Question

For a Newtonian fluid, a plot of shear stress (on Y axis) against shear rate (on X axis) will result in a straight line .

• A. parallel to the X axis
• B. parallel to the Y axis
• C. with a negative slope
• D. with a positive slope

Hint:

Newtonian fluid means shear stress equals viscosity times shear rate, a straight line through the origin.

Answer 1

The Correct Option is D

Step 1: Recall the defining relation for a Newtonian fluid.
A Newtonian fluid is one where shear stress is directly proportional to shear rate, with the constant of proportionality being the viscosity, which stays the same at every shear rate.
\[ \tau = \mu \dot{\gamma} \]
Here \(\tau\) is the shear stress, \(\dot{\gamma}\) is the shear rate, and \(\mu\) is the constant viscosity.

Step 2: Read this equation as the equation of a straight line.
Plotting \(\tau\) (Y axis) against \(\dot{\gamma}\) (X axis), this equation has the form \(y = mx\), a straight line through the origin whose slope \(m\) equals the viscosity \(\mu\).
Since viscosity is always a positive physical quantity (a fluid always resists shear, never assists it), the slope \(\mu\) is always positive.

Step 3: Eliminate the other options.
A line parallel to the X axis (option A) would mean shear stress stays fixed no matter how fast the fluid is sheared; that describes an ideal plastic, not a Newtonian fluid.
A line parallel to the Y axis (option B) would mean shear stress changes with no change in shear rate at all, which has no physical meaning here.
A negative slope (option C) would mean shear stress falls as shear rate rises, which never happens for any real fluid since viscosity cannot be negative.

Final Answer:
The shear stress versus shear rate plot for a Newtonian fluid is a straight line through the origin with slope equal to the constant, positive viscosity.
\[ \boxed{\text{(D) with a positive slope}} \]