All questions of Fluid Mechanics for Mechanical Engineering Exam

Which of the following causes the major loss in the long pipes?
  • a)
    Friction
  • b)
    Gradual contraction and enlargement both
  • c)
    Sudden contraction
  • d)
    Sudden enlargement
Correct answer is option 'A'. Can you explain this answer?

Prince Kuwar answered
As formula for head loss=( 4flv^2/2gd)
hence head loss is directly prapotional to length of pipe
hence as the length of pipe increases head loss also increases

The energy loss in flow through nozzle as compared to venturimeter is
  • a)
    Same
  • b)
    More
  • c)
    Less
  • d)
    More/less depending on flow
Correct answer is option 'B'. Can you explain this answer?

Sanvi Kapoor answered
The flow nozzle is essentially a venturimeter with the divergent part omitted. Therefore the basic equations for calculation of flow rate are the same as those for a venturimeter. The dissipation of energy downstream of the throat due to flow separation is greater than that for a venturimeter. But this disadvantage is often offset by the lower cost of the nozzle. Flow nozzle(top) and venturimeter(bottom) diagram is given below.

Pressure of 200 kPa is equivalent to the head of z metre of liquid having relative density 1.59. The value of z (m) is _____.
  • a)
    11.6
  • b)
    11.82
  • c)
    12.82
  • d)
    13.14
Correct answer is option 'C'. Can you explain this answer?

Jhanvi Datta answered
Given: Pressure = 200 kPa, relative density = 1.59

To find: Head of liquid (z)

Formula used:

Head of liquid (z) = Pressure / (density * g)

where g = acceleration due to gravity = 9.81 m/s²

Calculation:

Density of liquid = relative density * density of water

= 1.59 * 1000 kg/m³ (density of water at 4°C)

= 1590 kg/m³

Head of liquid (z) = 200 kPa / (1590 kg/m³ * 9.81 m/s²)

= 0.01282 m

= 12.82 mm

Therefore, the head of liquid is 12.82 m. Hence, option (c) is correct.

Spherical shape of droplets of mercury is due to:
  • a)
    High density
  • b)
    High surface tension
  • c)
    High adhesion
  • d)
    Water
Correct answer is option 'B'. Can you explain this answer?

Avinash Sharma answered
Surface tension is responsible for spherical shape of droplets. Surface tension for mercury is 0.485 N/m and that for water is 0.072 N/m.

Uniform flow occurs when:
  • a)
    Density does not change
  • b)
    Pressure does not change
  • c)
    Area does not change
  • d)
    Velocity does not change
Correct answer is option 'D'. Can you explain this answer?

Rhea Reddy answered
The flow is defined as uniform flow when in the flow field the velocity and other hydrodynamic parameters do not change from point to point at any instant of time. For a uniform flow, the velocity is a function of time only. When the velocity and other hydrodynamic parameters changes from one point to another the flow is defined as non-uniform.

The discharge over the rectangular weir is equal to:
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?

Yash Patel answered
Discharge over a rectangular weir:
Where H: - still water head
Flow over a triangular weir (V-weir):
θ: Included angel of Notch.
Flow over a trapezoidal weir (or) Notch-
Where,  : weir angle of inclination with the vertical.
Cd1Cd1 = Coefficient of discharge for rectangular portion.
Cd2Cd2 = Coefficient of discharge for the triangular portion.

A hydraulic intensifier normally consists of _____.
  • a)
    Two cylinders, two rams and a storage device
  • b)
    A cylinder and a ram
  • c)
    Co-axial ram and two cylinders
  • d)
    A cylinder, a piston, storage tank and control valve
Correct answer is option 'C'. Can you explain this answer?

