Hazen-Williams Calculator: hf = 10.67 L Q^1.852 / (C^1.852 D^4.87)

The head loss in a full water pipe, from the flow, the diameter and the pipe C factor.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • h_f = \frac{10.67\,L\,Q^{1.852}}{C^{1.852}D^{4.87}}
  • Q = \left(\frac{h_fC^{1.852}D^{4.87}}{10.67\,L}\right)^{1/1.852}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the head loss: head loss = (10.67 x length of the pipe x flow^1.852) / (hazen-williams c factor^1.852 x inside diameter of the pipe^4.87)
  2. Put the values in (every value in its SI unit): head loss = (10.67 x 100 x 0.05^1.852) / (130^1.852 x 0.2^4.87)
  3. The answer: head loss: 1.2812 m
  4. The same answer in other units: 12.5643 kPa

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Flow; Head loss (leave it as it is if this is what you are finding) 1.2812 m; Length of the pipe (leave it as it is if this is what you are finding) 100 m; Hazen-Williams C factor (leave it as it is if this is what you are finding) 130; Inside diameter of the pipe (leave it as it is if this is what you are finding) 0.2 m.

  1. The formula, arranged to find the flow: flow = ((head loss x hazen-williams c factor^1.852 x inside diameter of the pipe^4.87) / (10.67 x length of the pipe))^0.53996
  2. Put the values in (every value in its SI unit): flow = ((1.2812 x 130^1.852 x 0.2^4.87) / (10.67 x 100))^0.53996
  3. The answer: flow: 0.05 m3/s
  4. The same answer in other units: 50 L/s; 180 m3/h

Common questions

What is the Hazen-Williams equation?

An empirical formula for the head loss of water flowing in a pipe, based on the flow, the diameter, the length and a roughness factor C.

What C value should I use?

About 140 for new plastic or lined pipe, 130 for new cast iron or steel, and lower for old pipes. Check the water authority rules for design values.

How is it different from Darcy-Weisbach?

Hazen-Williams uses a fixed C and does not change with the Reynolds number, so it only suits water at normal temperatures.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any water supply or hydraulics text (the Hazen-Williams equation).

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