Question

If a 400-mm diameter pipe with a pipe roughness coefficient of 100 flows full of pressurized water with a head loss of 0.4 ft per 1,000 ft of pipeline, what is the flow rate? Use the Hazen-Williams method

Answer 1

Q = 913.9 gpm

Step-by-step explanation:

The Hazen Williams equation can be written as follows:

`P = (4.52\ Q^(1.85))/(C^(1.85)d^(4.87))`

where,

P = Friction Loss per foot of pipe =
`(0.4)/(1000\ ft)` = 4 x 10⁻⁴

Q = Flow Rate in gallon/min (gpm) = ?

d = pipe diameter in inches = (400 mm)(0.0393701 in/1 mm) = 15.75 in

C = roughness coefficient = 100

Therefore,

`4\ x \ 10^(-4) = (4.52\ Q^(1.85))/((100)^(1.85)(15.75)^(4.87))\\\\Q^(1.85) = (4\ x \ 10^(-4))/(1.33\ x\ 10^(-9)) \\\\Q = (300384.75)^(1)/(1.85)`

Q = 913.9 gpm