Answer:
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.