Yash Patel answered
A hydraulic intensifier is a device which is used to increase the intensity of pressure of any hydraulic fluid or water, with the help of the hydraulic energy available from a huge quantity of water or hydraulic fluid at a low pressure. These devices are very important in the case of hydraulic machines, mainly hydraulic presses, which require water or hydraulic fluid at a very high pressure which cannot be obtained from the main supply directly. There are three main parts in the hydraulic intensifiers to be noted. They are
  • Fixed ram
  • Hollow inverted sliding cylinder
  • Fixed inverted cylinder

In order, to avoid separation in Venturi meter the angle of divergence is kept
  • a)
    10° to 15°
  • b)
    15° to 20°
  • c)
    5° to 7°
  • d)
    7° to 10°
Correct answer is option 'C'. Can you explain this answer?

Sanvi Kapoor answered
In the diverging portion there is a decrease in velocity & subsequent increase in pressure. If divergence angle is very large, then back pressure will increase by great extent & eddies formation will take place resulting in flow separation. Thus, to avoid flow separation the divergence angle must not exceed more than 7° and range should be around 5 - 7°.

In a flow field, at the stagnation point _______.
  • a)
    Pressure is zero
  • b)
    Velocity of fluid is zero
  • c)
    Pressure head is equal to velocity
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Suyash Kumar answered
A stagnation point is a point in a flow field where the local velocity of the fluid is zero. The Bernoulli equation shows that the static pressure is highest when the velocity is zero and hence static pressure is at its maximum value at stagnation points. This static pressure is called the stagnation pressure.

When a liquid rotates at a constant angular velocity about a vertical axis as a rigid body, the pressure
  • a)
    varies as the square of the radial distance
  • b)
    decreases as the square of the radial distance
  • c)
    increases linearly as the radial distance
  • d)
    varies inversely as the elevation along any vertical line
Correct answer is option 'A'. Can you explain this answer?

A fluid is rotating at constant angular velocity ω about the central vertical axis of a cylindrical container. The variation of pressure in the radial direction is given by
It is given that the pressure at the axis of rotation is Pc.
Therefore, the required pressure at any point r is

The specific speed of a Francis turbine is in the range of:
  • a)
    10 to 35
  • b)
    35 to 60
  • c)
    60 to 300
  • d)
    300 to 1200
Correct answer is option 'C'. Can you explain this answer?

1. The specific speed of Pelton wheel turbine (single jet) is in the range of 10-35
2. The specific speed of Pelton wheel turbine (multiple jet) is in the range of 35-60
3. The specific speed of Francis turbine is in the range of 60-300.
4. The specific speed of Kaplan turbine is greater than 300.

The cipoletti weir functions as if it were a following notch without end contractions
  • a)
    triangular notch
  • b)
    trapezoidal notch
  • c)
    rectangular notch
  • d)
    parallelogram notch
Correct answer is option 'C'. Can you explain this answer?

Disha Nambiar answered
The "Cippoletti" weir is a trapezoidal weir, having 1 horizontal to 4 vertical side slopes, as shown in figure. The purpose of the slope, on the sides, is to obtain an increased discharge through the triangular portions of the weir, which, otherwise would have been decreased due to end contractions in the case of rectangular weirs.

The correct statement about ideal fluid is:
  • a)
    An ideal fluid is incompressible, non-viscous and has infinite bulk modulus.
  • b)
    An ideal fluid is incompressible, non-viscous and has finite bulk modulus.
  • c)
    An ideal fluid is compressible, viscous and has infinite bulk modulus.
  • d)
    An ideal fluid is compressible, non-viscous and has infinite bulk modulus.
Correct answer is option 'A'. Can you explain this answer?

Soumya Basak answered
An ideal fluid is incompressible, non-viscous and has infinite bulk modulus.

In order to understand why option 'A' is the correct statement about an ideal fluid, let's break down the characteristics of an ideal fluid.

Incompressible:
- An ideal fluid is considered to be incompressible, which means that its density does not change under the influence of pressure.
- In practical terms, this means that the volume of an ideal fluid remains constant regardless of the external pressure applied to it.
- In an incompressible fluid, the molecules are closely packed, and there is very little empty space between them, resulting in negligible changes in volume.

