Question

1. The following times were recorded at 20 °C for standardization of a viscometer with standard fluid. For the same temperature, the standard fluid has a viscosity n = 0.5526 mPa-s and density p=0.7264 g/cm'. The four times are 242.3, 250.9, 246.8 and 249.2 s. Calculate average time, standard deviation of time t, and viscometer constant A.

Answer 1

The recorded times are, t₁ = 242.3 s, t₂ = 250.9 s, t₃ = 246.8, t₄ = 249.2 s

The avarage time is = (t₁ + t₂ + t₃ + t₄)/4 = (242.3 + 250.9+ 246.8 + 249.2)/4 = 247.3

The standerd deviation of time $\sigma$ _t is given as, {_$\sum$(t_i - t_av)²/(N - 1)}^1/2

= [{(242.3 - 247.3)² + (250.9 - 247.3)² + (246.8 - 247.3)² + (249.2 - 247.3)²}/(4-1)]^1/2

= {(25 + 12.96 + 0.25 + 3.61)/3}^1/2

$\sigma$_t = 3.73 s

Viscosity of a liquid of density $\rho$ is given as, $\eta$ =A $\rho$ t

A = viscometer constant, t = flow time

so, A = $\eta$ /$\rho$t

Here, $\eta$ = 0.5526 mPa-s, $\rho$ = 0.7264 g/cm³ t = 247.3$\pm$3.73 s (mPa = kg⋅m⁻¹⋅s⁻²/1000)

A = (0.5526 mPa-s)/{(0.7264 g/cm³)x(247.3$\pm$3.73 s)} = (3.0765x10^-3$\pm$0.0465x10^-3) g⋅m⁻¹⋅s⁻²/g.cm^-3

= (3.0765x10^-3$\pm$0.0465x10^-3)x10⁶ m²⋅s⁻²