What is the Hazen-Williams equation?

The Hazen-Williams equation is Q = 0.2785 × C × d^2.63 × S^0.54, an empirical formula for calculating water flow rate in pressurized pipes. Q is flow rate in GPM, C is the roughness coefficient (150 for PVC, 130 for copper), d is internal pipe diameter in inches, and S is the hydraulic slope.

How do you convert psi to gallons per minute?

Pressure alone cannot be converted to GPM without knowing the pipe size and length. Use Hazen-Williams: S = pressure(psi) × 2.30666 / pipe length(ft), then Q = 0.2785 × C × d^2.63 × S^0.54.

What is mass flow rate and how is it calculated?

Mass flow rate (?) measures the mass of fluid passing a point per unit time. Formula: ? = ? × Q, where ? is fluid density (kg/m³) and Q is volumetric flow rate (m³/s). For water at 20°C (? = 998.2 kg/m³), a volumetric flow of 1 L/s gives a mass flow of 0.9982 kg/s.

What is the difference between volumetric and mass flow rate?

Volumetric flow rate Q measures volume per unit time (m³/s, GPM, L/min). Mass flow rate ? measures mass per unit time (kg/s, lb/min) and equals ? = ? × Q. For incompressible fluids like water the relationship is straightforward. For gases, density changes with temperature and pressure, making mass flow rate more meaningful for engineering calculations.

💧 Engineering Calculator

Pipe Flow Calculator — GPM, PSI & Flow Rate

Q: How do you calculate flow rate in a pipe?

For pressurized water pipes, use the Hazen-Williams equation: Q = 0.2785 × C × d^2.63 × S^0.54, where Q is flow rate in GPM, C is the pipe roughness coefficient, d is the internal diameter in inches, and S is the hydraulic slope (head loss per unit length). First calculate S = pressure(psi) × 2.30666 / pipe length(ft), then substitute into the formula.

Q: What is the flow rate of a 1 inch pipe at 40 psi?

For a 1-inch Schedule 40 PVC pipe (ID 1.049 inches, C=150) at 40 psi over 100 feet: S = 0.9227; Q = 0.2785 × 150 × 1.049^2.63 × 0.9227^0.54 ˜ 45.5 GPM.

Q: What is volumetric flow rate?

Volumetric flow rate Q measures the volume of fluid passing a cross-section per unit time. The fundamental formula is Q = A × v, where A is the cross-sectional area of the pipe (m²) and v is the mean fluid velocity (m/s). Common units include m³/s, L/s, L/min, GPM, and CFM.

Q: How does pipe diameter affect flow rate?

Pipe diameter has a very large effect on flow rate. In Hazen-Williams, Q is proportional to d^2.63 — doubling the diameter increases flow by 2^2.63 ˜ 6.2 times. In volumetric flow Q = A × v, area A = pd²/4, so flow is proportional to d² at constant velocity.

Q: What is the Hazen-Williams C coefficient for PVC pipe?

The Hazen-Williams C coefficient for PVC pipe is 150 — the highest commonly used value, reflecting PVC's very smooth interior. HDPE also uses C=150. Copper uses C=130-140, concrete C=120, and old cast iron C=80-100.

Q: How do you calculate gravity flow in a pipe?

Use Manning's equation: Q = (1/n) × A × R^(2/3) × S^(1/2), where n is Manning's roughness coefficient, A is the cross-sectional flow area (m²), R is the hydraulic radius (m), and S is slope (m/m). For a full circular pipe: A = pd²/4, R = d/4.

This pipe flow calculator finds pipe flow rate in GPM using Hazen-Williams, converts PSI to GPM for any pipe size, and includes Hagen-Poiseuille for laminar flow, Manning's equation for gravity flow, volumetric flow rate (Q = A×v), and mass flow rate (ṁ = ρ×Q). A complete gpm calculator covering 1/2 inch to 12 inch pipe with step-by-step working.

💧 Hazen-Williams Pipe Flow Calculator

Q = 0.2785 × C × d^2.63 × S^0.54

Q = flow (GPM) | C = roughness coefficient | d = diameter (in) | S = head loss / pipe length

Pipe Material (auto-fills C)

C Coefficient

Internal Pipe Diameter

Pressure Drop

Pipe Length

⇄ PSI to GPM Calculator

Pressure alone does not determine flow — pipe size and length are also required.

