Your company is planning to build a pipeline to transport gasoline from the refinery to a field of storage tanks. The parameters for the prototype system are a pipe diameter of 1 m, with a flow velocity of 0.5 m/s at 25°C. The model system will use water at STP with a geometric scaling factor of 1 : 20. What fluid velocity is required in the model system to guarantee kinematic similarity in the form of equal Reynolds numbers?

The model system will need water flowing at a velocity of 2.07 meters per second to guarantee kinematic similarity in the form of equal Reynolds numbers.

Explanation:

The Reynolds number () is a dimensionless criterion use for flow regime of fluids, which is defined as:

(Eq. 1)

Where:

- Density, measured in kilograms per cubic meter.

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

- Average flow velocity, measured in meters per second.

- Pipe diameter, measured in meters.

We need to find the equivalent velocity of water used in the prototype system. In this case, we assume that . That is:

(Eq. 2)

Where subindex is used for water and for gasoline.

If we know that , , , , , and , then we get the following formula:

The fluid velocity for the prototype system is:

The model system will need water flowing at a velocity of 2.07 meters per second to guarantee kinematic similarity in the form of equal Reynolds numbers.

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