This example case considers the flow of water in a 6 inch Schedule 40 pipeline and compares the results when using the Moody Friction Factor vs the Hazen Williams formula for the same flowing conditions. A hand calculation will initially be carried out to determine the pressure loss for the two scenarios. A model will then be developed to make a comparison with the hand calculation.

**Problem Statement:**

720 GPM of water at 95 F flows in a 6 inch Sch 40 steel pipe at a velocity of 8 ft/s. The pipeline has a total length of 1000 ft (equivalent length). Determine the friction loss using the Moody Friction Factor and the Hazen Williams formula.

**Solution:**

Re = ρvD/μ

Where;

ρ is taken as 62.057 lbm/ft^{3}

μ is taken as 0.000484 lbm/ft sec.

v is 8 ft/s.

D is 6.065 in.

Re = (62.057)(8)(6.065)/(0.000484)

Re = 5.2 x 10^{5}

The relative roughness of new steel pipe can be calculated as;

ϵ/D = (0.0002 ft / 6.065 in)(12 in/ft)

ϵ/D = 0.0004

Considering the Re of 5.2 x 10^{5} and relative roughness of 0.0004, we arrive at a friction factor of 0.017 approximately.

The head loss due to friction can be determined as follows;

Hf = f (L/D) (V^{2} / 2g)

Hf = (0.017) (1000 ft / 6.065 in) (12 in/ft) (8ft/s)^{2} / (2(32.2 ft/s^{2})

Hf = 33.4 ft

Modeling this scenario yields the following results.

**Figure 1: 6 Inch Pipe – Moody Friction Factor.**

The modeled value for friction loss is 32.3 ft fluid which is close to the hand calculation value of 33.4 ft. The difference can be attributed to the simplifications of the hand calculation by comparison to the modeled solution.

Let’s now consider the Hazen Williams approach using the following equation:

H = C_{f} L Q^{1.852} / C^{1.852} D^{4.87}

Where;

C_{f} is the unit conversion fact (4.72).

L is the pipe length (1000 ft).

Q is the volumetric flow rate (8 ft/s)(0.20063 ft^{2}) = 1.605 ft^{3}/s.

C is the Hazen Williams coefficient, initially considered to be 100 for steel pipe. Note, this is a conservative value and allows for future scaling of the internal pipe surface. The American Iron & Steel Institute’s Committee for Steel Pipe Producers recommends a C value of 140.

H = (4.72) (1000) (1.605)^{1.852} / (100)^{1.852} (0.505)^{4.87}

H = 11337 / 181.6

H = 62.4 ft.

Modeling this scenario yields the following results.

**Figure 2: 6 Inch Pipe – Hazen Williams (C = 100).**

The modeled solution (62.1 ft fluid) compares well with the hand calculation results of 62.4 ft.

Note, if we use a C value of 140 for clean or new steel pipework, we get;

H = 11337 / (140)^{1.852} (0.505)^{4.87}

H = 33.5 ft.

Modeling this scenario yields the following results.

**Figure 3: 6 Inch Pipe – Hazen Williams (C = 140).**

The modeled value for friction loss is 33.3 ft fluid which is close to the hand calculation value of 33.5 ft. Again, the difference can be attributed to the simplifications of the hand calculation by comparison to the modeled solution.

We have already calculated a friction loss of 33.4 ft using the Moody Friction Factor. Conversely, if we use a roughness value for corroded steel pipe (0.013 ft), we get;

ϵ/D = (0.013 ft / 6.065 in)(12 in/ft)

ϵ/D = 0.03

From the Moody diagram, the friction factor is approximately 0.0265. This increases the friction loss by a factor of 0.0265 / 0.017 which yields,

H = 33.4 ft (0.0265/0.017)

H = 52.1 ft

Review this scenario in a model yields the following results.

**Figure 4: 6 Inch Pipe – Fixed Friction Factor of 0.0265.**

Let’s summarise the results.

This study demonstrates the following;

- There is good agreement between the Darcy-Weisbach and Hazen Williams equations for clean pipework.
- The results are sensitive to the roughness and C factor values for corroded or old pipework installations.

**References:**

- Piping Systems Manual (Brian Silowash).