Question

Question 2 A process instrument reading 2 (volts) is thought to be related to a process stream flow rate V (L/s) and pressure P (kPa) by the expression: Z = avbps Using the three data points shown in the table above, calculate the constants a, b and cand indicate their units. In this particular case there is no regression to be performed, but only 3 equations in 3 unknowns to solve. 1 1.02 V (L/S P (kPa) z (volts) 1.20 11.2 2.58 1.75 10.2 3.72 91 3.50 Question 3 Before an experiment two instruments, a thermocouple and a flow meter, are tested in a lab. The thermocouple measures temperature in °C while the flow meter measures flow rate in liters per second. Five identical measurements of a solid at constant temperature result in the following thermocouple readings: | T (°C) - Thermocouple 124.4 128.1 126.6 122.8 130.5 Similarly, five identical measurements of the same flow rate result in the following flow meter readings: V (L/s) - Flow meter 0.082 0.079 0.078 0.08 0.075 (a) For each instrument, calculate the sample mean, range, and the standard deviation (b) is the thermocouple a more precise instrument than the flow meter? Explain your answer.

Answer 1

Solution given Z= aub pc Here z in volts ů in us p an kea Three data -points are Ho Point 6 given z = 2.58 volts, v= 1.20 Ls P = 11.2 kPa So when we put this in equation 0.58 = a (1.2006 (11.2) ③ we get taling Jog natural itural both sides we both side we get get In (2.50) = in [ac1.2016 (1125) Now we apply properties of dog o dog (mn) = logn + loga o dogm" - nlogm termos 0.947 = ora) + ben(1-20) + C In (11-2) os - 10.947 = in (a) + 0.1823 b + 2.4159 C we can put A = ln(a) 0.947 = A + 0.1823 b t 2.virar

Now Point ② 2= 3.72 volts = 175 45 | p-to-2 keer i from equation 0 after taking dog naturat In (z) - In (a) + b enſü) + con(P) In ( 3.72) = in (a) + b In (1.75) + C 47(10.2) .. we put A= un(a) >1.313 = A + 0.559 6 + 2-32207 Now Point ® 2= 3.50 Volts | v= 1.02 4s, P = 9.1 kPa - from equation' 8 dn (3:50) = ln(0) + ben (102) + c ln(9.1) 5) 1.1.2527 = In(a) + 0.0198 6 + 2.208267 1 - 2s24 - A + 0.0198 b + 2.2of2c-G) Now so .. we have 3 equations and 3 unknown, after soving above three equation we get - A - 5.367 = Inla) a = 214-21) I values of constants > b= 0.5060 a, b, c ca - 1.867