Calculating the nonlinear speed of Erosion

[DreamHarvest]

Hi there,

I'm trying to find a calculation to work out the speed of erosion and required rotation of water to cause erosion on a selection of 10 rocks.

This is theoretical rather than an actual conducted experiment.

Each rock has a density of 100 to 1000, ie rock one is 100, rock 2 is 200 etc.

the amount of water in the glass is fixed.

one of the rocks is placed within the glass and the water is rotated. the minimum speed that the water can be stirred to cause erosion on rock 1 is 150 on a scale of 0 - 999 when at full structural health. if the water is rotated above 200 the glass begins to crack, but as the rock begins to erode the speed that the water must be stirred increases, ie at a structural health of 75 the speed must increase to 200 and the glass damage threshold increase to 250.

What equation would I use to work this out for every rock so that the scale never goes above 999 and so that as each rock is eroded the speed of erosion must increase.

 

[berkeman]

Hi there,

I'm trying to find a calculation to work out the speed of erosion and required rotation of water to cause erosion on a selection of 10 rocks.

This is theoretical rather than an actual conducted experiment.

Each rock has a density of 100 to 1000, ie rock one is 100, rock 2 is 200 etc.

the amount of water in the glass is fixed.

one of the rocks is placed within the glass and the water is rotated. the minimum speed that the water can be stirred to cause erosion on rock 1 is 150 on a scale of 0 - 999 when at full structural health. if the water is rotated above 200 the glass begins to crack, but as the rock begins to erode the speed that the water must be stirred increases, ie at a structural health of 75 the speed must increase to 200 and the glass damage threshold increase to 250.

What equation would I use to work this out for every rock so that the scale never goes above 999 and so that as each rock is eroded the speed of erosion must increase.

Welcome to the PF.

Please include units in your post. In science, units are very important. It would also help a lot if you could include a drawing or picture of your envisioned experimental setup.

 

[DreamHarvest]

In this case the type of unit is irrelevant as its for a game where the rocks are assigned a health value of 100 to 1000.

The speed of rotation can be a value of 0 - 999 as this is set within the variable.

What I want to do is have it so as when the health of the rock diminishes the speed of rotation must go up within a threshold. If you rotate to slow no erosion takes place, if you rotate to fast it damages the glass until it breaks. However I don't want the damage threshold and the speed of rotation threshold to increase in a linear fashion. Is there an equation that could be used for this?

Thanks for the help.

 

[mfb]

For a game, you can use any equation you like. You can even write down a table with arbitrary values for whatever relation you want to fix.

Bonus points if you get some player to reverse-engineer the game, and search for an underlying formula for the table.

 

[LudusRex]

I would suggest using the Hjulstrom curve equation to calculate the nonlinear speed of erosion in this scenario. This equation takes into account the sediment size, water velocity, and shear stress to determine the minimum velocity required for erosion to occur.

However, since this experiment is theoretical and not based on actual data, it may be difficult to accurately calculate the speed of erosion for each individual rock. The Hjulstrom curve is typically used for larger scale erosion studies and may not be suitable for this specific scenario.

Instead, I would recommend conducting controlled experiments with varying water velocities and rock densities to gather data and create a more accurate model for erosion in this specific situation. This will provide more reliable results and allow for a more precise equation to be developed for calculating the speed of erosion on each rock.