DavidMartin wrote:I have to work out the height of sludge at 20% (cake) falling from a conveyor. Assuming it will fall in a cone like fashion and a 12m base diameter, how do i work this out?
I'm not sure what the quoted 20% is, percentage of slope or percent of cake? Anyway, unless it's slope %, it's not needed to calculate the height.
The angle of repose (angle of slope from horizontal) and the height of the cone will be determined largely by the amount of liquid in the sludge, similar to a slump test when dealing with concrete. The more water present in the mix, the flatter the angle of repose and the shorter the height of the pile.
If the cake has been dewatered and pressed, the angle of repose could be over 30Âº.
To determine what the the maximum height of the pile would be, you need to know the angle of repose of the material. Unfortunately, the previous poster is correct so you'll need a sample pile to find it (which could be the beginning of the pile you're interested in determining height).
Height = Tangent of angle * radius of base
Example: If Theta = 30Âº
Tan 30Âº * 6 m
0.57735 * 6 m = Height of pile 3.46 m