Pressure

Pipe Length

Pipe Material

Your Pipe Size (highlighted in table)

Pipe Size	ID (in)	GPM	L/min	Vel (ft/s)	Vel (m/s)	Re	Regime

📋 Formula Used

🧪 Hagen-Poiseuille Laminar Flow Calculator

Q = (π × r⁴ × ΔP) / (8 × μ × L)

Valid for laminar flow only (Re < 2300) in straight circular pipes

Fluid

Dynamic Viscosity μ

Fluid Density ρ (kg/m³)

Pipe Radius r

Pressure Drop ΔP

Pipe Length L

⏎ Gravity Flow (Manning's Equation) Calculator

Q = (1/n) × A × R^2/3 × S^1/2

n = roughness | A = flow area (m²) | R = hydraulic radius (m) | S = slope (m/m)

Pipe Material (Manning's n)

Manning's n

Pipe Diameter

Pipe Slope

Fill Ratio h/d (0–1)

1.0 = full pipe

▦ Volumetric Flow Rate Calculator — Q = A × v

Calculate volumetric flow rate from pipe diameter and fluid velocity, or solve for velocity or diameter. The fundamental formula Q = A × v applies to any fluid in any pipe.

Q = A × v = (πd²/4) × v

Q = flow rate (m³/s) | A = pipe cross-section area (m²) | v = mean fluid velocity (m/s)

Internal Pipe Diameter

Flow Velocity v

⚖ Mass Flow Rate Calculator — ṁ = ρ × Q

Calculate mass flow rate from volumetric flow rate and fluid density. Essential for HVAC, combustion engineering, and chemical processes where density varies with temperature or pressure.

ṁ = ρ × Q

ṁ = mass flow rate (kg/s) | ρ = fluid density (kg/m³) | Q = volumetric flow rate (m³/s)

Volumetric Flow Rate Q

Fluid

💧 Water (20°C) — ρ = 998.2 kg/m³

Pipe Flow Rate Formula — Hazen-Williams Equation

The Hazen-Williams equation is the most widely used formula for calculating water flow rate in pressurized pipes: Q = 0.2785 × C × d^2.63 × S^0.54

Q = 0.2785 × C × d^2.63 × S^0.54

Q = GPM | C = roughness coefficient | d = internal diameter (inches) | S = psi × 2.307 / L(ft)

Q = volumetric flow rate in US gallons per minute (GPM)
C = Hazen-Williams roughness coefficient (PVC=150, copper=130, old cast iron=100)
d = actual internal pipe diameter in inches (NOT nominal size)
S = hydraulic slope = ΔP(psi) × 2.30666 / L(ft)

Slope from pressure: S = ΔP(psi) × 2.30666 / L(ft) — where 1 psi = 2.30666 ft of water head

Additional Flow Rate Formulas

Q = A × v (Volumetric Flow)

A = pipe cross-section area (m²) | v = mean velocity (m/s)

ṁ = ρ × Q (Mass Flow Rate)

ρ = fluid density (kg/m³) | Q = volumetric flow rate (m³/s)

Q = π × r⁴ × ΔP / (8 × μ × L) (Hagen-Poiseuille)

Laminar flow only — Re < 2300

Q = (1/n) × A × R^2/3 × S^1/2 (Manning's)

Gravity flow, partially-filled pipes, drainage, open channels

When to Use Each Formula

Hazen-Williams: Pressurized water distribution and plumbing — most practical for residential and commercial systems
Q = A × v: When velocity is known or measured — fundamental for any fluid
ṁ = ρ × Q: When mass flow matters — HVAC, combustion, chemical engineering
Hagen-Poiseuille: Laminar flow (Re < 2300), viscous fluids, medical tubing, laboratory work
Manning's: Gravity-fed drainage, sewers, culverts, partially-filled pipes

How to Calculate Flow Rate

Flow rate measures the volume of fluid passing a point per unit time. There are three main methods depending on what information you have:

Method 1 — From velocity and pipe area: Q = A × v (cross-section area × velocity). This is the most fundamental formula and works for any fluid.

Method 2 — From pressure and pipe dimensions: Use the Hazen-Williams equation Q = 0.2785 × C × d^2.63 × S^0.54 for turbulent water flow, or Hagen-Poiseuille for laminar flow of viscous fluids.

Method 3 — From volume and time: Q = V ÷ t (total volume collected divided by time taken). Used in experimental measurement and bucket tests.

