 m/s).
Static pressure at the pipe end with a valve shut: 10 × 0.433 = 4.33 psi (0.30 bar).
A 100-gallon trough fills in about 6 minutes.
Swapping to ¾-inch pipe (ID 0.824 in) on the same run cuts the flow to about 9.3 GPM; going up to 1¼-inch (ID 1.380 in) raises it to about 34.7 GPM.
❓ FAQ
Frequently Asked Questions
How do I calculate gravity feed flow rate from a water tank?
Use the Hazen-Williams equation for pipe friction: flow depends on tank height (head), pipe inside diameter, pipe length, and pipe roughness. You find the flow at which the friction loss plus the small entrance and outlet losses use up the whole head. Taller tanks, wider pipes, shorter runs, and smoother pipe material all increase gravity flow. This calculator does the maths — enter your three main measurements and it outputs flow in GPM, L/min and m³/hr.
How much height (head) do I need for a gravity-fed shower?
Showers made for gravity systems are commonly rated to work from about 1 m (3.3 ft) of head above the shower head — a gentle flow; more height gives a stronger shower. The pipe is rarely the limit: 2 m of head can push about 59 L/min (16 GPM) out of an open 10 m run of 25 mm (1") PVC, far more than a shower uses. What limits a gravity shower is the pressure at the head — about 0.2 bar (2.8 psi) at 2 m. Use the minimum tank height calculator to size the height for the pressure your shower needs.
What is the Hazen-Williams equation used for?
The Hazen-Williams equation is an empirical formula used to calculate water flow rate through a pressurised pipe. It accounts for pipe diameter, pipe length, hydraulic gradient (the slope driving flow), and a roughness coefficient (C) that varies by pipe material. It applies to water at ordinary temperatures (roughly 40–75 °F, 4–24 °C) in turbulent flow. It was developed for larger pipes, so for small household pipe (under about 2 in / 50 mm) and slow flows it is an estimate; the Darcy-Weisbach equation is more exact.
What pipe diameter is best for a gravity-fed rooftop tank?
For a household gravity supply, 25 mm (1 inch) pipe is a common choice for the main run from the tank, because gravity systems have little pressure to spare. Many systems use 32 mm (1¼") or 40 mm (1½") pipe to cut friction on long runs. Use this calculator with your actual tank height and pipe length to confirm the flow rate meets your household demand — typically 8–15 L/min for a single bathroom.
How does pipe friction affect gravity flow rate?
Friction is the main limiter of gravity flow. It increases with pipe length, flow velocity, and pipe roughness. In a free-flowing gravity pipe the flow settles at the rate where friction (plus the small entrance and outlet losses) uses up the whole head — in a long pipe, friction takes almost all of it. This is why short, straight, large-diameter, smooth-bore pipes always outperform long, narrow, rough ones in gravity systems.
Can I use this calculator for gravity-fed drip irrigation?
Yes. Enter the height of your header tank above the drip emitters, the main supply pipe diameter and length, and select PVC (C=150) as the pipe material. The resulting flow in L/hr tells you the total system capacity. Divide by the number of emitters to check per-emitter flow against the emitter's rated output. Pressure matters as much as flow: drip tubing makers commonly recommend about 8–15 psi (0.55–1 bar), which needs roughly 18–35 ft (5.5–10.5 m) of head, while ultra-low-pressure drip designs run from tanks only 2–5 ft (0.6–1.5 m) up. Check the emitter's rated pressure.
What is a good flow rate for a gravity-fed water system?
For a single household tap or shower: 6–15 L/min is comfortable. Kitchen taps typically use 6–8 L/min; showers need 8–15 L/min. For a full house with multiple simultaneous outlets, aim for 20–40 L/min at the main supply pipe. Agricultural irrigation flow requirements vary widely by crop type and emitter count — use our Drip Irrigation Tank Size Calculator for crop-specific guidance.
Why does my gravity water flow reduce over time?
Gravity flow naturally decreases as the tank empties because the head (driving height) drops. Through 10 m of 25 mm (1") pipe, 3 m of head pushes about 73 L/min (19 GPM), but only about 41 L/min (11 GPM) at 1 m. Scale from hard water, sediment and biofilm also narrow the pipe over time, increasing friction. A float (ball) valve that keeps the tank topped up holds the head — and the flow — steadier; a pressure-reducing valve is only needed if the head is very high.
✅ Sources & Review
Sources and review
The method and figures on this page come from these references:
Hazen-Williams equation in SI form, Q = 0.2785 C D2.63 S0.54 (US form Q = 0.2813 C d2.63 S0.54 in GPM and inches), as given in standard water-supply hydraulics texts; entrance loss coefficient 0.5 for a plain tank outlet.
Toro Agricultural Irrigation — Hazen-Williams Equation: C values by pipe material (PVC 150; polyethylene 140; new cast iron 130, design 100; concrete 120 new, 100 design).
Schedule 40 PVC inside diameters per ASTM D1785 dimensions (¾" 0.824 in, 1" 1.049 in, 1¼" 1.380 in).
NIST SP 811 — unit conversions (1 US gallon = 3.785 L; 1 ft of water = 0.433 psi).
Reviewed by John Mac, PE, Water Systems Specialist
Texas-licensed Professional Engineer with 13+ years in residential water storage and 180+ tank projects. John writes and reviews every calculator on this site.
