Fluid Kinematics MCQ Quiz - Objective Question with Answer for Fluid Kinematics - Download Free PDF

Last updated on Jun 11, 2025

Latest Fluid Kinematics MCQ Objective Questions

Fluid Kinematics Question 1:

Dimension of circulation is

Answer (Detailed Solution Below)

Option 3 :

Fluid Kinematics Question 1 Detailed Solution

Explanation:

Circulation

  • Circulation is a concept in fluid dynamics that measures the total "rotational effect" of a fluid flow around a closed contour or loop. It is mathematically defined as the line integral of the velocity vector along a closed curve. The dimension of circulation can be derived from its physical definition and mathematical representation.

Circulation is defined as the line integral of velocity over a closed loop:

Where:

  • = velocity (dimension = )
  • = length element (dimension = )

Therefore,

 

Fluid Kinematics Question 2:

In a flow, velocity vector is given by  . The equation of streamline passing through the point (1,1) will be:

  1. 9x3y3=8
  2. 9x - y = 8 
  3. 9x- y= 8 
  4. 9x- y= 8

Answer (Detailed Solution Below)

Option 3 : 9x- y= 8 

Fluid Kinematics Question 2 Detailed Solution

Concept:

For a 2D flow, the equation of a streamline is given by:

Given:

So,

Cross-multiplying:

Integrating both sides:

Multiply by 3:

Using point (1,1):

 

Fluid Kinematics Question 3:

Which of the following sets of equations represents the possible 2-D, incompressible flow?

  1. x+yxy
  2. x+2yx2yt2

Answer (Detailed Solution Below)

Option 3 : x+yxy

Fluid Kinematics Question 3 Detailed Solution

Concept:

For 2D incompressible flow, the continuity equation must hold:

Check for Option 3:

 

Fluid Kinematics Question 4:

Which of the following function is a valid potential function (ϕ)?

  1. x2 _ 3x2y

Answer (Detailed Solution Below)

Option 3 :

Fluid Kinematics Question 4 Detailed Solution

Concept:

A function is a valid potential function if its mixed second-order partial derivatives are equal:

Check for Option:

Since the mixed partials are equal, the function is a valid potential function.

Fluid Kinematics Question 5:

Which one of the following statements is true to two-dimensional flow of ideal fluids?

  1. Both potential function and stream function must exist for every flow
  2. Stream function may or may not exist
  3. Stream function will exist but potential function may or may not exist
  4. Potential function exists if stream function exists

Answer (Detailed Solution Below)

Option 3 : Stream function will exist but potential function may or may not exist

Fluid Kinematics Question 5 Detailed Solution

Explanation:

Two-Dimensional Flow of Ideal Fluids

  • In fluid mechanics, two-dimensional flow refers to a flow scenario where the velocity components are functions of only two spatial coordinates, typically x and y, and the flow parameters do not vary in the third coordinate (z). For an ideal fluid, which is incompressible and inviscid, the flow can be analyzed using mathematical tools such as the stream function and potential function.

Option 3: "Stream function will exist but potential function may or may not exist."

This statement is correct because, in the case of two-dimensional flow of ideal fluids:

  1. Stream Function: The stream function (ψ) always exists for two-dimensional, incompressible flows. The stream function is a scalar function whose contours represent streamlines. It helps visualize the flow pattern and satisfies the condition for continuity in two-dimensional flow. For incompressible flow, the continuity equation ensures the existence of the stream function.
  2. Potential Function: The potential function (φ) exists only if the flow is irrotational. For a flow to be irrotational, the vorticity (the curl of the velocity field) must be zero. Hence, while the stream function exists for all two-dimensional incompressible flows, the potential function may or may not exist depending on whether the flow is irrotational or not.

Top Fluid Kinematics MCQ Objective Questions

In a stream line steady flow, two points A and B on a stream line are 1 m apart and the flow velocity varies uniformly from 2 m/s to 5 m/s. What is the acceleration of fluid at B?

  1. 3 m/s2
  2. 6 m/s2
  3. 9m/s2
  4. 15 m/s2

Answer (Detailed Solution Below)

Option 4 : 15 m/s2

Fluid Kinematics Question 6 Detailed Solution

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Concept:

For flow along a stream line acceleration is given as

If V = f(s, t)

Then, 

 

For steady flow 

Then  

Since V = f(s) only for steady flow therefore 

Therefore 

Calculation:

Given, VA = 2 m/s, VB = 5 m/s, and distance s = 1 m

So acceleration of fluid at B is

A vortex flow is

  1. rotational flow
  2. irrotational flow
  3. both 1 and 2 
  4. free shear flow

Answer (Detailed Solution Below)

Option 3 : both 1 and 2 

Fluid Kinematics Question 7 Detailed Solution

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Concept:

Vortex flow:

The motion of a fluid in a curved path is known as vortex flow.

