Water is flowing out of a tube at a near constant volumetric flowrate, V .If a g

Question

Water is flowing out of a tube at a near constant volumetric flowrate, V .If a graduated cylinder is used to collect a certain volume, v , of the water, and a timer is used to measure the time, t, required to collect the volume of water, the volumetric flowrate, V , can be indirectly measured in terms of the direct measurements of volume, V , and time, t, where V = v/ t . Show that the relative uncertainty in volumetric flowrate, (deltaV/v), is equal to the sum of the relative uncertainties in volume, (deltav/v), and time, (deltat/t).

Explanation / Answer

take log base e both side of eqn...

=> lnV = lnv - lnt => differentiate both sides...

we get deltaV/V = deltav/v + deltat/t .... here + sign is there instead of - as uncertainities are always added not subtracted...

hence the answer

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