Volume flow rate calculation
 

Hi,

I have questions, hopefully someone could help me to explain this.
In the 3D cylindrical tube, the volume flow rate (VFR) at the inlet is 0.0000549 m3/s.

Case 1: The result taken at the plane named it as Plane 6 (Figure 1)
Case 2: The plane was subdivided into several planes using “bounded planes” at Plane 6 (Figure 2).

Then the VFRs at Plane 6 and subplanes were checked.
The results shown in Figure 3.

Summary of the results:
Summary:
a) Case 1: The summation of the volume flow rate is positive at this region (highlighted in yellow)
b) Case 2: Some subplanes show negative volume flow rate and the summation is less than Case 1 (highlighted in grey)
c) When the negative VFR in case 2 has been changed to all +ve, the summation is comparable with Case 1 (highlighted in blue)
d) By VFR definition, the volume flow rate through a surface is computed by summing the dot product of the facet area vector and the facet velocity vector. The dot product of area and average x, y and z velocity shows agreement with the VFR of Plane 6 (Case 1) and VFR of +ve VFR at subplanes (Highlighted in red)

My main curiosity is:
1) Why there is negative VFR for the subplanes while the manual calculated dot product of average area with x, y and z directions showed all positive results?

Thank u so much.

Naima