When a cylindrical vessel containing some liquid is rotated about its vertical axis, the vortex flow will be followed by liquid.

Vortex motion is of two types:

1. Forced vortex:

  • In the forced vortex, fluid moves on the curve under the influence of external torque.
  • Due to the external torque, a forced vortex is a rotational flow.
  • As there is the continuous expenditure of energy, Bernoulli's equation is not valid for forced vortex.
  • For forced vortex, v = rω is applicable.
  • Examples: 
    • The flow of water through a runner of the turbine.
    • Rotation of water in the washing machine.

2. Free vortex:

  • When no external torque is required to rotate the fluid mass, that type of flow is called a free vortex.
  • As there is no torque in the free vortex, so free vortex is an irrotational flow.
  • For free vortex, a moment of momentum is constant i.e. vr = constant.
  • Examples:
    • The flow of liquid through a hole provided at the bottom of a container.
    • Draining the bathtub.

∴vortex flow is both rotational and irrotational flow depending on the torque applied.

Which of the following statements are correct for an incompressible flow?

I) In incompressible flows, variation in density is negligible.

II) Incompressible flows are always laminar.

III) Incompressible flows can be internal as well as external.

  1. only I and II
  2. I, II and III
  3. Only II and III
  4. only I and III

Answer (Detailed Solution Below)

Option 4 : only I and III

Fluid Kinematics Question 8 Detailed Solution

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Explanation:

Incompressible flow: It is that type of flow in which the density is constant for the fluid flow. Liquids are generally incompressible while gases are compressible.

Mathematically, ρ = Constant.

These can be laminar or turbulent, external or internal.

Laminar and Turbulent flow is considered to be incompressible if the density is constant or the fluid expands with little energy in compressing the flow. Hence a flow with varying density (Incompressible) flow could be Laminar & Turbulent.

Additional Information

Compressible flow: The flow in which the density of the fluid changes from point to point or the density is not constant for the fluid

Mathematically, for compressible flow ρ ≠ Constant

If velocity potential (ϕ) exists in a fluid flow, then the flow is said to be:

  1. turbulent
  2. irrotational
  3. rotational
  4. laminar

Answer (Detailed Solution Below)

Option 2 : irrotational

Fluid Kinematics Question 9 Detailed Solution

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Explanation:

Velocity Potential function

  • This function is defined as a function of space and time in a flow such that the negative derivation of this function with respect to any direction gives the velocity of the fluid in that direction.

Properties of Velocity Potential function:

  • If velocity potential (ϕ) exists, there will be a flow.
  • Velocity potential function exists for flow then the flow must be irrotational.
  • If velocity potential (ϕ) satisfies the Laplace equation, it represents the possible steady incompressible irrotational flow.

Additional Information

Stream Function:

  • It is the scalar function of space and time.
  • The partial derivative of stream function with respect to any direction gives the velocity component perpendicular to that direction. Hence it remains constant for a streamline
  • Stream function defines only for the two-dimensional flow which is steady and incompressible..

Properties of stream function:

  1. If ψ exists, it follows continuity equation and the flow may be rotational or irrotational.
  2. If ψ satisfies the Laplace equation, then the flow is irrotational.

A flow field which has only convective acceleration is

  1. a steady uniform flow
  2. an unsteady uniform flow
  3. a steady non-uniform flow
  4. an unsteady non-uniform flow

Answer (Detailed Solution Below)

Option 3 : a steady non-uniform flow

Fluid Kinematics Question 10 Detailed Solution

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Explanation:

Total acceleration of a flow is given by:

The total derivative,

The total differential D/Dt is known as the material or substantial derivative with respect to time.

The first term  in the right hand side is known as temporal or local derivative which expresses the rate of change with time, at a fixed position.

The last three terms  in the right hand side of  are together known as convective derivative which represents the time rate of change due to change in position in the field.

Type of Flow

Material Acceleration

 

Temporal

Convective

Steady Uniform flow

0

0

Steady non-uniform flow

0

exists

Unsteady Uniform flow

exists

0

Unsteady non-uniform flow

exists

exists

The motion of outgoing water from the hole made at the midpoint of a completely filled open cylindrical tank with water is ___________.

