↑(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)

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 )