Problem Graphic

Upon returning from a one-month trip to Europe, Bob shockingly discovers he left the water running from the tap the whole time that he was gone. Using a rotameter, he would like to find out the water flow rate, determine how much water is wasted, and what is the cost associated with it. The float of the rotameter is 10 mm from its base.

Determine the water flow rate based on the position of the float. Find the total volume and cost of the water wasted.

• The float of the rotameter is a 316 stainless steel ball with a radius of 3 mm and the density of the ball is 8,040 kg/m³.
• Assume the drag coefficient is 0.5 and the density of the water is 1000 kg/m³.
• The area of the tapered tube is
  A = (π/4) (6 + 0.15y) mm²
• The cost of the water is $1.75/1000 gals.
• Assume Bob was gone for 30 days.