(Solved):   (15 pts) One method of determining the velocity of flow through a pipe is to collect water ...

 

(15 pts) One method of determining the velocity of flow through a pipe is to collect water from the outlet of the pipe in a container. The mass flow rate \( \dot{m} \) is then determined by the total mass \( m \) of the fluid collected divided by the time interval of the measurement. \[ \dot{m}=\frac{\Delta m}{\Delta t} \] Assuming the pipe and flow combination we're interested in is fairly small we can use a graduated beaker to collect the fluid. After some experimentation we've determined that the scale for measuring the mass of the beaker has an uncertainty of \( +/-2 \mathrm{~g} \). The analog stopwatch used for measuring the time has an advertised accuracy of \( +/-0.15 \) sec. a. If the empty beaker has a measured mass of \( 25 \mathrm{~g} \), and the full beaker has a measured mass of \( 250 \mathrm{~g} \), what is the uncertainty in the measured fluid mass? b. If the time interval is \( 20 \mathrm{sec} \), what is the uncertainty in the mass flow rate? c. Which uncertainty has the greatest effect on the final uncertainty?