Water (10°C) flows through a 50-cm smooth pipe at a rate of 0.05 m3 /s. What is the friction factor ƒ?

The friction factor is approximately 0.0179.

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:

(Eq. 1)

Where:

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

- Dynamic viscosity, measured in kilograms per meter-second.

- Inner diameter of pipe, measured in meters.

- Flow average speed, measured in meters per second.

- Reynolds number, dimensionless.

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

(Eq. 2)

Where:

- Volume flow, measured in cubic meters per second.

- Inner diameter of pipe, measured in meters.

If we know that and , the flow average speed is:

The properties of water at given conditions () are, respectively:

And the Reynolds Number is:

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:

(Eq. 3)

Where:

- Friction factor, dimensionless.

- Smoothness factor, dimensionless.

If we know that and , then we get that:

The friction factor is approximately 0.0179.

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