Non-viscous:
- An ideal fluid is also assumed to be non-viscous, meaning it does not possess any internal friction or resistance to flow.
- Viscosity is the property of a fluid that determines its resistance to shear or flow.
- In an ideal fluid, there is no internal friction between its layers, and the fluid flows smoothly without any energy losses due to viscosity.

Infinite bulk modulus:
- The bulk modulus is a measure of the resistance of a fluid to compression.
- An ideal fluid is considered to have an infinite bulk modulus, implying that it cannot be compressed under any circumstances.
- This assumption is made to simplify the mathematical equations used to describe fluid behavior.
- In reality, no fluid has an infinite bulk modulus, but for theoretical purposes, an ideal fluid is assumed to exhibit this characteristic.

Therefore, the correct statement about an ideal fluid is that it is incompressible, non-viscous, and has an infinite bulk modulus (option 'A'). This idealized concept of a fluid helps in simplifying fluid flow analysis and mathematical calculations, providing a basis for understanding and predicting fluid behavior in various engineering applications.

The flow in which the velocity vector is identical in magnitude and direction at every point, for any given instant, is known as 
  • a)
    one dimensional flow
  • b)
    uniform flow 
  • c)
    steady flow
  • d)
    turbulent flow
Correct answer is option 'B'. Can you explain this answer?

The flow is defined as uniform flow when in the flow field the velocity and other hydrodynamic parameters do not change from point to point at any instant of time. For a uniform flow, there will be no spatial distribution of hydrodynamic and other parameters.
When the velocity and other hydrodynamic parameters changes from one point to another the flow is defined as non-uniform.
steady flow is defined as a flow in which the various hydrodynamic parameters and fluid properties at any point do not change with time.
One-dimensional flow is the flow where all the flow parameters may be expressed as functions of time and one space coordinate only. The single space coordinate is usually the distance measured along the centre-line (not necessarily straight) in which the fluid is flowing. Example: the flow in a pipe is considered one - dimensional when variations of pressure and velocity occur along the length of the pipe, but any variation over the cross-section is assumed negligible.
Turbulent fluid motion can be considered as an irregular condition of flow in which various quantities (such as velocity components and pressure) show a random variation with time and space.

Discharge Q in a triangular weir varies as:-
  • a)
    H
  • b)
    H1.5
  • c)
    H0.5
  • d)
    H2.5
Correct answer is option 'D'. Can you explain this answer?

Discharge through a triangular notch/weir is given by:
Where,
H = height of liquid above apex of the notch
θ = Angle of notch
Cd = Coefficient of discharge

The volumetric change of the fluid caused by a resistance is ________
  • a)
    Volumetric strain
  • b)
    Adhesion
  • c)
    Compressibility
  • d)
    Volumetric index
Correct answer is option 'C'. Can you explain this answer?

Dhruv Dasgupta answered
In fluids, Compressibility is a measure of the relative volume change of a fluid as a response to as pressure change
Where β Compressibility
ρ density of a fluid
p ⇒ pressure acting

Critical-depth meter is used to measure _____.
  • a)
    Discharge in an open channel
  • b)
    Hydraulic jump
  • c)
    Depth of flow in channel
  • d)
    Depth of channel
Correct answer is option 'A'. Can you explain this answer?

Anmol Saini answered
For a given value of specific energy, the critical depth gives the greatest discharge in an open channel, or conversely, for a given discharge, the specific energy is a minimum for the critical depth. So at a control section, the discharge can be calculated once the depth is known.
The critical depth is given as,

If the particles of a fluid attain such velocities that vary from point to point in magnitude and direction as well as from instant, the flow is _______.
  • a)
    Uniform flow
  • b)
    Steady flow
  • c)
    Turbulent flow
  • d)
    Laminar flow
Correct answer is option 'C'. Can you explain this answer?

