Problem Diagram

Rotameter

The flow rate of the faucet is given by Q = u_mA_m

The float of the rotameter is 10 mm from its base (i.e., y =10 mm). Hence, the area of the annular space is

The mean velocity of the water passing through the annular space is given by

The volume and frontal area of the ball are calculated to be
       
     

Now, the mean velocity u_m can be calculated as

The volume flow rate is thus given by

     Q = (1.05 m/s)(15.9 mm²) = 16.7 (10^-6) m³/s

The total volume of the water wasted in a 30-day period is
      V_total = (16.7)(10^-6)(30)(24)(60)(60) = 43.3 m³

The corresponding cost is
   = (43.3 m³) ($1.75/1000 gal) (1 gal/0.003785 m³)
   = $20.02