How to Work Out Water Flow Rate

For water in a pipe, the simplest approach is:

Measure the pipe's actual internal diameter in inches (not nominal size)
Know your supply pressure in psi and pipe length in feet
Find your pipe material's C coefficient (PVC = 150, copper = 130)
Calculate S = pressure(psi) × 2.307 / length(ft)
Apply: Q = 0.2785 × C × d^2.63 × S^0.54

For a quick answer, use the pipe size reference table below — find your pipe size and pressure to read off the GPM directly.

How to Calculate GPM from Pipe Size and Pressure

Follow this five-step process using the Hazen-Williams equation Q = 0.2785 × C × d^2.63 × S^0.54 to find GPM from pipe size and pressure.

Worked Example: Flow Rate of 1 Inch Pipe at 40 psi

1-inch Schedule 40 PVC, 40 psi, 100 feet

Internal diameter: d = 1.049 in (actual ID — NOT 1.0 in nominal)
C = 150 (PVC)
S = 40 × 2.307 / 100 = 0.9228
d^2.63 = 1.049^2.63 = 1.1310
S^0.54 = 0.9228^0.54 = 0.9600
Q = 0.2785 × 150 × 1.1310 × 0.9600 = 45.5 GPM

1/2-inch Copper (Type K), 60 psi, 50 feet

d = 0.527 in, C = 130
S = 60 × 2.307 / 50 = 2.768
Q = 0.2785 × 130 × 0.527^2.63 × 2.768^0.54 = 8.5 GPM

Garden Hose (5/8 inch, ID=0.625 in), 45 psi, 50 feet

d = 0.625 in, C = 150 (smooth rubber/plastic)
S = 45 × 2.307 / 50 = 2.076
Q = 0.2785 × 150 × 0.625^2.63 × 2.076^0.54 = 17.2 GPM

Pipe Size to Flow Rate Reference Table — GPM at Common Pressures

All values use Hazen-Williams with C=150 (PVC), pipe length 100 feet, actual Schedule 40 internal diameters. The 1-inch row is highlighted. Q = 0.2785 × C × d^2.63 × S^0.54

Pipe Size ▲	ID (in)	20 psi	40 psi	60 psi	80 psi	100 psi
1/2"	0.622	11.8	17.3	21.8	25.7	29.2
3/4"	0.824	24.3	35.5	44.8	52.7	59.9
1"	1.049	44.5	65.1	82.0	96.6	109.9
1.5"	1.610	111.2	162.6	204.9	241.3	274.3
2"	2.067	202.8	296.5	373.6	440.0	500.1
3"	3.068	540.8	790.8	996.5	1,173.6	1,334.0
4"	4.026	1,049.3	1,534.1	1,933.1	2,277.1	2,588.7
6"	6.065	2,962.5	4,331.0	5,458.3	6,430.0	7,308.1

C=150 (PVC), 100 ft pipe, actual Sch 40 internal diameters. All values in GPM. For other materials multiply by (C/150)¹.

Nominal vs Actual Internal Pipe Diameters

Always use the actual internal diameter — using the nominal size is the most common calculation error:

Nominal Size	Sch 40 PVC ID	Type K Copper ID	Sch 40 Steel ID
1/2"	0.622 in	0.527 in	0.622 in
3/4"	0.824 in	0.745 in	0.824 in
1"	1.049 in	0.995 in	1.049 in
1.5"	1.610 in	1.481 in	1.610 in
2"	2.067 in	1.959 in	2.067 in
3"	3.068 in	2.907 in	3.068 in
4"	4.026 in	3.857 in	4.026 in

PSI to GPM — How to Convert Pressure to Flow Rate

Pressure (psi) cannot be directly converted to GPM without pipe size and length. Use Hazen-Williams where flow is proportional to S^0.54 — not linear with pressure.

Converting 60 psi to GPM — 1-inch PVC, 100 ft

S = 60 × 2.30666 / 100 = 1.384
Q = 0.2785 × 150 × 1.049^2.63 × 1.384^0.54 = 57.9 GPM

PSI to GPM Reference — 1-inch PVC, 100 feet

Pressure (psi)	GPM	L/min	m³/h
10 psi	28.1	106.3	6.38
20 psi	40.3	152.6	9.15
30 psi	50.4	190.6	11.44
40 psi	59.4	224.7	13.48
50 psi	67.7	256.2	15.37
60 psi	75.3	284.9	17.10
80 psi	89.3	337.7	20.26
100 psi	102.2	386.7	23.21

Volumetric Flow Rate vs Mass Flow Rate

Volumetric flow rate Q measures volume per unit time (m³/s, GPM, L/min). Mass flow rate ṁ measures mass per unit time (kg/s, lb/s) and equals ṁ = ρ × Q where ρ is fluid density.

