Consider use of the hot-film sensor described in Problem 7.60 to determine the velocity of water entering the cooling system of an electric power plant from an adjoining lake. The sensor is mounted within an intake pipe, and its controls are set to maintain an average hot- film temperature that is 5°C larger than the fluid temperature (T_s.hf – T_∞ = 5°C).

(a) If an independent measurement of the water temperature yields a value of Tx = 17°C, use the Churchill-Bernstein correlation to estimate the velocity of the water under conditions for which the power input to the sensor maintains a heat flux of q"_hf = 4 x 10⁴ W/m² from the film to the water.

(b) If the sensor is exposed to the water for an extended period, its surface will be fouled by an accumulation of deposits from the water. Consider conditions for which the deposits form a 0.1-mm- thick shell around the sensor and have a thermal conductivity of kd = 2 W/m ∙ K. For T_∞ = 17°C and the flow velocity determined in part (a), what heat flux must be supplied to the sensor to maintain its temperature at T_s.hf = 22°C? What is the corresponding error in the velocity measurement? Note: conduction across the deposit may be approximated as that across a plane wall.