Engineering Questions with Answers - Multiple Choice Questions
Computational Fluid Dynamics – Governing Equations – Stress and Strain Tensor
1 - Question
Which among these forces used in momentum equation is a tensor?
a) Gravitational forces
b) Pressure forces
c) Viscous forces
d) Electromagnetic forces
View Answer
Explanation: Viscous forces are tensors. The other forces given here (Gravitational, viscous and electromagnetic forces) are vectors.
2 - Question
What do the two subscripts of stress tensors represent?
a) Directions of stress and strain
b) Directions of stress and normal to the surface on which they are acting
c) Directions of strain and normal to the surface on which they are acting
d) Direction of stress and the flow direction
View Answer
Explanation: The two subscripts of stress tensors indicate the direction of the stress and that of the normal to the surface on which they act. So, stress tensors give the location and direction of the stresses.
3 - Question
Which of these fluids have their stress tensor linearly varying to the strain rate?
View Answer
Explanation: S-tress tensor linearly varies with the strain rate only for Newtonian fluids. For Newtonian fluid shear stress is proportional to du/dy. In the other cases, shear stress varies non-linearly with du/dy.
4 - Question
Which of the stress tensors from the diagram is represented by Τxy?
a) 3
b) 2
c) 1
d) 4
View Answer
Explanation: Τxy indicate that the stress component acts in the y-direction on a surface normal to the x-direction. Representing this in the diagram, 3 is the corresponding tensor.
5 - Question
The divergence of the stress tensor is _____
a) Scalar
b) Vector
c) 0
d) 1
View Answer
Explanation: Stress tensor is a square matrix given by Τxy = ⎡⎣⎢τxxτyxτzxτxyτyyτzyτxzτyzτzz⎤⎦⎥ The divergence of this will result in a vector ∇. Τ= ⎡⎣⎢⎢⎢⎢⎢∂τxx∂x+∂τyx∂y+∂τzx∂z∂τxy∂x+∂τyy∂y+∂τzy∂z∂τxz∂x+∂τyz∂y+∂τzz∂z⎤⎦⎥⎥⎥⎥⎥
6 - Question
What are the two viscosity coefficients involved in the relationship between stress tensor and strain rate of fluids?
a) Kinematic viscosity and bulk viscosity
b) Dynamic viscosity and kinematic viscosity
c) Dynamic viscosity and bulk viscosity
d) Kinematic viscosity and volume viscosity
View Answer
Explanation: The two viscosities involved in stress train relationship of fluids is dynamic viscosity coefficient and bulk viscosity coefficient. Bulk viscosity coefficient for diagonal elements respectively.
7 - Question
What is the relationship between bulk viscosity coefficient (λ) and the dynamic viscosity coefficient (μ)?
a) λ=−23 μ
b) λ=23 μ
c) λ=−13 μ
d) λ=−12 μ
View Answer
Explanation: The bulk viscosity coefficient represents fluid compressibility effects. λ=−23 μ is the relationship between the bulk viscosity coefficient and the dynamic viscosity coefficient.
8 - Question
Express the shear stress tensor(τ) of a three-dimensional fluid flow element in terms of the velocity vector(v).
a) τ=μ{(∇v⃗ )T}+λ(∇.v⃗ )I
b) τ=μ{(∇v⃗ )}+λ(∇.v⃗ )I
c) τ=μ{(∇v⃗ )T+(∇.v⃗ )T}
d) τ=μ{(∇v⃗ )T+(∇.v⃗ )T}+λ(∇.v⃗ )I
View Answer
Explanation: The shear stress tensor of a fluid element can be given by τ=μ{(∇v⃗ )T+(∇.v⃗ )T}+λ(∇.v⃗ )I. This is not applicable for practical cases. However, common fluids like air and water are assumed to be Newtonian for using this relationship
9 - Question
Express τyz in terms of velocity gradients.
a) τyz=μ(∂v∂z+∂w∂y)
b) τyz=μ(∂u∂z+∂u∂y)
c) τyz=μ(∂v∂x+∂w∂x)
d) τyz=μ(∂w∂z+∂v∂y)
View Answer
Explanation: For non-diagonal elements, τ=μ{∇v⃗ +(∇v⃗ )T} τyz=μ(∂v∂z+∂w∂y).
10 - Question
Viscous forces fall into which kind of the following forces acting on a body?
a) Pressure force
b) Tensile force
c) Body forces
d) Surface forces
View Answer
Explanation: The two types of forces acting on a fluid are body forces and surface forces. Body forces are the forces produced by the fluid element itself. Surface forces are the one acting on the fluid elements. Viscous forces act on the element and it comes under surface forces.