  1. forced vortex form
  2. irrotational
  3. rotational
  4. turbulent

Answer (Detailed Solution Below)

Option 2 : irrotational

Fluid Kinematics Question 11 Detailed Solution

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Explanation:

Free vortex

When the fluid mass is rotating about an axis without any external torque is known as a free vortex and free vortex motion is irrotational flow.

Forced vortex

When an external force is required to rotate the fluid mass at a constant angular velocity about an axis is known as a forced vortex.

By deriving the condition for free vortex flow by considering fundamental equations of vortex flow, Bernoulli’s equation will be valid, which ultimately proves the flow to be irrotational (one of the assumptions of Bernoulli’s equation).

When 0.1 m3/s water flows through a pipe of area 0.25 m2, which later reduces to 0.1 m2, what is the velocity of flow in the reduced pipe?

  1. 2.0 m/s
  2. 0.5 m/s
  3. 1.0 m/s
  4. 1.5 m/s

Answer (Detailed Solution Below)

Option 3 : 1.0 m/s

Fluid Kinematics Question 12 Detailed Solution

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Concept:

Continuity equation: It is the conservation of mass flow rate.

  • ρ1A1V1 =  ρ1A1V1

For incompressible fluid density will be constant thus continuity equation will be:

  • A1V1 = A2V2  

where, A1, A2 = area of section 1 & 2 respectively, V1, V2 = velocity of section 1 & 2 respectively

The flow rate of liquid is equal to Q = AV.

Calculation:

Given:

Area: A= 0.25 m2, A2 = 0.1 m2.

Flow rate: Q = 0.1 m3/s.

Q = A1V1 = A2V2 

∴ The velocity of flow in the reduced pipe is 1 m/s

In a free vortex, the flow is:

  1. rotational
  2. irrotational
  3. rotational or irrotational
  4. neither rotational or irrotational

Answer (Detailed Solution Below)

Option 2 : irrotational

Fluid Kinematics Question 13 Detailed Solution

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Concept:

Vortex flow:

The motion of a fluid in a curved path is known as vortex flow.

When a cylindrical vessel containing some liquid is rotated about its vertical axis, the vortex flow will be followed by liquid.

Vortex motion is of two types:

1. Forced vortex:

  • In the forced vortex, fluid moves on the curve under the influence of external torque.
  • Due to the external torque, a forced vortex is a rotational flow.
  • As there is the continuous expenditure of energy, Bernoulli's equation is not valid for forced vortex.
  • For forced vortex, v = rω is applicable.
  • Examples: 
    • The flow of water through a runner of the turbine.
    • Rotation of water in the washing machine.

2. Free vortex:

  • When no external torque is required to rotate the fluid mass, that type of flow is called a free vortex.
  • As there is no torque in the free vortex, so free vortex is an irrotational flow.
  • For free vortex, a moment of momentum is constant i.e. vr = constant.
  • Examples:
    • The flow of liquid through a hole provided at the bottom of a container.
    • Draining the bathtub.

∴ Vortex flow is both rotational and irrotational flow depending on the torque applied.

For the continuity equation given by  to be valid, where  is the velocity vector, which one of the following is a necessary condition?

  1. Steady flow
  2. Irrotational flow
  3. Inviscid flow
  4. Steady and incompressible flow

Answer (Detailed Solution Below)

Option 4 : Steady and incompressible flow

Fluid Kinematics Question 14 Detailed Solution

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Explanation:

General Continuity equation:

For incompressible and steady flow:

∴ The flow needs to be steady and incompressible.

If a flow velocity field is given by :

  1. flow is three dimensional
  2. flow is physically possible and rotational
  3. flow is physically possible and irrotational
  4. flow is physically not possible

Answer (Detailed Solution Below)

Option 4 : flow is physically not possible

Fluid Kinematics Question 15 Detailed Solution

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Concept:

Any field which satisfied the continuity equation given below is considered as flow field

Where u, v, ω are x, y and z components of velocity field of flow.

Further ; The flow is said to be rotational is curl of velocity vector (i.e.  is not equal to zero, otherwise flow is irrotational.

i.e. If  then flow is irrotational.

Calculation:

Given:

Since given  has component in x and y direction and no component in ‘z’ direction, so it is a 2D velocity field.

Further  

Since  not a flow.

Since, the given velocity vector did not satisfied the continuity equation, so it did not represent the flow or flow is not possible.

Also, is there is no flow, hence is no sense of saying whether the flow is rotational or irrotational flow.

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