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  • An experiment is conducted to determine the coefficient of viscosity () of a liquid using the measurement of terminal

An experiment is conducted to determine the coefficient of viscosity (\eta) of a liquid using the measurement of terminal velocity. A spherical body of radius r = 0.02 m and density \rho = 800 kg/m3 is allowed to fall freely in the liquid. The terminal velocity of the sphere is observed to be vt = 0.1 m/s. Given that the acceleration due to gravity is g = 9.81 m/s2, calculate the coefficient of viscosity of the liquid.

Option: 1

1.08 * 10-2 Pa.s


Option: 2

2.08 * 10-3 Pa.s


Option: 3

1.08 * 10-4 Pa.s


Option: 4

1.08 * 10-3 Pa.s


Answers (1)

best_answer

Given values:

Radius of the spherical body (r) = 0.02 m
Density of the spherical body (\rho) = 800 kg/m3
Terminal velocity (vt) = 0.1 m/s
Acceleration due to gravity (g) = 9.81 m/s2

The terminal velocity (vt) of a spherical body falling through a liquid is given by the formula:

                    v_{t} = \frac{2}{9} \frac{r^{2} (\rho - \rho_{liquid}) g}{\eta}

where \rho_{liquid} is the density of the liquid.

Solve for the coefficient of viscosity (\eta):

                    \eta = \frac{2}{9} \frac{r^{2} (\rho - \rho_{liquid}) g}{v_{t}}

Step 1: Calculate the density of the liquid (\rho_{liquid}):

                    \rho_{liquid} = \rho - \frac{4}{3} \pi r^{3}

Step 2: Substitute the values and calculate the coefficient of viscosity (\eta):

                    \eta = \frac{2}{9} \frac{(0.02 m)^{2} (800 kg/m^{3} - \rho_{liquid}) 9.81 m/s^{2}}{0.1 m/s}

Step 3: Calculate the density of the liquid:

\rho_{liquid} = 800 kg/m^{3} - \frac{4}{3}\pi (0.02m)^{3} = 800 kg/m^{3} - 0.00107 kg/m^{3} = 799.998 kg/m^{3}

Step 4: Substitute the calculated value of \rho_{liquid} and the given values and calculate \eta:

                    \eta = \frac{2}9{} \frac{(0.02m)^{2} (800 kg/m^{3} - 799.998 kg/m^{3}) 9.81 m/s^{2}}{0.1 m/s}

Step 5: Calculate \eta:

                    \eta = 1.08 * 10-3 Pa.s

The coefficient of viscosity of the liquid is 1.08 * 10-3 Pa.s

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Gunjita

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