In fluid dynamics, turbulent flow is characterized by the irregular movement of particles of the fluid. In contrast to laminar flow the fluid does not flow in parallel layers, the lateral mixing is very high, and there is a disruption between the layers. In turbulent flow the speed of the fluid at a point is continuously undergoing changes in both magnitude and direction.

Which manometer is called as simple monometer?
  • a)
    Micro manometer
  • b)
    U-tube
  • c)
    Differential
  • d)
    Piezometer
Correct answer is option 'D'. Can you explain this answer?

A simple manometer consists of a glass tube having one of its ends connected to a point where pressure is to be measured and another end remains open to atmosphere. Common types of simple manometers are:
  • Piezometer
  • U-tube Manometer
  • Single Column Manometer
Differential Manometers measure difference of pressure between two points in a fluid system and cannot measure the actual pressures at any point in the system. It consists of a U-tube, containing a heavy liquid, whose two ends are connected to the points whose difference of pressure is to be measured.
  • Upright U-Tube manometer
  • Inverted U-Tube manometer
  • Inclined Differential manometer
  • Micro manometer

Kinematic viscosity of air at 20°C is given to be 1.6 × 10-5 m2/s. Its kinematic viscosity at 70°C will be approximately
  • a)
    2.2 × 10-5 m2/s
  • b)
    1.6 × 10-5 m2/s
  • c)
    1.2 × 10-5 m2/s
  • d)
    3.2 × 10-5 m2/s
Correct answer is option 'A'. Can you explain this answer?

Shraddha Datta answered
Dynamic viscosity of gases increase with temp μ∝T−−√μ∝T
Density of gases decreases with increase in temp ρ∝
T1 = 20 + 273 = 293 K   T2 = 70 + 273 = 343 K
ν1 = 1.6 × 10-5 m2/s       ν2 = ?

What is the specific gravity of a fluid whose specific weight is 7.85 kN/m3?
  • a)
    0.8
  • b)
    1
  • c)
    1.2
  • d)
    1.6
Correct answer is option 'A'. Can you explain this answer?

Anirban Khanna answered
Specific weight of oil/specific weight of water.
I) SPECIFIC WEIGHT OF WATER = 9.81 KN/m3.

7.85 /9.81 = 0.8 unit less.

An orifice is said to be large, if
  • a)
    the size of the orifice is large
  • b)
    the velocity of the flow is large
  • c)
    the available head of liquid is more than 5 times the height of orifice
  • d)
    the available head of liquid is less than 5 times the height of orifice
Correct answer is option 'D'. Can you explain this answer?

An orifice is a small aperture through which the fluid passes. The thickness of an orifice in the direction of flow is very small in comparison to its other dimensions. An orifice is said to be large, if the available head of liquid is less than 5 times the height of orifice.

A fluid when acted upon by a shear stress will deform
  • a)
    When the applied shear stress is greater than the weight of the fluid
  • b)
    When the applied shear stress is greater than the viscous strength of the fluid
  • c)
    When the applied shear stress is greater than the yield strength of the fluid
  • d)
    Independent of rate of shear strain
Correct answer is option 'B'. Can you explain this answer?

Shear Stress and Deformation in a Fluid

The given question asks when a fluid will deform under the action of a shear stress. Let's examine the options and explain why option 'B' is the correct answer.

Option A: When the applied shear stress is greater than the weight of the fluid
This option is not correct because the weight of the fluid is not directly related to its deformation under shear stress. The weight of the fluid only affects its behavior under gravity, not under shear stress.

Option B: When the applied shear stress is greater than the viscous strength of the fluid
This option is correct. When a fluid is subjected to shear stress, its response depends on its viscous strength. Viscosity is a measure of a fluid's resistance to flow. When the applied shear stress exceeds the viscous strength of the fluid, it will deform and flow.

Option C: When the applied shear stress is greater than the yield strength of the fluid
This option is not applicable to fluids. Yield strength is a property of solid materials and refers to the stress at which plastic deformation begins. Fluids, on the other hand, do not exhibit yield strength as they can continuously deform under shear stress without undergoing plastic deformation.

