Question

Fire Stoke’s 1st comparison of pressure forces and friction forces acting on any given fluid element shows that

• A. the pressure forces and friction forces are almost same
• B. the pressure force is much larger than friction forces
• C. the friction force is much larger than pressure forces
• D. the friction force is zero and pressure force is finite

Hint:

In inviscid flow models, friction forces are often neglected relative to pressure forces.

Answer 1

The Correct Option is B

To compare the pressure forces and friction forces acting on a fluid element, we consider Stoke's analysis focused on fluid dynamics within the framework of continuum mechanics. In the context of laminar flow, the Navier-Stokes equations are employed, where pressure and viscous forces play pivotal roles.

Let's break down the forces:

• Pressure Forces: These are normal forces arising from pressure differences within the fluid. They act perpendicular to the fluid surface and can exert considerable magnitude, especially in cases of high-pressure flows or when dealing with large fluid columns.
• Friction Forces: Also known as viscous forces, these are tangential forces arising due to the fluid’s viscosity and are related to the fluid layer's velocity gradients. They work to resist the motion between layers of fluid and are comparatively smaller than pressure forces, particularly in lower viscosity fluids or slow-moving flows.

 

Stokes' First Comparison: In high Reynolds number conditions (indicating either high velocity or low viscosity), the influence of viscous forces is minimized, resulting in pressure forces dominating over friction forces. This scenario leads to the conclusion:

Correct Answer: the pressure force is much larger than friction forces.