# Airflow velocity and volume loss due to friction

I have a vacuum that the manufacturer claims capable of moving 20,000 cfm of air. In my application we often connect 150 feet of 6 inch diameter, smooth bore, flexible tubing to the vacuum. I know that friction loss from the tubing will reduce the airflow (and thus the velocity) but I have been unable to measure or calculate how much is lost and how much remains. I have tried measuring the air velocity with both an anemometer and a manometer, but the range on both of my tools is too small to provide an accurate result. I am certain there must be a way to calculate this but multiple google searches have not provided a formula that I can use.

## 1 Answer

The problem is a standard one in fluid flow, and mostly discussed in books on fluid mechanics. Say the volumetric flow rate is Q m^3/s(cfm of air in your case). The pipe length is L, diameter D, density ρ,and kinematic viscosity ν for the flowing fluid- all in SI units.

First calculate the Reynolds number; Re=vD/ν, where v is mean velocity over the diameter D. Then calculate the roughness value which is the actual roughness of the pipe divided by diameter. In the present case it is a smooth pipe and this specifies the curve for friction versus Re in the Moodi Chart. Now use this chart to find the friction factor.. that is use the smooth curve for the given Re and read the friction factor f in the vertical axis.Use other lines in the chart for turbulent flows.

The pressure loss formula depends on whether the Re is in the laminar or turbulent region. For laminar flow(Re<2500 as calculated above),f=64/Re and it is non-dimensional. The pressure loss in SI units is Δp=(fL/D) .5 ρ v^2 in Pascal. This formula is correct for turbulent flows too, but f should then be calculated from Moody or any other formula.

Note that Δp is signed and effects positive and negative pressures, but the reduction is obtained using the absolute values regardless of sign- since it is lost mechanical energy converted to heat.That is your available pressure positive or negative is reduced towards zero as a result.

Note also that the vacuum machine specification should give head(pressure) as well as flow rate. These are taken from the characteristics of the machine that can vary greatly with design. The reduction in pressure is measured from this head/pressure and the final (absolute value) result should remain above zero. If not, the required flow can't be realized and will be reduced. Note that the power of the machine is P= ρQΔp. So if you know the power, you can find out the head.Actual power delivered is slightly less(around 10%)than electric power due to efficiency and losses in the machine itself.This should be given too in the specs.