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

Answer:

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

Explanation:

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

$\Delta p = \rho \cdot f \cdot \frac{L}{D}\cdot \frac{v^{2}}{2}$

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:

$f = \frac{2 \cdot \Delta p \cdot D}{\rho \cdot L \cdot v^{2}}$

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

$v = \frac{4 \cdot \dot V}{\pi \cdot D^{2}}$

Given that $\dot V = 0.017\,\frac{m^{3}}{s}$ and $D = 0.06\,m$, the velocity of the flow is:

$v = \frac{4\cdot \left(0.017\,\frac{m^{3}}{s} \right)}{\pi \cdot (0.06\,m)^{2}}$

$v \approx 6.013\,\frac{m}{s}$

Now, if $\Delta p = 135000\,Pa$, $\rho = 1000\,\frac{kg}{m^{3}}$ and $L = 10\,m$. The friction factor is:

$f = \frac{2\cdot (135000\,Pa)\cdot (0.06\,m)}{\left(1000\,\frac{kg}{m^{3}} \right)\cdot (10\,m)\cdot \left(6.013\,\frac{m}{s} \right)^{2}}$

$f = 0.045$

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