The viscosity of a liquid can be calculated using equation: = Br, where B is cal

Question

The viscosity of a liquid can be calculated using equation: = Br, where B is calibration constant 6. t of the viscometer, is the density of the liquid and , is time of flow through the viscometer. In one experiment, water was used to calibrate the viscometer at time of flow was measured as 200.3±0.2 s. At 250°C, the density and viscosity of water are 0.99708 gmL and 8,909 x 103 g-cm s , respectively. Using the same viscometer, the time of flow was 425.6±0.5 s at 250°C for an unknown liquid with density 0.85667 g·mL 1 Determine constant B and the viscosity of the unknown liquid with error analysis.

Explanation / Answer

For ease of typing I will be using coefficient of viscosity as N. density of liquid as p ; B as calibaration constant of calorimeter and t as time of flow

So, N = Bpt ;

for water we have t=200.3-+0.2 p = 0.99708 g mL-1 N = 0.008909 g cm-1 s-1

error =0.2/200.3 =0.001 = 0.1%

B = 0.008909/( 0.99708*200.3) = 4.46 * 10-5 mL cm-1 s-2 with an error of 0.1 %

For Unknown Liquid ;

N = 425.6 * 0.85667 * 4.46 * 10-5

N = 1.62 * 10-2 g cm-1 s-1

% error = sq.root(a2 + b2)

where % error = final % error

a = % error of 1st quantity

b = % error of second quantity

% error of time of flow of second liquid = 0.5/425.6 = 0.12

% error = sq.root( 0.01 + 0.0144)

% error = 0.16%

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