Model Laws - Dimensional Analysis - Applied Hydraulics

TL;DR

Model laws for dynamic similarity are based on dominant forces and are used to ensure similarity between model and prototype.

Transcript

hello students today we are going to study model laws for dynamic similarity between model and prototype ratio of dimensionless number that is the reynold number fraud number ios number weber's number mesh number should be same for model and prototype but it is difficult to satisfy all the forces ratios hence models are designed on the basis of rat... Read More

Key Insights

• 👮 Model laws for dynamic similarity are based on dominant forces in a flow phenomena.
• 👮 Reynolds model law is used when viscous forces are dominant.
• 👮 Fröhlich model law is applicable when gravity forces are important in addition to inertia forces.
• 👮 Euler's model law is used when pressure forces are dominant.
• 👮 Weber's model law is applied when surface tension forces are dominant.
• 👮 Mesh model law is used when compressibility forces are dominant.
• 👮 Each model law has specific applications and equations for achieving dynamic similarity.

Questions & Answers

Q: What are model laws for dynamic similarity based on?

Model laws for dynamic similarity are based on the forces that are dominant in a flow phenomena. Different laws are used depending on the dominating forces.

Q: When is Reynolds model law used?

Reynolds model law is used when only viscous forces are dominant, such as in laminar flow or flow around completely submerged objects.

Q: In which situations is Fröhlich model law applicable?

Fröhlich model law is applicable when gravity forces are important in addition to the inertia force. It is used in free surface flow scenarios like flow over spillways and hydraulic jumps.

Q: When is Euler's model law used?

Euler's model law is applied when apart from inertia forces, only pressure forces are dominant. It is used in cases like pipe flow at high pressure or for pressure due to the sudden closure of valves.

Q: What is Weber's model law used for?

Weber's model law is applied when apart from inertia forces, surface tension forces are dominant. It is used in situations like capillary rise, flow over weirs, and flow of blood in veins and arteries.

Q: When is mesh model law used?

Mesh model law is used when apart from inertia forces, compressibility forces are dominant. It is applied in aerodynamic testing and the flow of gases through pipes at high velocity.

Summary & Key Takeaways

• Model laws for dynamic similarity are based on forces dominating in a flow phenomena.

• Reynolds model law is used when only viscous forces are dominant.

• Fröhlich model law is applied when gravity forces are important in addition to inertia force.

• Euler's model law is used when pressure forces are dominant.

• Weber's model law is applied when surface tension forces are dominant.

• Mesh model law is used when compressibility forces are dominant.