The coefficient of viscosity m of a liquid is to be calculated via an experiment

Question

The coefficient of viscosity m of a liquid is to be calculated via an experiment measuring the rate of flow of the liquid through a tube of length L and radius r, which uses Poiseuille’s equation in the form.

Where:

Q         :           is the rate of flow

P         :           is the pressure difference between the ends of the tube

Q can be measured to within 3%, P to within 2%, r to within 0.05% and L within 0.1%.

a.Model the change of coefficient of viscosity with the pressure.

b.Model the change of coefficient of viscosity with the flow rate.

c.Model the change of coefficient of viscosity with the length.

d.Analyse the problem mathematically and find the maximum percentage error in the calculated value of the coefficient viscosity

Explanation / Answer

a) the change of coefficient of viscosity with the pressure = >   coefficient of viscosity is directly proportional to pressure .    So, change of coefficient of viscosity with the pressure = 2%

b) the change of coefficient of viscosity with the flow rate => coefficient of viscosity is inversely proportional to flow rate .    So, change of coefficient of viscosity with the flow rate = 2.91 %

c)    the change of coefficient of viscosity with the length => coefficient of viscosity is inversely proportional to length .    So, change of coefficient of viscosity with the length = 0.099 %

d)    the maximum percentage error in the calculated value of the coefficient viscosity = 0.871 %

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