Pipe Pressure Drop Calculator

How to use this tool

Enter the flow, pick a pipe from the list or type its inside diameter, and enter the length. The tool gives the pressure drop by Darcy Weisbach and by Hazen Williams side by side, with the velocity and Reynolds number. For the pressure left at the far end, add the elevation change (positive when the outlet is higher) and the inlet pressure, and choose which method the outlet figure uses. Fittings are optional: count elbows, tees and valves, or add a total K or an equivalent length.

The input people most often get wrong is the diameter. Pipe is sold by nominal size, and the bore is different: 2 in PVC Schedule 40 measures 2.047 in inside, Schedule 80 measures 1.913 in, and 2 in copper type L measures 1.985 in. Loss varies with roughly the fifth power of the bore, so that matters. The pipe list fills in the diameter, C factor and roughness, and you can overwrite any of them. The tool is for water only, with density and viscosity taken from the temperature you enter.

What the calculation is doing

Darcy Weisbach is the physical method. Velocity is flow divided by the area of the bore, and the Reynolds number, velocity × diameter ÷ kinematic viscosity, says whether the flow is laminar (below 2,000) or turbulent (above 4,000). Laminar flow has friction factor 64 ÷ Re. Turbulent flow uses the Colebrook equation, 1 ÷ √f = −2 log10(ε ÷ 3.7D + 2.51 ÷ (Re √f)), which the tool solves by iteration, with the explicit Swamee Jain estimate as a cross check. Head loss is f × (L ÷ D) × v² ÷ 2g, and pressure is head × density × g.

Hazen Williams uses one coefficient instead: head loss = 10.67 × L × Q^1.852 ÷ (C^1.852 × D^4.8704) in metres and cubic metres per second, or Pd = 4.52 × Q^1.852 × L ÷ (C^1.852 × d^4.8704) psi in gpm, inches and feet. The exponents were fitted to experiments on water, not derived. Fittings add K × v² ÷ 2g in Darcy Weisbach and an equivalent length, K × D ÷ f, in Hazen Williams. Outlet pressure is the inlet pressure less friction, fittings and ρ × g × elevation.

Hazen Williams is an empirical fit, and where it drifts

Hazen Williams is empirical. It was fitted to experiments on water at ordinary temperatures in turbulent flow, and the coefficient C quietly absorbs the roughness, the viscosity and the Reynolds number. That makes it quick, and reliable only near the conditions it was fitted to. The usual stated range is water in pipes from 2 in to 6 ft, below 10 ft/s, between 5 and 25 °C, in turbulent flow, and the tool warns when you step outside it. The Hazen formula elsewhere on this site is the soil permeability rule for sand, not the pipe one.

How far does it stray? Across the ten pipes in the table below, Hazen Williams runs from 21% below to 20% above Darcy Weisbach. At ordinary velocities of 2 to 6 ft/s the steel and PVC cases sit within 8% of it. The outliers are predictable: C 140 on smooth polyethylene reads 13 to 20% high, because Darcy Weisbach treats those pipes as behaving like a C of 150 to 154, and at 0.5 ft/s it falls 21% short even though the flow is turbulent.

Hazen Williams against Darcy Weisbach, pipe by pipe

Pressure drop per 100 ft at 60 °F, with C and roughness from the pipe list.

Hazen Williams also cannot see temperature. The same 30 gpm through 2 in PVC, per 100 ft:

Hot water is thinner, so Darcy Weisbach falls 18% between 60 and 140 °F while Hazen Williams stays put. At 40 °F the loss is 8% higher than at 60 °F. Only one of the two knows the water changed.

A worked example you can check on paper

The default: 30 gpm through 200 ft of 2 in PVC Schedule 40 (inside diameter 2.047 in, roughness 0.0015 mm, C 150), water at 60 °F, outlet 10 ft higher, inlet 60 psi. Flow 0.001893 m³/s and bore 0.05199 m give an area of 0.002123 m² and a velocity of 0.8914 m/s, which is 2.92 ft/s. At 15.56 °C the density is 999.01 kg/m³ and the viscosity 1.121 mPa·s, so ν = 1.122 mm²/s and Re = 0.8914 × 0.05199 ÷ 0.00000112 = 41,305.

