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I have used the Hazen-Williams equation to calculate head loss for falling water in a vertical pipe I am using in a hydroelectricity project of mine.

Hazen-Williams equation:

Hazen-Williams equation

These are the properties in my project:

  1. C (roughness constant)= 150
  2. q (flow rate) = 25.1 l/s
  3. dh (internal hydraulic diameter of pipe) = 25.68 mm

The pipe is an annulus shape and vertically orientated.

However, when I plug my values into the Hazen-Williams equation, I get a water head loss of 1002m per 100m of pipe, which seems highly improbable!

Could someone shed a light on where I have gone wrong here?

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  • $\begingroup$ Test using the page here: engineeringtoolbox.com/hazen-williams-water-d_797.html which may point you in the right direction. $\endgroup$
    – Solar Mike
    Aug 8 '21 at 18:13
  • $\begingroup$ That is the site I used which gave that rather unlikely value for head loss above!! $\endgroup$ Aug 8 '21 at 18:15
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    $\begingroup$ I used that site for the equation and then used excel for the result, and double checked the result with the site’s calculator. $\endgroup$ Aug 8 '21 at 18:18
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    $\begingroup$ Well, it gave me, using your numbers 48.5m/s for a 100m length. So you need to do some checking of your base information. $\endgroup$
    – Solar Mike
    Aug 8 '21 at 18:20
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    $\begingroup$ So, 25l/s through a 25mm pipe and you don’t expect high losses? $\endgroup$
    – Solar Mike
    Aug 8 '21 at 19:07
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There are three types of mistakes that may cause the seemly erroneous result:

  • Inconsistency in matching the units of an empirical formula and input data. (You shouldn't list the imperical formula followed with a set of metric data. The formula of each system and its respective units of data are typed below for your reference.)

  • The expectation is unrealistic, or the setup violates the limitations of the formula (see notes at the end).

  • Erroneous/questionable input data. This seems to be the main cause of your problem. Please double-check your flow rate calculation.

FYI -

$1)$ The the Hazen-Williams formula in SI units is:

$h_f = 10.67 L Q^{1.852} / (C^{1.852}d^{4.8704})$

  • $h_f$ = head loss in meters (water) over the length of pipe
  • $L$ = length of pipe in meters
  • $Q$ = volumetric flow rate, m3/s (cubic meters per second)
  • $C$ = pipe roughness coefficient
  • $d$ = inside pipe diameter, m (meters)

Reference

$2)$ The imperial form of the Hazen-Williams formula is:

$h_f = 0.002083 L (100/C)^{1.85}$ x $(gpm^{1.85}/d^{4.8655})$

where: $h_f$ = head loss in feet of water $L$ = length of pipe in feet $C$ = friction coefficient $gpm$ = gallons per minute (USA gallons not imperial gallons) $d$ = inside diameter of the pipe in inches

Common Friction Factor Values of C used for design purposes are:

Asbestos Cement 140 Brass tube 130 Cast-Iron tube 100 Concrete tube110 Copper tube130 Corrugated steel tube 60 Galvanized tubing 120 Glass tube130 Lead piping130 Plastic pipe140 PVC pipe 150 General smooth pipes 140 Steel pipe 120 Steel riveted pipes 100 Tar coated cast iron tube 100 Tin tubing130 Wood Stave 110

Note 1: The empirical nature of the friction factor C makes the ëHazen-Williamsí formula unsuitable for accurate prediction of head loss

Note 2: The results are only valid for fluids which have a kinematic viscosity of 1.13 centistokes, where the fluid velocity is less than 10 feet per sec and the pipe size is greater than 2" diameter. Water at 60º F (15.5º C) has a kinematic viscosity of 1.13 centistokes

Reference

Calculator for both units systems. engineeringtoolbox

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  • $\begingroup$ Visible on the link I gave, but no answer to the problem. And you could not even type in the values... $\endgroup$
    – Solar Mike
    Aug 8 '21 at 18:29
  • $\begingroup$ Still failed to show the results of what you suggest. $\endgroup$
    – Solar Mike
    Aug 8 '21 at 18:38
  • $\begingroup$ @SolarMike I didn't suggest anything but indicating "consistency" in engineering calculation. You don't list Imperial formula but plugin metric data and wish to magically turn out the correct answer. However, the OP's problem wasn't solely caused by inconsistency, could be caused by limitation of this equation. $\endgroup$
    – r13
    Aug 8 '21 at 19:25
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    $\begingroup$ the page I linked to has the equations with inputs for both imperial and SI units, imperial first and SI secind, told you that earlier… Don’t understand how you cannot see both… $\endgroup$
    – Solar Mike
    Aug 8 '21 at 19:30
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    $\begingroup$ @SolarMike What I left out in my comment? You shall prepare your own answer rather than chasing the tail. $\endgroup$
    – r13
    Aug 8 '21 at 20:00

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