The exact relationship between the unit temperature TC) and the water flow rate
ID: 1023058 • Letter: T
Question
The exact relationship between the unit temperature TC) and the water flow rate extremely complex, and it is desired to derive a simple empirical formula to approximate relationship over a limited range of flow rates and temperatures. Data are taken for T versus of T versus on rectangular and semilog coordinates are distinctly curved (ruling out T = a + b The exact relationship between the unit temperature 70°C) and the water flow rate (LS) is this . Plots and T- ae as possible empirical functions), but a log plot appears as follows: 300 TCC) 200 - 100 10 100 (US) A line drawn through the data goes through the points (o, = 25 LS, T, = 21000) and (2 = 40L/s, T2 = 120°C). (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 85, 175, and 290°C. (e) 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. 2.43 A chomiaExplanation / Answer
From the data poinr given. y= mTn, where y is the flow rate and T is the temperature
Ln y= lnm+ n ln T
Where y is the flow rate and T is the temperature
From the data points given
Ln 25= lnm + nln210 (1), 3.2= lnm+ n 5.35 (1)
Ln 40 = lnm+ nln120 (2), 3.68= lnm+ n*4.78 (2)
Eq.2- Eq.1 gives 0.46= n*(-0.570), therefore, n= -0.807
From Eq.1 3.22= lnm-0.807*5.34 , m= 1862
The equation is y= 1862*(T)-0.807
at 85 deg.c. y= 1862*(85)-0.807 =51.63 L L/s
at 175 deg.c , y= 1862*(175)-0.807= 28.83 L/s
at 290deg.c, y= 1862*(290)-0.807 =19.17 L/s
the temperature 175 deg.c is in between the temperatures 120 deg.c and 210 deg.. Hence it is expected to have more confidence while 290 deg.c is far away from the temperature value compared to 85 to 120), it is expected to have least confidence.
2. The requires plot is lnx= a/T+ b
where T is in K and b is constant
The plot of lnx vs 1/T is drawn ans shown below
from the plot a= -2494 ( T units) b= 5.623 dimensionless
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