For water at 20°C (ρ ≈ 998 kg/m³): 1 L/s volumetric = 0.998 kg/s mass flow. For air (ρ ≈ 1.204 kg/m³): 1 m³/s volumetric = 1.204 kg/s mass flow. Mass flow rate is critical in HVAC, combustion engineering, and chemical processes where fluid density changes with temperature or pressure — in those cases, specifying mass flow is unambiguous regardless of operating conditions.

Gravity Flow in Pipe Calculator — Manning's Equation

Manning's equation Q = (1/n) × A × R^2/3 × S^1/2 applies to drainage, sewers, culverts, and irrigation where the pipe is not fully pressurized. Slope S = vertical drop / horizontal distance.

Concrete Drainage Pipe d=300mm, slope=1%, n=0.012

A = π × 0.09/4 = 0.07069 m²
R = 0.300/4 = 0.075 m
Q = (1/0.012) × 0.07069 × 0.075^2/3 × 0.01^0.5 = 0.1057 m³/s = 105.7 L/s = 1676 GPM

Hazen-Williams C Coefficient for Common Pipe Materials

Pipe Material	C Value	Condition
PVC Plastic	150	New
HDPE	150	New
Copper	130–140	New
Copper	100–110	Old/corroded
Ductile iron (lined)	140	New
Cast iron	130	New
Cast iron	80–100	Old/corroded
Galvanized steel	120	New
Concrete (smooth)	120–130	New
Concrete (rough)	100	Older
Steel (welded)	120	New

Worked Examples

1. Flow Rate in 1-inch Pipe at 40 psi

1" Sch 40 PVC (ID=1.049 in, C=150), 40 psi, 100 ft: S=0.9227. Q=0.2785×150×1.049^2.63×0.9227^0.54=45.5 GPM. Velocity=45.5×0.408/1.049²=16.8 ft/s.

2. Volumetric Flow Rate from Velocity

1" pipe (ID=1.049 in=0.02664 m), velocity=2 m/s: A=p×0.02664²/4=5.576×10?4 m². Q=A×v=5.576×10?4×2=1.115×10?³ m³/s = 17.7 GPM = 66.9 L/min.

3. Mass Flow Rate of Water

Q=20 GPM water: Q=20×6.309×10?5=1.262×10?³ m³/s. ṁ=?×Q=998.2×1.262×10?³=1.260 kg/s = 4,535 kg/h = 4.535 tonne/h = 2.778 lb/s.

4. Mass Flow Rate of Air

Q=1 m³/s air (?=1.204 kg/m³): ṁ=1.204×1=1.204 kg/s = 72.2 kg/min = 4,334 kg/h. Air mass flow is critical in ventilation and combustion — at 50°C, ?˜1.093 kg/m³, so same volumetric flow gives less mass flow.

5. Finding Pipe Diameter from Target Flow and Velocity

Need 50 GPM at max 5 ft/s: Q=50 GPM=0.003155 m³/s. A=Q/v=0.003155/1.524=0.002071 m². d=v(4A/p)=v(0.008284/p)=0.0513 m=2.02 in. Use 2-inch pipe (ID=2.067 in) ?.

6. Garden Hose GPM at 45 psi

5/8" hose (ID=0.625 in, C=150), 45 psi, 50 ft: S=45×2.307/50=2.076. Q=0.2785×150×0.625^2.63×2.076^0.54=17.2 GPM = 65.1 L/min. Mass flow (water): ?=998.2×17.2×6.309×10?5=1.083 kg/s.

Frequently Asked Questions

How do you calculate flow rate in a pipe? ▼

Use Hazen-Williams: Q = 0.2785 × C × d^2.63 × S^0.54 (GPM) for pressurized water, or Q = A × v for known velocity. Calculate S = psi × 2.307 / length(ft). For 1-inch PVC at 40 psi over 100 ft: Q ˜ 45.5 GPM.

What is volumetric flow rate? ▼

Volumetric flow rate Q is the volume of fluid passing a cross-section per unit time. Formula: Q = A × v, where A is pipe cross-section area (m²) and v is mean velocity (m/s). Common units: m³/s, L/s, L/min, GPM (gallons per minute), CFM (cubic feet per minute).

