14.1.3. Dimensional Groups in Fluid Mechanics

Try these first

1. 1.

   What does dimensional analysis help us achieve in fluid mechanics?

   Hint

   Think about how it relates to scaling and modeling.

2. 2.

   State the formula for Reynolds number.

   Hint

   Remember the symbols involved.

3. 3.

   What does the Reynolds number quantify?

   • Viscous forces
   • Inertial forces
   • Ratio of inertial to viscous forces

   Hint

   What does it compare?

4. 4.

   The Froude number relates which two forces?

   • Viscous to inertial
   • Gravity to inertial
   • Pressure to inertial

   Hint

   Think about the forces acting on fluids in channels.

5. 5.

   A cylindrical tube with a radius of 0.05 m carries water (density 1000 kg/m³, viscosity 0.001 Pa.s) at a velocity of 2 m/s. Calculate the Reynolds number and interpret the flow.

   Hint

   Use the provided values to derive your result.

6. 6.

   You have a fluid (viscosity = 0.002 Pa.s) flowing with a velocity of 4 m/s in a channel of height 1 m. Calculate the Froude number and assess flow dominance.

   Hint

   Remember the formula for Froude number!