Hi guys... I'm working generally on modelling an upward current classifier and specifically sizing a pump for it.

I wanted to share my calculations in case anyone can see something I'm doing wrong.

Generally I've been modelling the pebble or whatever substance as a sphere with the general downward force being

**(weight - buoyancy)** and the general upward force being

**drag**.

My weight and buoyancy formulae look like

**(density * volume * force_of_gravity)**.

My drag formula looks like

**(drag_coefficient * face_area * ((fluid_density * (fluid_velocity^2)) / 2))**.

To figure out my pump size (or at least the pump size required to keep a particle of the given properties stationary in the fluid), I find the general downward force, make it positive, then plug that in as the answer to the drag formula and solve for the

**fluid_velocity**. I used a drag coefficient of 0.7 and calculated the area from the volume of the pebble roughly as

**(area ^ 2/3)**.

I then convert the velocity to flow rate for a 15cm diameter pipe using the formula

**((velocity * (PI * diameter^2)) / 4)** and convert from cm^3/s to GPH using a 1.052 conversion factor.

The data I got from all this jalopy was as follow:

**Pebble Size (cm^3)** | **GPH for Gold (density 19.3)** | **GPH for Lead (density 11.0)** | **GPH for Copper (density 8.0)** | **GPH for Magnetite (density 5.0)** |

0.216 (1/4") | 10603.26 | 7838.15 | 6557.87 | 4957.28 |

0.108 (3/16") | 5950.88 | 4399.02 | 3680.48 | 2782.18 |

0.032 (1/8") | 2159.5 | 1596.35 | 1335.6 | 1009.62 |

This kinda makes sense to me but thought some physics-inclined folks here might have some more input

Cheers!

Steven