Question

For flowing water, what is the magnitude of the velocity gradient needed to produce a shear stress of 1.0 n/m2 ?

Answer 1

The magnitude of velocity gradient of water is $\b{\boxed{892.86\text{ s}^{-1}}}$ or $\b{\boxed{892.86\text{ /s}}}$ .

Further Explanation:

Shear stress is the stress developed along the cross section of any material or fluid. It is the ratio of force and area and denoted by τ.

Newton’s law of viscosity states, “The shear stress between two adjacent fluid layers is proportional to the velocity gradient between two layers”.

Formula for shear stress by law of viscosity:

$\boxed{\tau=\mu\left({\dfrac{{du}}{{dy}}}\right)}$

Here, τ is the shear stress, μ is the dynamic viscosity and $\dfrac{du}{dy}$ is the velocity gradient.

Velocity gradient is the change in velocity of fluid in radial direction of cross section.

Viscosity is property of a fluid by virtue of which it offers resistance to movement of one layer of fluid over an adjacent layer.

Given:

The shear stress in the fluid is $1\text{ N}/\text{m}^2$.

Concept:

The formula for velocity gradient:

$\left({\dfrac{{du}}{{dy}}}\right)=\dfrac{\tau}{\mu}$

Substitute $1\text{ N}/\text{m}^2$ for τ and $1.12\times10^-3\text{ Ns}/\text{m}^2$ for μ in above equation.

$\begin{aligned}\dfrac{du}{dy}&=\dfrac{1}{1.12\times10^-3}\text{ s}^-1\\&=892.86\text{ s}^-1\end{aligned}$

Thus, the magnitude of velocity gradient of water is $\boxed{892.86\text{ s}^{-1}}$ or $\boxed{892.86\text{ /s}}$ .

Learn More:

1. Volume of gas after expansion: brainly.com/question/9979757

2. Principle of conservation of momentum: brainly.com/question/9484203

3. Average translational kinetic energy: brainly.com/question/9078768

Answer Details:

Grade: College

Subject: Physics

Chapter: Kinematics

Keywords:

Flowing, water, magnitude, velocity, gradient, shear, stress, 1.0 N/m2, 892.86/s, 1.12*10^-3 Ns/m^2, viscosity, fluid, dynamic, adjacent, layers and property.

Answer 2

Shear stress = 1.0 N/m² (Pa)

For water, the dynamic viscosity = 10⁻³ Pa-s at 20°C.
The velocity gradient required = (Shear stress)/(Dynamic viscosity)
= (1.0 Pa)/( 10⁻³ Pa-s)
= 10³ 1/s

Answer:  10³  s⁻¹