How Does Friction Factor Relate to Velocity in Fluid Dynamics?

[gmax137]

There's a couple of recent threads on friction - rather than hijack those here's a new thread with a few questions I have.

What I'm trying to understand is the relationship between the friction force (on an object moving through a fluid) and the velocity of the object. A few places I see "friction force is linear with velocity for laminar flow and goes as velocity squared for turbulent flow." I'm trying to undestand this on a physical level.

I'm more familiar with fluid flow through pipes. In this case, the problems are usually solved by using a friction factor (f) multipied by velocity squared: f*(v^2)/2g. The factor f is found from the Moody chart, which shows f as a function of reynolds number. At low Re, f is proportional to 1/Re; at fully turbulent flow (high Re), f is constant. Since Re is proportional to v, this gives us the described behavior: when Re is low the losses go as v^2/v (ie, linear in v) and when Re is high the losses go as v^2.

OK, so now my questions: 1) why is the loss =f*v^2? and (2) why is the shape of f vs Re as shown on the Moody chart? I'm looking for the physics behind this. Anyone able to give me a clue?

Thanks

 

[A.T.]

A few places I see "friction force is linear with velocity for laminar flow and goes as velocity squared for turbulent flow." I'm trying to undestand this on a physical level.

The velocity squared dependency can be explained as follows in simplified terms: If you double your velocity, you double the number of molecules that hit you per time unit. But the average collision velocity doubles as well. So the momentum transferred to you per time unit(force) is four times bigger.

 

[astrokreng]

I can provide some insights into the relationship between friction factor and velocity in fluid flow. First, it's important to understand that friction force is a result of the interaction between the fluid and the surface of the object moving through it. This interaction creates a shear stress, which is the force per unit area acting parallel to the surface.

In laminar flow, the fluid particles move in a smooth, orderly manner, with minimal mixing and disturbance. This results in a linear relationship between friction force and velocity, because the shear stress is proportional to the velocity gradient. As the velocity increases, the shear stress also increases proportionally, resulting in a linear increase in friction force.

In turbulent flow, on the other hand, the fluid particles move in a chaotic, irregular manner, with significant mixing and disturbance. This creates a turbulent boundary layer, where the velocity gradient is much steeper and the shear stress is much higher compared to laminar flow. As a result, the friction force is no longer proportional to the velocity gradient, but rather to the square of the velocity. This is because the shear stress is now a function of both the velocity gradient and the velocity itself.

The friction factor, as shown on the Moody chart, reflects the behavior of the fluid flow in different regimes. At low Reynolds numbers, the flow is laminar and the friction factor is inversely proportional to the Reynolds number. This is because laminar flow is dominated by viscous forces, and the friction force is directly related to the viscosity of the fluid. As the Reynolds number increases and the flow becomes more turbulent, the friction factor becomes relatively constant. This is because the turbulent flow is dominated by inertial forces, and the friction force is now related to the density and velocity of the fluid.

In summary, the relationship between friction force and velocity is a result of the different flow regimes and the dominant forces at play in each regime. The physics behind this lies in the interaction between the fluid and the surface, and how that interaction changes with changes in velocity and flow conditions. The Moody chart provides a visualization of this relationship and helps engineers and scientists understand and predict the behavior of fluid flow in different situations.