Relative roughness is 0.0000015 ÷ 0.05199 = 0.0000288. Colebrook converges to f = 0.021904 in 14 steps, and Swamee Jain gives 0.021791. Darcy Weisbach: h = 0.0219 × 60.96 ÷ 0.05199 × 0.04052 m = 1.04 m, which is 3.41 ft or 1.48 psi. Hazen Williams: 10.67 × 60.96 × 0.001893^1.852 ÷ (150^1.852 × 0.05199^4.8704) = 0.9865 m, or 1.4 psi, 5.2% lower. The US form, 4.52 × 30^1.852 × 200 ÷ (150^1.852 × 2.047^4.8704), gives 1.4 psi.

Lifting the water 10 ft costs 10 × 0.4330 = 4.33 psi, because a foot of water is about 0.433 psi. The outlet pressure is 60 − 1.48 − 4.33 = 54.2 psi. The lift outweighs the friction here, but in 1 1/2 in pipe the same flow would lose 4.95 psi over the same 200 ft.

Mistakes that catch people out

Using the nominal size as the bore. A 2 in pipe is not 2 in inside. Pick it from the list or read the inside diameter from the maker.

Leaving out the fittings. In a short run of small pipe, elbows and valves can cost as much as the straight pipe. Six threaded elbows and a gate valve in 80 ft of 1 in copper add the equivalent of about 72 ft more.

Applying Hazen Williams to hot water or small bores. It has no temperature input and is stated for pipes over 2 in. At 140 °F in 1 in copper it reads 27% above Darcy Weisbach, so use the Darcy Weisbach figure.

Getting the elevation sign wrong. Enter a positive number when the outlet is above the inlet and a negative one downhill, where gravity gives back about 0.433 psi per foot.

Ignoring velocity. A low pressure drop does not make a pipe fit. Above about 5 ft/s in PVC or 8 ft/s in cold water copper, noise, erosion and water hammer become the problem, and the warning under the results covers it.

Popular calculations

Each opens the calculator with those figures filled in, and everything can be changed once it is open. Cases use the pipe list, so the inside diameter, C factor and roughness are the verified ones.

Home, well and irrigation lines

Municipal and larger mains

Metric cases

Hazen Williams against Darcy Weisbach

How this was checked

The engine was compared with published tables and examples, then with a separate implementation. Twenty rows of the Spears PVC Schedule 40 friction loss tables (hosted by Texas A and M AgriLife Extension), at C 150 for 1 1/2, 2, 2 1/2 and 3 in pipe, are reproduced to table rounding by the older constants 0.2083 and 4.8655, the worst row 0.004 ft per 100 ft out. The tool uses the exact constants 10.67 and 4.8704, which run 1.1 to 1.4% below those tables. The Engineering ToolBox example, 200 gpm in 3.048 in pipe at C 140, is published as 9 ft per 100 ft: the older form gives 9.007 and the tool 8.878. A problem from the Universitat Politècnica de València (steel, C 130, 120 mm, 50 m³/h, 100 m, 12 °C) is published as 1.44 m; its own constants give 1.4416 m and the tool 1.4392 m.

For Darcy Weisbach, Example 4.1 in Maurer, Hydrology and Water Resources (Santa Clara University) gives 2.120 m/s, Reynolds number 1.036 million and f = 0.0133; the tool computes 2.119 m/s, 1.0355 million and 0.01328. Crane TP 410 problem 7.1 gives f = 0.0179 from the chart, against 0.01797 from Colebrook. The Colebrook iteration matches an independent bisection solver at 143 points from Re 4,000 to 100 million, to 2 parts in 10^15. Laminar flow reproduces the Hagen Poiseuille pressure drop exactly, and the fully rough limit agrees with the von Kármán constant to 0.2%.

Swamee Jain is usually quoted as within 1% of Colebrook, and that holds only part of the way. Over its stated range, Reynolds number 5,000 to 100 million and relative roughness 10^−6 to 10^−2, the worst error is 2.8%, at the rough, low Reynolds corner; above Re 10,000 with relative roughness to 0.001 it is within 0.9%. That is why it is a cross check here and Colebrook gives the answer. Water density follows Kell (1975), within 0.014 kg/m³ of the Engineering ToolBox table from 4 to 100 °C, and viscosity follows equation 37 of Huber and others (2009), within 0.02% of the tabulated values from 10 to 100 °C. Every address in the lists above was opened and checked for a distinct title, the right answer, a chart that renders, and clean CSV, image and print output holding only the values entered.

