Question

Water flows through a horizontal 60-mm-diameter galvanized iron pipe at a rate of 0.017 m3/s. If the pressure drop is 135 kPa per 10 m of pipe, determine the friction factor.

Answer 1

The friction factor of a 60-mm-diameter galvanized iron pipe is 0.045.

Step-by-step explanation:

Losses due to friction flowing through iron pipe is determined by the Darcy-Weisbach model:

`\Delta p = \rho \cdot f \cdot (L)/(D)\cdot (v^(2))/(2)`

Where:

`\Delta p` - Pressure drop, measured in pascals.

`\rho` - Density of water, measured in kilograms per cubic meter.

`f` - Friction factor, dimensionless.

`L` - Length of the pipe, measured in meters.

`D` - Diameter of the pipe, measured in meters.

`v` - Velocity of the flow, measured in meters per second.

The friction factor is now cleared:

`f = (2 \cdot \Delta p \cdot D)/(\rho \cdot L \cdot v^(2))`

The flow velocity is equal to the volume flow divided by the cross area of the iron pipe. That is:

`v = (4 \cdot \dot V)/(\pi \cdot D^(2))`

Given that
`\dot V = 0.017\,(m^(3))/(s)` and
`D = 0.06\,m`, the velocity of the flow is:

`v = (4\cdot \left(0.017\,(m^(3))/(s) \right))/(\pi \cdot (0.06\,m)^(2))`

`v \approx 6.013\,(m)/(s)`

Now, if
`\Delta p = 135000\,Pa`,
`\rho = 1000\,(kg)/(m^(3))` and
`L = 10\,m`. The friction factor is:

`f = (2\cdot (135000\,Pa)\cdot (0.06\,m))/(\left(1000\,(kg)/(m^(3)) \right)\cdot (10\,m)\cdot \left(6.013\,(m)/(s) \right)^(2))`

`f = 0.045`

The friction factor of a 60-mm-diameter galvanized iron pipe is 0.045.