A dude is running with the constant speed of 5 meters per second. He is holding a funnel with the smaller side facing his face. The air will enter the larger side of the funnel. Find the exit velocity of air out of smaller side of the funnel. Assume the diameter of smaller side of the funnel 10 cm and the bigger side 20 cm. Try to send your solutions to me by next week otherwise I will post the solution next week this time :-)
Question proposed by my Fluid Mechanics II Dr. Raad.
Solution:
Based on the Euler equation total energy of the streamlines will be kept constant and the sum of all of those including the potential energy, kinetic energy and Pressure term will not be changing. Knowing that Potential energy will not change for the stream line and the Pressure at both ends will be atmospheric and equal, the only term that leaves is the kinetic energy and we arrive at
V1=V2=5 m/sec
The common mistake is that many engineers write the continuity of mass at both ends of the funnel and arrive at V1xA1=V2xA2
Knowing the V1=?, A1=1/4xA2 , V2=5m/sec , A2
So:
V1= 20 m/sec and that is wrong because the continuity will be only conserved only inside any cross section of the funnel. What happens at the large side of the funnel is that, at converging wall near the internal wall, the flow will be eddy shape and do not enter the funnel.
