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# MCQs on Navier-Stokes Equations of Motion

Navier- Stokes equation describes the motion of __________

a) Solid substance

b) Non-viscous fluid

c) Viscous fluid

d) Gas

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c

Explanation: The equation described by Navier- Stokes is for a viscous fluid. The balanced equation arises from Newton’s Second Law of fluid motion. It assumes that the stress in the fluid is equal to the sum of a diffusing viscous term and a pressure term.

Froude number depends upon_________

a) Flow velocity, external field and characteristic length

b) Flow velocity and mass

c) Mass flow rate and volume

d) Characteristic length and volume

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a

Explanation: The Froude number is a dimensionless number. It is defined as the ratio of flow inertia to the external field. The Froude number is based on the speed-length ratio.

Continuum mechanics is a branch of mechanics that deals with________

a) Fluid particles

b) Discrete particles

c) Kinematics and mechanical behaviour

d) Hydrostatic Pressure

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c

Explanation: Continuum mechanics is a branch that deals with the analysis of kinematics and mechanical behaviour of materials. It can be modelled as a continuous mass rather than as discrete particles.

Which among the following cannot be used as an alternative term for a “solenoidal vector field”?

a) Incompressible vector field

b) Divergence- free vector field

c) Transverse vector field

d) Continuous random field

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d

Explanation: A random field comes under a stochastic process. It can take up values that are multidimensional vectors or points on some manifold. A random field is a list of random numbers whose indices are identified with a discrete set of points in space.

The Navier- Stokes equation can be used in which of the following applications?

a) Automobiles

b) Ocean Currents

c) Airplanes

d) Thermometer

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b

Explanation: An ocean current is a continuous direct movement of seawater. Ocean currents are forces generated by acting upon the mean flow. Therefore, ocean currents satisfy Navier-Stokes equation as they have a primary horizontal water movement.

Which among the following is not an example of magneto fluids?

a) Plasma

b) Liquid metals

c) Salt water

d) Alcohol

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d

Explanation: Alcohol is an organic compound on which a hydroxyl functional group is bounded to a saturated carbon atom. Alcohols work as an antifreeze solution at cool temperatures. Thus, it is not a magneto fluid.

What is the velocity profile for Poiseuille flow?

a) Zero

b) Constant

c) Linear

d) Quadratic

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d

Explanation: The velocity profile for Poiseuille flow is zero at either side of the channel and non-zero in the middle. Therefore, Quadratic equation is the only possible option here.

What are the Newtonian constitutive assumptions regarding relationship between stress tensor and velocity gradients?

a) Linear and isotropic

b) Constant

c) Linear

d) Non-Uniform

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a

Explanation: Newtonian fluid is a fluid in which the viscous stresses arise due to its flow. The flow experiences a strain rate at every point. The strain rate is related to the constant viscosity tensor that does not depend upon the stress and velocity of the flow. Thus, the relationship is linear and isotropic.

What is the incompressibility condition in Navier-Stokes equation?

a) ∇.u=0

b) ∇.u>0

c) ∇.u<0

d) ∇.u=1

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a

Explanation: This comes from the relation between the divergence of the flow. It also relates the Jacobian transformation with Lagrangian and Eulerian coordinates. Thus, ∇.u=0.

The velocity profile of the Couette flow is _______

a) Quadratic

b) Constant

c) Linear

d) Zero

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c

Explanation: Couette flow is a flow of viscous fluid in the space between two surfaces. One surface moves tangentially with respect to the other. The configuration often takes the form of the two parallel plates or the gaps in between two cylinders.