1. Group 2 Volumetric Flowrate and Average Velocity Sage Ross Randy Goll Lisa Gourley Marci Wyatt Jennifer Oberlag April 21, 2001

2. Problem Statement Fluid flows through a conduit with a quarter circle cross-section. The profile of the velocity in the z-direction can be approximated by: With the coordinate system as shown and where v A is a constant equal to 20 cm/s and R=30 cm. Find the Volumetric flowrate Q and the average velocity.

3. The circular shape of the conduit suggests that we use cylindrical coordinates to solve the problem. v A =20 cm/s R=30 cm 3 dimensional view of conduit Quarter circle cross section ])/4(1[ ])/(1[ )/( 22  RrRrvv Az

4. We need to use the following equations to solve the problem:

5. Solution Volumetric flowrate across element dA: To find the volumetric flow we must integrate: Such that:and The limits for integration can be found from geometry. Substitute the given value for v z : Integrate with respect to 

6. Evaluate the integral at the limits: Simplify and integrate with respect to r: Simplify and evaluate:

7. The average velocity is found by diving volumetric flowrate by area. vzvz V ave represents the average of all of the velocities over the velocity profile.