Statement (I): The shear strain graph for a Newtonian fluid is li
Statement (I): The shear strain graph for a Newtonian fluid is linear.
Statement (II): The coefficient of viscosity μ of the fluid is not a constant.
A. Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)
B. Both Statement (I) and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement (I)
C. Statement (I) is true but Statement (II) is false
D. Statement (I) is false but Statement (II) is true (II) is true:
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
Concept:
Newtonian fluid:
- A Newtonian fluid is a fluid in which the viscous shear stresses arising from its flow, at every point, are linearly correlated to the rate of change of its deformation over time.
- It means for Newtonian fluid, shear stress is directly proportional to shear strain rate. For a Newtonian fluid,\({\rm{\tau }} = {\rm{\mu }}\frac{{{\rm{du}}}}{{{\rm{dx}}}}\) where τ is shear stress, \(\frac{{{\rm{du}}}}{{{\rm{dx}}}}\) is shear strain rate and μ is coefficient of viscosity.
- Shear stress vs shear strain rate plot for Newtonian fluid and as well as other various fluids has been shown in the following diagram:
The shear strain graph (shear stress vs shear strain rate) for a Newtonian fluid is linear. Hence, statement 1 is true.
- At a constant temperature, the coefficient of viscosity (μ) of a Newtonian fluid is always constant no matter what amount of shear stress is applied.
- Also, from the shear strain graph this can be verified. Coefficient of viscosity μ is the slope of shear stress vs shear strain rate plot which is constant for a Newtonian fluid.
∴ For Newtonian fluid, the coefficient of viscosity μ is a constant. Hence, statement 2 is false.
