Static water pressure is density times gravity times height, 998 × 9.81 = 9.79 kPa or 0.098 bar per metre, so an 18 m static head gives 1.76 bar before any flow. Friction then subtracts head along the pipe: at 0.33 L/s through 250 m of 32 mm pipe the loss is 1.92 m, leaving 16.1 m or 1.57 bar at the tap, but the same flow in 25 mm pipe loses 6.39 m and leaves 11.6 m or 1.14 bar.
Calculating head pressure turns the height of a water surface above a tap into pressure, then subtracts what friction takes along the pipe. It is the arithmetic behind the parent page’s rule of 0.1 bar per metre.
Static Pressure Is The Weight Of The Water Above The Point
A column of water of height h presses on its base with ρ × g × h. With density ρ = 998 kg/m³ (water at 20°C, a standard handbook value I recall rather than a figure from this wiki) and g = 9.81 m/s²:
- Per metre: 998 × 9.81 × 1 = 9,790 Pa = 9.79 kPa = 0.0979 bar.
- In psi: 9,790 ÷ 6,895 = 1.42 psi, matching the parent page’s 1.4 psi.
| Head | Pressure |
|---|---|
| 5 m | 0.49 bar, 7.1 psi |
| 10 m | 0.98 bar, 14.2 psi |
| 20 m | 1.96 bar, 28.4 psi |
| 30 m | 2.94 bar, 42.6 psi |
The parent page’s “0.1 bar per metre” overstates by about 2%, which is fine for planning and safe on the design side for the lowest tap.
Pressure depends only on vertical height of the water surface above the point, never on the length of the pipe or its diameter. A thin pipe and a wide pipe from the same source give the same static pressure.
Dynamic Pressure: Friction Subtracts Head
When water flows, the pipe wall resists it and head is lost along the length. Pipe Sizing gives the Hazen-Williams form, in SI units:
h_f = 10.67 × L × Q^1.852 ÷ (C^1.852 × d^4.87)
with h_f in metres, L in metres, Q in m³/s, C a roughness coefficient and d the internal diameter in metres. That page designs plastic pipe with C = 140.
Worked Example: Friction In Two Pipe Sizes
Inputs: source surface 18 m above the tap, pipe length 250 m, flow 0.33 L/s = 0.00033 m³/s (the bucket-test flow, 20 L in 60 s), C = 140.
- 32 mm bore: h_f = 10.67 × 250 × 0.00033^1.852 ÷ (140^1.852 × 0.032^4.87) = 1.92 m.
- 25 mm bore: same flow and length, d = 0.025: h_f = 6.39 m.
- Static pressure before flow: 18 × 0.0979 = 1.76 bar (0.098 bar per metre rounded).
- Head left at the tap: 18 − 1.92 = 16.08 m, about 16.1 m, = 16.08 × 0.0979 = 1.57 bar for the 32 mm pipe; 18 − 6.39 = 11.61 m, about 11.6 m, = 1.14 bar for the 25 mm pipe.
At the lower flow of 0.2 L/s the losses are 0.76 m and 2.53 m. A 40 mm pipe at 0.33 L/s loses 0.65 m. The diameter enters as the 4.87th power: from 25 mm to 32 mm the loss falls by a factor of 6.39 ÷ 1.92 = 3.3, so a small step in diameter gives a large saving. Use the internal bore, not the label size: the sizing page shows a 45 mm bore on a 50 mm label has 67% more friction than a full 50 mm bore.
The Pressure Line Must Stay Above The Pipe
Draw the hydraulic grade line: start at the source water surface, and subtract friction loss along the pipe. The pressure at any point is the height of that line above the pipe.
- If the pipe crosses a ridge 1 m below the source level and friction to that point is 0.38 m (half of 0.76 m at 0.2 L/s in 32 mm), the line is at 100 − 0.38 = 99.62 m against a pipe crest at 99 m: positive pressure head of 0.62 m, about 0.06 bar.
- If the crest were at the source level, 100 m, the pressure head would be 99.62 − 100 = −0.38 m: below atmospheric. Air comes out of the water and collects at the crest, and the flow falls.
Keep crests well below the grade line, and fit air release at every high point (Air Valves).
Flow At A Tap: Head Does Not Set It Alone
A tap discharging to air passes about Q = C_d × A × √(2 × g × h). For a tap bore of 12 mm (A = π × 0.006² = 1.13 × 10⁻⁴ m²) at 10 m head and C_d = 0.6, the textbook value for a sharp-edged hole that I recall:
- Speed √(2 × 9.81 × 10) = 14.0 m/s.
- Flow = 0.6 × 1.13 × 10⁻⁴ × 14.0 = 9.5 × 10⁻⁴ m³/s = 0.95 L/s.
That is the ideal upper limit with no friction in the line. A real kitchen tap passes much less, because the pipe, valves and any fine outlet add loss, so flow is usually limited by the pipe, not the head. Velocity head, v² ÷ 2g, is small at pipe speeds: 1 m/s gives 0.051 m, 3 m/s gives 0.46 m.
Surge Adds To Static Head
Closing a valve fast stops the moving water and raises pressure above the static figure. Tap Types gives about 3 bar extra for a ball valve slammed shut on a pipe running at 1 m/s. That is 300,000 Pa ÷ (1,000 kg/m³ × 1 m/s) = 300 m/s of pressure-wave speed implied. Add the surge to the static head when choosing pipe pressure class: a 20 m head (1.96 bar) plus 3 bar is about 5 bar.
Measuring The Head: How Accurate?
A clear tube level carries about ±3 mm per setup (Water Tube Level). Even with 20 setups the worst case is 20 × 3 = 60 mm = 0.006 bar, negligible against the 10 m figures here. The uncertainty that matters is the flow and the pipe bore, not the height.
What You Need
- Measured static head in metres
- Pipe length, bore and material (C value)
- Design flow at the tap (Flow Measurement)
- A calculator or the equation worked by hand
Common Mistakes
- Using the label diameter instead of the bore.
- Using the straight-line distance instead of pipe length.
- Ignoring the pipe crests between source and tap.
- Forgetting surge when picking pipe.
Safety
The calculated pressure is a minimum for the pipe, not a limit on the danger
Static head at the lowest point of a steep line can reach several bar (10 m is 0.98 bar, so 60 m is 5.9 bar), and a fast valve closure can add about 3 bar. Choose pipe and fittings rated above both, test new lines with water and never with compressed air, and keep non-drinking pipes apart from the drinking supply.
What’s Next
- Learn next: Break Pressure Tanks — cap the pressure on a steep line
- Combine with: Tank Sizing & Placement — set the head with the tank’s height