Fluid Kinematics MCQ Quiz - Objective Question with Answer for Fluid Kinematics - Download Free PDF
Last updated on Jun 4, 2025
Latest Fluid Kinematics MCQ Objective Questions
Fluid Kinematics Question 1:
In a flow, velocity vector is given by
Answer (Detailed Solution Below)
Fluid Kinematics Question 1 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 2:
Which of the following sets of equations represents the possible 2-D, incompressible flow?
Answer (Detailed Solution Below)
Fluid Kinematics Question 2 Detailed Solution
Concept:
For 2D incompressible flow, the continuity equation must hold:
Check for Option 3:
Fluid Kinematics Question 3:
Which of the following function is a valid potential function (ϕ)?
Answer (Detailed Solution Below)
Fluid Kinematics Question 3 Detailed Solution
Concept:
A function
Check for Option:
Since the mixed partials are equal, the function is a valid potential function.
Fluid Kinematics Question 4:
Which one of the following statements is true to two-dimensional flow of ideal fluids?
Answer (Detailed Solution Below)
Fluid Kinematics Question 4 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:
- 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.
- 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.
Fluid Kinematics Question 5:
The fluid forces considered in the Navier-Stokes equation are
Answer (Detailed Solution Below)
Fluid Kinematics Question 5 Detailed Solution
Explanation:
Navier-Stokes Equation:
- The Navier-Stokes equation is a set of partial differential equations that describe the motion of fluid substances. These equations are fundamental in fluid dynamics and are used to analyze the behavior of fluids under various forces and conditions. The forces considered in the Navier-Stokes equation govern the dynamics of fluid flow and are integral to understanding fluid behavior in engineering and natural systems.
1. Gravity Forces: Gravity is a body force acting on the fluid due to the weight of the fluid particles. It is represented as a gravitational acceleration term multiplied by the fluid density. Gravity plays a significant role in fluid flow, especially in natural systems like rivers, oceans, and the atmosphere. In the Navier-Stokes equation, the gravity force is accounted for by the body force term, which contributes to the overall momentum balance.
2. Pressure Forces: Pressure forces arise due to the variation in pressure within the fluid. These forces act perpendicular to the surface of a fluid element and are responsible for driving fluid motion in many situations, such as in pipelines, pumps, and atmospheric flows. The pressure gradient term in the Navier-Stokes equation captures the effect of pressure forces on fluid motion.
3. Viscous Forces: Viscous forces are internal frictional forces within a fluid that resist relative motion between adjacent fluid layers. These forces are a result of the fluid's viscosity and play a crucial role in determining the flow characteristics, such as laminar or turbulent flow. The viscous forces are represented by the viscous stress tensor in the Navier-Stokes equation, which accounts for the shear stresses due to velocity gradients within the fluid.
Navier-Stokes Equation:
The Navier-Stokes equation can be expressed in its general form as:
ρ (∂v/∂t + v · ∇v) = -∇p + μ∇²v + ρg
Where:
- ρ = Fluid density
- v = Velocity vector
- t = Time
- p = Pressure
- μ = Dynamic viscosity
- g = Gravitational acceleration
- ∇ = Gradient operator
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?
Answer (Detailed Solution Below)
Fluid Kinematics Question 6 Detailed Solution
Download Solution PDFConcept:
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
Answer (Detailed Solution Below)
Fluid Kinematics Question 7 Detailed Solution
Download Solution PDFConcept:
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.
Answer (Detailed Solution Below)
Fluid Kinematics Question 8 Detailed Solution
Download Solution PDFExplanation:
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:
Answer (Detailed Solution Below)
Fluid Kinematics Question 9 Detailed Solution
Download Solution PDFExplanation:
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:
- If ψ exists, it follows continuity equation and the flow may be rotational or irrotational.
- If ψ satisfies the Laplace equation, then the flow is irrotational.
A flow field which has only convective acceleration is
Answer (Detailed Solution Below)
Fluid Kinematics Question 10 Detailed Solution
Download Solution PDFExplanation:
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
The last three terms
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 ___________.
Answer (Detailed Solution Below)
Fluid Kinematics Question 11 Detailed Solution
Download Solution PDFExplanation:
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?
Answer (Detailed Solution Below)
Fluid Kinematics Question 12 Detailed Solution
Download Solution PDFConcept:
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: A1 = 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:
Answer (Detailed Solution Below)
Fluid Kinematics Question 13 Detailed Solution
Download Solution PDFConcept:
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
Answer (Detailed Solution Below)
Fluid Kinematics Question 14 Detailed Solution
Download Solution PDFExplanation:
General Continuity equation:
For incompressible and steady flow:
∴ The flow needs to be steady and incompressible.
If a flow velocity field is given by
Answer (Detailed Solution Below)
Fluid Kinematics Question 15 Detailed Solution
Download Solution PDFConcept:
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.
i.e. If
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
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.