Pipe bores come from the Texas A and M and Rain Bird charts for PVC Schedule 40 and 80 (average wall, so 1/2 in Schedule 40 is 0.602 in, against 0.622 in at minimum wall), the ASTM B88 dimensions for copper K, L and M as listed by Engineering ToolBox and McMaster Carr, Uponor catalogue sizes for PEX, the DriscoPlex 6300 sheet for HDPE SDR 11, and outside diameter less twice the wall for steel. Roughness and fitting K values follow the pipe flow lecture notes of Purdue University (ME 308). Velocity notes cite the Copper Development Association, Spears and University of Florida IFAS Extension. Your own pipe may differ from any table, so treat the result as an estimate and check it against the maker data.

Common questions

How do I calculate the pressure drop in a pipe?

Work out the velocity from the flow and the inside diameter, then the Reynolds number, then the friction factor, and put them into the Darcy Weisbach equation: head loss = f × (L ÷ D) × v² ÷ 2g. Multiply the head loss by the density of water and g to get pressure. For 30 gpm through 200 ft of 2 in PVC Schedule 40 that is 3.41 ft of head, or 1.48 psi.

What is the Hazen Williams formula and what C value should I use?

It is an empirical formula for the friction loss of water in a full pipe: head loss = 10.67 × L × Q^1.852 ÷ (C^1.852 × D^4.8704) in SI units. C is a roughness coefficient found by experiment. Common values are 150 for PVC and fibreglass, 140 for polyethylene, PEX, new copper and cement lined iron, 120 for galvanized iron and around 100 for steel or cast iron when designing for the long term. Higher C means a smoother pipe and less loss.

Should I use Hazen Williams or Darcy Weisbach?

Use Hazen Williams when a code or a supplier table is written in it, as with sprinkler and waterworks design, and the water is cool and the velocity moderate. Use Darcy Weisbach for anything else: hot water, small pipes, high or very low velocity, oils, or any fluid other than water. In the table above the two agree within about 8% for steel and PVC at velocities of 2 to 6 ft/s, and drift apart outside that.

What water velocity is too high in a pipe?

No single number fits every pipe. The Copper Development Association gives 5 to 8 ft/s for cold water in copper tube, 4 to 5 ft/s for hot water below 140 °F and 2 to 3 ft/s above it, to limit erosion corrosion. Spears does not recommend more than 5 ft/s in closed end PVC systems, and University of Florida extension guidance for irrigation is 5 ft/s or less. The calculator flags velocity against those figures and does not invent limits of its own.

How much pressure do fittings and valves take?

Each fitting adds a loss of K × v² ÷ 2g, where K comes from a table. Threaded 90 degree elbows are about K 1.5 and flanged ones about 0.3, a fully open gate valve 0.15 and a swing check valve 2. With 6 threaded elbows and a gate valve in 80 ft of 1 in copper carrying 12 gpm, the fittings add about as much loss as another 72 ft of straight pipe.

Does the temperature of the water change the pressure drop?

Yes, through viscosity. Water at 40 °F is about 3.3 times as viscous as water at 140 °F, which lowers the Reynolds number and raises the friction factor. In 2 in PVC at 30 gpm, Darcy Weisbach falls from 0.796 psi per 100 ft at 40 °F to 0.605 psi at 140 °F. Hazen Williams has no temperature input, so it stays near 0.7 psi throughout, which is why it drifts from Darcy Weisbach in hot water.

Related Calculators and Reference

• Pressure Converter: move a result between psi, bar, kPa and other units when a pump curve or code uses a different one.
• Hydrostatic Pressure Equation: the elevation term, 0.433 psi for every foot of water, worked from ρ × g × h.
• Viscosity of Water: the property behind the Reynolds number, and why hot water flows differently from cold.
• Culvert Flow Calculator: pipe capacity by Manning for gravity flow, where this tool assumes a full pipe under pressure.
• Water Heater Size Calculator: peak hot water demand in gpm, the flow to enter here for a hot water line.
• Reynolds Number Calculator: whether pipe, duct or plate flow is laminar or turbulent, and the critical velocity.
• University of Florida IFAS Extension, Hydraulic Considerations for Citrus Microirrigation Systems: friction loss, pipe sizing and velocity limits for water systems, from an extension service.