the Legacy of Hazen-Williams equation  

A "flavour" in pipe frictional loss calculation, Hazen-Williams' empirical equation is the most commonly adopted method since its pipe friction coefficient, C, is not a function of velocity or pipe diameter or Reynolds Number. It is to note that Hazen-Williams equation is only valid for water (preferably 4 - 25 oC or 40 - 75 oF).

Engineering calculations are estimates, to the best of his/her knowledge. Work smart! We don't need complex equations or complicated iterative methods to solve simple engineering applications, and the result remains as an approximation of reality. Knowing its limitations is more important than anything else. Hazen-Williams equation does not account for temperature and viscosity of the water. It is used for turbulent pressurised pipe flow.

In SI units, the Hazen-Williams equation is as follows:

where

P = frictional loss of pressure (bar per m of pipe)

Q = flow (lpm)

D = pipe internal diameter (mm)

C = Hazen-Williams coefficient for the type of pipe

What are Minor Losses in pipes . . .   

These are local head (energy) losses caused by valves, elbows, bends, tees, reducers, etc.

In mPPD, two methods are used to compute the minor losses caused by valves and fittings as follows:

(1) Equivalent Length (Le) method for Hazen-Williams and Darcy-Weisbach equations.

(2) Resistance coefficient ('classic' K) method for Darcy-Weisbach equation.

Again a "flavour" in accounting for minor losses, Le is the equivalent length of pipe with same resistance as the fitting/valve. The published Le/D data in Crane TP 401 and others is for C = 120 (steel pipe). The Le can be converted as necessary for pipes of other C values by multiplying a factor as stated in NFPA and others:  

There is no Le/D data available for reducer, expander, entrance, exit, orifice, nozzle, etc. In this case, Le/D can be determined using the following formula: 

For example, if we know K for sudden Exit into a tank is 1 and f is 0.012192 ( solved by colebrook equation ), then Le/D = 1/0.012192 = 82.

Did you know ? . . . pressure drop vs head loss  

Don't confuse yourself with pressure drop and head loss.

Pipes in series . . .  

Pipes of different diameters connected end to end to form a pipe line is said to be in series. The total friction loss is the sum of all the friction losses in each section of the pipe plus local losses.

In mPPD, each row (pipe) is calculated and presented separately for velocity, Reynolds number, friction factor, friction loss and summation of pressure drop. Different pipe material can be specified for each row (pipe).

Note: For multiple Series pipe with a loop ring main on Windows, see easy Pipe Friction (ePF) Loop (Windows).

Let's get stuff done . . . Easy Pipe Friction way 

The following illustrates easy pipe friction with mPPD and its capability. Determine the pipe friction loss with water mass flow of 15 kg/s from Tank A to B as illustrated in the schematic below. 

(1) Sharp entrance.

(2) 100mm dia Ductile iron pipe, 5m length.

(3) 1 Strainer.

(4) 1 Gate valve.

(5) 1 Check valve.

(6) 100mm dia Ductile iron pipe, 10m length.

(7) 1 Standard elbow.

(8) 1 Reducer.

(9) 50mm dia Copper pipe, 100m length.

(10) 1 Standard elbow.

(11) 50mm dia Copper pipe, 10m length.

(12) 1 Butterfly valve.

(13) Sharp exit into tank.

Step 1: convert mass flow to volumetric flow (using the built-in flow converter)   

Remarks: The above example illustration (using Hazen-Williams equation and Le method) shows that the pipe size is undersized from row 9 to 13.

Worked Example 1 . . . Quickly Estimating Pressure Drop in Pipe (English Units)  

Consider a 16-in (ID = 15.624-in) Sch 40S stainless steel system. The piping system contains 100 ft of pipe, 6 long-radius (R/D=1.5) 90o elbows, 2 side-outlet tees, 2 gate valves (fully open) and an exit into a tank. The water flow rate is 13.314 ft³/s. What is the pressure drop through this system?

Compare the results computed by:

(1) Darcy-Weisbach equation with K method.

(2) Darcy-Weisbach equation with Le method.

(3) Hazen-Williams equation with Le method.

(d) Hooper's 2-K method (refer to Windows program: Pipe_f.Loss)

The table below shows the results computed by the different methods in mPPD program.

(1) Darcy-weisbach equation + K method

(2) Darcy-Weisbach equation + Le method

(3) Hazen-Williams + Le method

(4) Hooper's 2-K method (see Windows program: Pipe_f.Loss) 

Worked Example 2 . . . fire hydrant system (SI units)  

Determine the total pressure drop in pipes, valves and fittings for the fire hydrant piping system as shown in the schematic below.

Compare the pressure drop computed using:

(a) Darcy equation with Le method.

(b) Hazen equation with Le method.

Design data:

Q (flow rate) = 38 l/s.

Pipe material = Ductile iron pipe.

Pipes, valves and fittings data:

(1) Pipe total run = 100m, 150mm diameter

(2) Isolation gate valve = 1 no.

(3) Standard 90o elbow = 4 nos.

(4) Meter = 1 no.

(5) Gate valve = 1 no.

(6) Check valve = 1 no.

(7) Check valve = 1 no.

(8) Tee = 1 no.

(9) Reducer = 1 no.

(10) Pipe total run = 3m, 100mm diameter

(11) Gate valve = 1 no.

(12) Standard 90o elbow = 1 no.

The following are the results computed by mPPD program:

Results:

(a) Darcy equation with Le method  

b) Hazen method with Le method