Linda wants to drain the water out of an open top 55 gallon rain barrel. She has the choice of using either a 2-inch diameter hose, two 1-inch diameter hoses or 4 1/2 inch diameter hoses.
Which hose size will drain the barrel faster? Will they drain equally as fast?

• Foe the constant velocity, flow rate scales with r² (the area).
  1st case: 1 Pipe with D=2" or r=1", so Flow is proportional to 1² = 1 units
  2nd case: 2 Pipe with D=1" or r=1/2", so Flow is proportional to (1/2)²+(1/2)² = 1/2 units
  3rd case: 1 Pipe with D=9/2" or r=9/4", so Flow is proportional to (9/4)² = 81/16 units.
  So, ratio of draining under above 3 cases respectively = 1 : 1/2 : 81/16 = 16 : 8 : 81
  Therefore, with faster rate, 4½ inch diameter hose will drain the barrel faster.
• 5 years agoHelpfull: Yes(0) No(0)