Consider the case of air exhausted by a very small point source (Figure 3.36). We can assume a sphere with a surface area of A m2 at any radius r from the point of extract.
Let v = velocity m/s at radius r, assumed to be equal over the sphere.
= velocity measured on centre line (m/s) = distance from open end (m)
= area of open ended duct (m2)
10r + A
The actual extract is shown in Figure 3.37.
Figure 3.37 Actual extract from open ended duct
Laboratory and site tests have confirmed the general correctness of the equation.
To take the example of a circular exhaust opening having the following dimensions
Face area = 0.093 m2
Velocity = 0.5 m/s
At distance = 0.61 m
Then Q = 0.5(10 x0.612 + 0.093) = 1.907 m3/s
If the same velocity was required at 1.22 m then Q = 0.5(10 x 1,222 + 0.093) = 7.489
It will be noted that Q is proportional to slightly less than the distance squared.
Note also that the velocity v varies directly as Q irrespective of the face velocity into the opening.
These points emphasise that when extracting dust, the hood must be as close as possible to the source of production and that to increase the velocity at a given distance must involve an increase in Q. The limitation on Q is of course due to economic factors. If velocity is insufficient to extract the dust effectively, it might be thought that a reduction in the size of the opening for a given volumetric flowrate would increase its “pulling power”, but this is not so.
Figure 3.42 Positions of tappings for flow measurements
Ce also varies to some extent with velocity, see Figure 3.43
Figure 3.38 Flattening of velocity contours at hood face centre
Figure 3.39 Circular exhaust openings (Dala Valle’s tests on 100 mm to 400 diameter)
Distance from opening In diameter
The centreline velocity is a useful guide in practice. In normally shaped hoods as used in dust collecting, the velocity contours are flat in the regions opposite the main portion of the hood (see Figure 3.38).
The graphical representation of Dalla Valle’s tests is shown in Figure 3.39.
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