1 Answer

EasyPush · Answer 1 · 2021-07-13T22:22:01+0000

Answer:

The friction factor
is approximately 0.0179.

Step-by-step explanation:

At first we need to know what flow regime water flow is found in. Reynolds number offers an appropriate dimensionless indicator for flow in pipes and whose formula is:

$Re_(D) = (\rho \cdot v\cdot D)/(\mu)$ (Eq. 1)

Where:

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

$\mu$ - Dynamic viscosity, measured in kilograms per meter-second.

- Inner diameter of pipe, measured in meters.

- Flow average speed, measured in meters per second.

Re_(D) - Reynolds number, dimensionless.

The average speed of water is determined by the following expression:

$v = (4 \cdot \dot V)/(\pi \cdot D^(2))$ (Eq. 2)

Where:

$\dot V$ - Volume flow, measured in cubic meters per second.

- Inner diameter of pipe, measured in meters.

If we know that
$\dot V = 0.05\,(m^(3))/(s)$ and
$D = 0.5\,m$ , the flow average speed is:

$v = (4\cdot \left(0.05\,(m^(3))/(s) \right))/(\pi\cdot (0.5\,m)^(2))$

$v\approx 0.255\,(m)/(s)$

The properties of water at given conditions (
$T = 10\,^(\circ)C$ ) are, respectively:

$\rho = 999.7\,(kg)/(m^(3))$

$\mu = 1.307* 10^(-3)\,(kg)/(m\cdot s)$

And the Reynolds Number is:

$Re_(D) = (\left(999.7\,(kg)/(m^(3)) \right)\cdot \left(0.255\,(m)/(s) \right)\cdot (0.5\,m))/(1.307* 10^(-3)\,(kg)/(m\cdot s) )$

Re_(D) = 97522.380

Which means that water is in turbulent flow. There are several empirical and semi-empirical expression to estimate friction factor, we decided to use the Haaland approximation due to its exactness and simplicity:

$(1)/(√(f)) = -1.8\cdot \log_(10)\left[(6.9)/(Re)+\left((\epsilon)/(3.7\cdot D)\right)^(1.11) \right]$ (Eq. 3)