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.

Questions

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

Approach

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/m^{3}.

Assume the drag coefficient is 0.5 and the density of the water is
1000 kg/m^{3}.

The area of the tapered tube is
A = (π/4) (6 + 0.15y) mm^{2}

The cost of the water is $1.75/1000 gals.

Assume Bob was gone for 30 days.

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