Your boss asks you to calculate the flow through a natural$-$gas pipeline where the gas is

at a constant $140\backslash$deg F$.$ Since it is $26$ in$.$ in diameter, it is impossible to run the gas through any kind

of meter or measuring device. you decide to add $100$ lb CO$2$ per minute to the gas through a

small $1/2$ in$.$ piece of pipe, collect samples of the gas downstream, and analyze them for CO$2.$

Several consecutive samples after $1$ hr $($so read the time column as $1$ hr $0$ min, $1$ hr $10$ min, etc$)$

are:

time $\%$CO$2$

$0$ min $2\mathrm{.}0$

$10$ min $2\mathrm{.}2$

$20$ min $1\mathrm{.}9$

$30$ min $2\mathrm{.}1$

$40$ min $2\mathrm{.}0$

a$)$ Calculate the flow of gas in pounds per minute at the point of injection.

b$)$ Unfortunately for you, the gas upstream of the point of injection of CO$2$ already contained

$1\mathrm{.}0$ percent CO$2.$ How much was your original flow estimate in error $($in percent$)?$