What is mass flow rate and how is it different from volumetric flow rate? ▼

Mass flow rate ? = ? × Q measures mass per unit time (kg/s, lb/s). Volumetric flow rate Q measures volume per unit time (m³/s, GPM). For water (?˜998 kg/m³): 1 GPM = 0.0631 L/s = 0.0630 kg/s. Mass flow is preferred in engineering when fluid density varies with temperature or pressure.

How do you convert PSI to GPM? ▼

PSI alone cannot be converted to GPM — pipe size and length are also needed. Calculate S = psi × 2.307 / pipe length(ft), then Q = 0.2785 × C × d^2.63 × S^0.54. For 1" PVC at 40 psi / 100 ft: Q ˜ 45.5 GPM.

What is the flow rate of a 1 inch pipe at 40 psi? ▼

For 1-inch Schedule 40 PVC (actual ID = 1.049 inches, C=150) over 100 feet at 40 psi: Q = 0.2785 × 150 × 1.049^2.63 × 0.9227^0.54 ˜ 45.5 GPM. Over 50 feet: ~65 GPM; over 200 feet: ~32 GPM.

How does pipe diameter affect flow rate? ▼

Hugely. In Hazen-Williams Q ? d^2.63 — doubling diameter increases flow 6.2×. In Q=A×v, area A=pd²/4 so flow is proportional to d² at constant velocity. In Hagen-Poiseuille, Q ? r4 — doubling radius multiplies flow by 16.

How do you calculate gravity flow in a pipe? ▼

Use Manning's: Q = (1/n) × A × R^2/3 × S^1/2. For full circular pipe: A = pd²/4, R = d/4. S = vertical drop / horizontal distance. 300mm concrete (n=0.012), 1% slope: Q = 0.1057 m³/s = 105.7 L/s = 1676 GPM.

What is the Hazen-Williams C coefficient for PVC pipe? ▼

C = 150 for PVC and HDPE — the highest common value. Copper (new) = 130–140. Cast iron (new) = 130. Galvanized steel = 120. Old cast iron = 80–100. Higher C = smoother pipe = more flow at same pressure.

What is the mass flow rate of water at 10 GPM? ▼

10 GPM water = 10 × 6.309×10?5 = 6.309×10?4 m³/s. ? = ? × Q = 998.2 × 6.309×10?4 = 0.630 kg/s = 37.8 kg/min = 2,268 kg/h = 1.389 lb/s. Use the mass flow calculator above for any fluid.

How do you find the required pipe size for a given flow rate? ▼

Rearrange Hazen-Williams: d = (Q / (0.2785 × C × S^0.54))^1/2.63. Or use Q=A×v: d = v(4Q / (p × v)). Enter your target flow and acceptable velocity in Mode D of the volumetric flow calculator above.

Related Calculators

💧 Formula Reference

Q = 0.2785×C×d^2.63×S^0.54

Q = A × v (volumetric)

ṁ

ṁ = ρ × Q (mass flow)

Q = pr4?P/(8µL)

Man

Q = (1/n)AR^2/3S^1/2

S = psi × 2.307 / L(ft)

🔬 Fluid Densities (kg/m³)

Water (20°C)998.2

Seawater1025

Air (20°C)1.204

Engine oil875

Diesel850

Petrol720

Milk1030

📐 Common C Values

PVC/HDPE	C = 150
Ductile iron	C = 140
Copper (new)	C = 130
Concrete	C = 120
Old cast iron	C = 80–100

💧 Actual Pipe IDs (Sch 40)

1/2"	0.622 in
3/4"	0.824 in
1"	1.049 in
1.5"	1.610 in
2"	2.067 in
3"	3.068 in
4"	4.026 in

🚦 Velocity Guide

✓

< 5 ft/s — Normal residential

5–8 ft/s — Caution, check erosion

⚠

> 8 ft/s — Excessive, erosion risk

💧 Unit Conversions

GPM

1 GPM = 3.785 L/min = 0.0631 L/s

kg/s

1 kg/s = 60 kg/min = 3600 kg/h = 2.205 lb/s

PSI

1 psi = 6.895 kPa = 2.307 ft H2O

1 in = 25.4 mm = 0.0254 m

Pipe Flow Calculator – GPM, Flow Rate by Pipe Size, Pressure & Diameter