Fluid MechanicsHard
Question
A spherical body of radius $r$ and density $\sigma$ falls freely through a viscous liquid having density $\rho$ and viscosity $\eta$ and attains a terminal velocity $v_{0}$. Estimated maximum error in the quantity $\eta$ is : (Ignore errors associated with $\sigma,\rho$ and g , gravitational acceleration)
Options
A.$2\frac{\Delta r}{r} - \frac{\Delta v_{0}}{v_{0}}$
B.$\frac{2\Delta r}{r} + \frac{\Delta v_{0}}{v_{0}}$
C.$2\left\lbrack \frac{\Delta r}{r} + \frac{\Delta v_{0}}{v_{0}} \right\rbrack$
D.$2\left\lbrack \frac{\Delta r}{r} - \frac{\Delta v_{0}}{v_{0}} \right\rbrack$
Solution
$v_{0} = \frac{2}{9}\frac{r^{2}\text{ }g}{n}\left( \rho_{B} - \rho_{L} \right)$
$${n = \frac{2}{9}\frac{r^{2}\text{ }g}{v_{0}}\left( \rho_{B} - \rho_{L} \right) }{\frac{\Delta n}{n} = \frac{2\Delta r}{r} + \frac{\Delta v_{0}}{v_{0}}}$$
Create a free account to view solution
View Solution FreeMore Fluid Mechanics Questions
Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vert...Paint Gun depends upon :...The spring balance A read 2 kg. with a block m suspended from it. A balance B reads 5 kg. when a beaker with liquid is p...Surface tension of a liquid is 5 N/m. If its thin film is made in a ring of area 0.02 m2, then its surface energy will b...An L shaped glass tube is kept inside a bus that is moving with constant acceleration. During the motion, the level of t...