Question

The drag F on a sphere of volume V moving slowly with speed u in a fluid of viscosity η is l:iven by 3 wiie.reSXİ) s ia nurricTICial «x»nsiant.. Firnd i Inc, appr'«ixilii iai? (:lliintyc, e57 n P produced by small changes δν, δη and δυ in the volume, viscosity and speed. [5 marks]

Answer 1

If a function is

z = cx^ay^b then change in z is given by

Az Ar

Hence, F= TV^1/3_{$\eta \nu$}

_{$\Delta F = F\sqrt{(\frac{\Delta T}{T})^2 + (\frac{\Delta V}{3V})^2 +(\frac{\Delta \eta }{\eta })^2 + (\frac{\Delta \nu }{\nu })^2}$}