Fluid Dynamics and a Fertilizer Truck

[Severian596]

The other day I was driving down the highway behind a Fertilizer Truck. It had a huge plastic reservoir of liquid fertilizer on the back, essentially a large cylinder lying on its side. The reservoir was not full and it was partially translucent, so I could see the fertilizer sloshing around in the cylinder. I reasoned (as anyone would I think) that to increase the stability of the truck--especially in the turns--you could simply fill the cylinder to the brim. That way you don't have all the sloshing.

So I started thinking to myself, what dictates the "stability" of fluid? I thought it must relate directly to the surface area of the fluid. More surface area means more sloshing. But then again, the shape of the container might also affect the sloshing, because I think that a martini glass sloshes like crazy compared to an inverted cone-shaped container with equal surface area...doesn't it? I'm looking at a coworker's coffee mug right now, and its sides have a negative slope rather than a positive slope (looking at a cross-section of the mug in the positive x-axis direction...I know there's an easier way to say that but oh well). So the mug is well-designed for less sloshing! Right?

But why? Can anyone point me in the direction for more information on fluid dynamics, and/or summarize what's most important for fluid stability/instability, container design or surface area, or something else? I'm perusing over the web page that follows this paragraph as I type, but I thought this may be a topic that someone out there would find fun. I think it's a neat topic because we intuitively know some things about fluids, even if we don't understand the equations or causal reasons behind it. I don't, and I'm curious.

http://www.allstar.fiu.edu/aero/Flow2.htm

Hey thanks guys & gals!

 

[Severian596]

I'm thinking that we could simulate the entire truck experiment by replacing the fluid with a pendulum whose mass equals the mass of the fertilizer. The only question then is how long should the pendulum's string be? Assuming I'm onto something the only question is what dictates how long we need to make the string to properly emulate a big cylinder filled with mass m of fertilizer?

 

[FredGarvin]

I think Severian, that you have eluded to one of the aspects...the distance the center of gravity of the fluid is allowed to displace. The greater that distance, the more "unstable" it can become. This is why baffles are usually placed in tanks to prevent this kind of agitation. They reduce the large mass of fluid into individual smaller segments and reduce the distance those fluid packets can move.

The other property that directly relates to stability would be the viscosity. A higher viscosity would mean a higher resistance to the displacement as well.

I am sure others will bring more aspects to the table. These were just off the top of my head.

 

[Severian596]

Ah! That makes complete sense, Fred, thanks so much! Bing! Perfect.

The length of the pendulum essentially dictates the motion of the center of gravity. But thinking about the center of mass for the fluid makes the pendulum analogy unnecessary. Discussing a point's motion is simple enough.

At that point, we have the initial center of mass, S, and the mass of the fluid, m, and viscosity v. We can find momentum transfer based on the velocity of S times m. Viscosity v affects the velocity.

Thanks so much! Perfect.