A temperature sensor mass flow meter consists of measuring the

temperature difference $($Delta$($T$))$ introduced into the fluid by a heating element

electrical power $($q$=10$W$)$: the heat capacity of the fluid is known

$($C$=103$m$2$s$-2$K$-1),$ the mass flow rate is then deduced m$=$Delta$($m$)/$Delta$($T$)$

which in the ideal case would be provided by relation: m$*$C$*$Delta$($T$)=$q

The measurement of temperatures upstream and downstream of heating is done by two identical T$1$ and T$2$ sensors$.$ A comparative analysis between two possible sensors $($see table$)$ must be carried out. A minimum flow corresponds to a difference of $25$C and maximum temperature sensor accuracy.

LM$335$:

sensitivity$=10$mV$/$K

Measurement range$=-50.\mathrm{.}150$C

Precision$=3\mathrm{.}5$K

Response time$=1$s

Thermocouple E:

sensitivity$=75$microV$/$C

Measurement range$=-200..\mathrm{.}1000$c

Precision$=0\mathrm{.}5\%$

Response time$=10$ms

For each of the sensors$,$ answer the following items:

a$)$ Sketch the setup and signal conditioning to acquire the measurement with

a $10-$bit A$/$D converter and $0$ to $2\mathrm{.}5$ Vdc input.

b$)$ Establish the relationship between temperature input and output, for each of the

sensors$.$ How accurate is this measurement?

c$)$ What is the relationship between flow rate and digital reading. What is the accuracy of the measurement flow rate?

d$)$ Compare the two solutions.