The temperature in a process unit is controlled by passing cooling water at a measured rate through a jacket that encloses the unit The exact relationship between the unit temperature T(C) and the water flow rate (L s) is extremely complex, and it is desired to derive a simple empirical formula to approximate this relationship over a limited range of flow rates and temperatures Data are taken for T versus Plots of T versus on rectangular and semilog coordinates are distinctly curved (ruling out T a b and T ae b as possible empirical functions), but a log plot appears as follows A line drawn through the data goes through the points ( 1 25 L s, T 1 210C) and ( 2 40 L s, T 2 120C) (a) What is the empirical relationship between and T (b) Using your derived equation, estimate the cooling water flow rates needed to maintain the process unit temperature at 85C, 175C, and 290C (c) In which of the three estimates in Part (b) would you have the most confidence and in which would you have the least confidence Explain your reasoning PROCESS Cooling water UNIT ROTAMETER p(liters s) T(C) Jacket

Question: The temperature in a process unit is controlled by passing cooling water at a measured rate through a jacket that encloses the unit. The exact

The temperature in a process unit is controlled by passing cooling water at a measured rate through a jacket that encloses the unit.

PROCESS Cooling water UNIT ROTAMETER p(liters/s) T(°C) Jacket

The exact relationship between the unit temperature T(°C) and the water flow rate ϕ (L/s) is extremely complex, and it is desired to derive a simple empirical formula to approximate this relationship over a limited range of flow rates and temperatures. Data are taken for T versus ϕ. Plots of T versus ϕ on rectangular and semilog coordinates are distinctly curved (ruling out T = aϕ + b and T = ae^bϕ as possible empirical functions), but a log plot appears as follows:

A line drawn through the data goes through the points (ϕ₁ = 25 L/s, T₁ = 210°C) and (ϕ₂ = 40 L/s, T₂ = 120°C).

(a) What is the empirical relationship between ϕ and T?

(b) Using your derived equation, estimate the cooling water flow rates needed to maintain the process unit temperature at 85°C, 175°C, and 290°C.

(c) In which of the three estimates in Part (b) would you have the most confidence and in which would you have the least confidence? Explain your reasoning.

PROCESS Cooling water UNIT ROTAMETER p(liters/s) T(C) Jacket

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