1. ↑(Valid for other tubes) ↑(Valid for square tubes only)
The fluid velocity in a square conduit has been given as
(for the coordinate system shown with origin on the centerline) x
Find the volumetric flow rate Q 2B dA y 2B 1
What is the volumetric flowrate across element dA? ( v . n ) dA
When we talk about volumetric flow, we must integrate:
Integrate with respect to x:
Vave = ν = Q/A or Vave = 4/9 νmax
↑(Valid for other tubes) ↑(Valid for square tubes only)

2. VOLUMETRIC FLOW RATE Velocity profile given: R r z 1
Use cylindrical coordinates: ( r, , z )
We want to find the columetric flowrate in the tube and the average velocity.
Let’s look at a cross-section of the conduit. 1
The velocity is such that fluid is carried across this surface. r R
( Element of area in polar coordinate is r d dr )