The rate of shear strain for a liquid is 10 s-1 and the coefficient of viscosity of the liquid is 0.5 N s/m2. Determine the shear stress develop in th

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The rate of shear strain for a liquid is 10 s-1 and the coefficient of viscosity of the liquid is 0.5 N s/m2. Determine the shear stress develop in the liquid:
1. 20 N/m2
2. 15 N/m2
3. 10 N/m2
4. 5 N/m2

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Correct Answer - Option 4 : 5 N/m2

Concept:

A fluid is a substance that continually deforms (flows) under applied shear stress or external force.

Fluids are a phase of matter and include liquids, gases, and plasmas. They are substances with zero shear modulus, or, in simpler terms, substances that cannot resist any shear force applied to them.

According to Newton’s law of viscosity:

• The shear stress is directly proportional to the rate of shear strain or the rate of angular deformation of a fluid particle. The fluid-particle tends to deform continuously when it is in motion.
• $τ = μ \dfrac{{du}}{{dy}}=\mu \dfrac{d θ}{dt}$
• where, τ = shear stress, μ = dynamic viscosity, du/dy = shear strain rate, dθ/dt = rate of deformation

Calculation:

Given:

du/dy = 10 s-1, μ =  0.5 N s/m2

Now,
$τ = μ \dfrac{{du}}{{dy}}=0.5 \times10 = 5$

τ = 5 N/m2

Thus, option (4) is the correct answer.