A particular steam boiler must be filled with 7.57 m³ (2000 US gallons) of water before being used. It is connected to the water supply by copper tubing 15 m long that has a diameter of 2.60 cm. The fill point (tube outlet) is 3 m above the inlet and the supply pressure is such that | ΔP| = 4.0 × 10⁵ Pa.

(a) How long would the filling take if water at 20 °C (Table 1.2) were used?

(b) An operator who knows that hot liquids flow more freely than cold ones decides to speed the filling by using water at 52 °C, for which μ = 5.29 × 10⁻⁴ Pa · s and ρ = 987 kg m⁻³. If the supply pressure is unchanged, how much time will be saved?

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Table 1.2 Viscosity, density, and kinematic viscosity of Newtonian liquids T(°C) (10-3 Pa.s) p(10³ kg m-³) v(10-6 m² s ¹) Liquid Water Benzene 20 20 1.002 0.652 0.9982 0.8765 1.004 0.744