# Home/shop vacuum system sizing/design question

1. Aug 13, 2012

### perfexion

I'm working on a home/shop use vacuum pick up system. I need to suck up some spherical objects about 3" in diameter which weigh about 2 oz.

First thing I want to do is size the blower for this project. Ignoring the losses of the hose I can calculate the velocity of the air at the inlet of the vacuum knowing that inlet diameter and the volumetric flow rate of the blower. Now, the objects at the inlet are comparable is size to the inlet area, so I figure I'm better off using just plane 1/2*rho*V^2*Cd*A for the estimate of the force on the object at the inlet rather than sediment entrainment equations or something.

For a 120CFM fan and 4" diameter inlet (letting rho=1.2 kg/m^3 and Cd = 0.45) I get something like 6.9 m/s of flow velocity and 0.06 N of pickup force at the inlet.

I have a few concerns with this admittedly crude calculation:
The first is that the velocity field around this spherical object is heavily affected by the fact that it's sitting on the ground. I'd expect to see a large reduction in the pickup force due to this fact.

The second thing is that once the object is actually inside the tube the effective cross sectional area decreases, the velocity around the object should speed up (small cross sectional area), the load on the blower goes up to the volumetric flow rate goes down, and because of all of this again I'd expect that prediction to be just bad. I would guess though that I get more force than predicted on the object inside my tube. I know it won't be as high as the blower sealed pressure times the cross sectional area of the tube, but I'd guess it's something like 1/8 to 1/3 of this.

The next issue is that I want this vacuum system to move objects which are not immediately adjacent to the inlet towards the inlet.

If I let the inlet be 1 inlet diameter above the floor (with the inlet area parallel to the floor) I can imagine a cylindrical volume of influence around the inlet. The diameter of this volume could be 2 inlet diameters, the top would be the plane of the inlet area, and the bottom would be the ground. I could calculate the area of the surface of this cylinder which will see inflow (the side, and the annular region of the top which is around the vacuum inlet).

Using this area I could estimate the average inflow velocity at this surface. For a 120CFM blower and a 4" inlet diameter I get something like 0.64 m/s. Using this velocity the force on a 3" spherical object would be something on the order of 1/1000 of a N. Not enough to get an irregular sphere weighing 2oz moving.

My question is do you think these calculations are on the right track for sizing the blower for this vacuum? Is there a better way to go about this?

For those who are wondering I also plan on putting a canister volume and filter further down the line (but before the blower) where these objects can accumulate. Really this thing is no different functionally than a shop vac from home depot or something, I just need to size the flow rate and tube to my particular needs.