2. The fluid velocity in a square conduit has been given as 2B x y dA Find the volumetric flow rate Q 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: (for the coordinate system shown with origin on the centerline) V ave =  ν  = Q/A or V ave = 4/9 ν max ↑( Valid for other tubes ) ↑( Valid for square tubes only )

3. VOLUMETRIC FLOW RATE Velocity profile given: 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 1 Rr The velocity is such that fluid is carried across this surface. ( Element of area in polar coordinate is r d  dr ) r z R