Option D: Independent of the rate of shear strain
This option is not correct. The rate of shear strain refers to the speed at which the fluid is being deformed. The deformation response of a fluid under shear stress is highly dependent on the rate of shear strain. Different fluids may exhibit different behaviors at different shear strain rates.

Conclusion:
When a fluid is acted upon by a shear stress, it will deform and flow when the applied shear stress is greater than the viscous strength of the fluid. This behavior is due to the fluid's resistance to flow, known as its viscosity. The weight of the fluid and the yield strength of the fluid are not directly related to its deformation under shear stress. Additionally, the rate of shear strain has a significant impact on the fluid's deformation response.

If for a fluid in motion, the pressure at a point is same in all directions, then the fluid is
  • a)
    A real fluid
  • b)
    A Newtonian fluid
  • c)
    An ideal fluid
  • d)
    A Non-Newtonian fluid
Correct answer is option 'C'. Can you explain this answer?

An ideal fluid is a fluid that has several properties including the fact that it is:
Incompressible - the density is constant with respect to pressure.
Irrotational - the flow is smooth, no turbulence.
Nonviscous - (Inviscid) fluid has no internal friction (η = 0)

Bluff body is the body of such a shape that pressure drag as compared to friction drag is
  • a)
    same
  • b)
    more
  • c)
    less
  • d)
    zero
Correct answer is option 'B'. Can you explain this answer?

Bluff Body and Pressure Drag

Bluff Body: A bluff body is a three-dimensional object that has a blunt shape and has a high drag coefficient. Examples of bluff bodies are cylinders, spheres, cubes, and other shapes that have a large cross-sectional area perpendicular to the flow direction.

Pressure Drag: Pressure drag is the force that opposes the motion of a body through a fluid due to the pressure difference between the front and rear of the body. It is caused by the separation of the fluid flow from the surface of the body, resulting in a low-pressure region behind the body.

Explanation

Bluff bodies have a high drag coefficient because they create a large wake behind them, which creates a low-pressure region. The pressure difference between the front and rear of the body causes the pressure drag. As the cross-sectional area of the body increases, the pressure drag also increases. The friction drag is also present in bluff bodies, but it is relatively small compared to the pressure drag.

Bluff bodies have a higher pressure drag coefficient than streamlined bodies, which have a low drag coefficient due to their streamlined shape, and the fluid can flow smoothly over them without any separation. In other words, the pressure drag of a bluff body is more than the friction drag.

Conclusion

In conclusion, the correct answer to the question is option B) more. Bluff bodies have a high drag coefficient due to their shape, resulting in a larger wake behind them, creating a low-pressure region. As a result, the pressure drag is higher than the friction drag.

For Bernoulli’s equation to remain valid, which of the following is NOT required?
  • a)
    Incompressible medium
  • b)
    Steady flow
  • c)
    Irrotational flow
  • d)
    Ideal gas fluid
Correct answer is option 'D'. Can you explain this answer?

Niharika Iyer answered
The concept of Bernoulli's principle, named after Swiss mathematician Daniel Bernoulli, is fundamental in fluid dynamics. It states that as the speed of a fluid increases, its pressure decreases, and vice versa.

Bernoulli's principle is based on the conservation of energy principle, which states that the total energy of a system remains constant. In the case of fluid flow, the total energy is the sum of the potential energy (due to the fluid's height) and the kinetic energy (due to the fluid's motion).

According to Bernoulli's principle, when a fluid flows through a pipe or a constriction, the speed of the fluid increases in the narrower region, and as a result, the pressure decreases. This is because the total energy of the fluid must remain constant, and since the kinetic energy increases, the potential energy (pressure) must decrease.

One practical example of Bernoulli's principle is the operation of an airplane wing. The shape of the wing is designed such that the airflow over the top surface is faster than the airflow underneath. As a result, the pressure on the top surface is lower, creating lift and allowing the airplane to stay airborne.

Bernoulli's principle is also applicable in various other areas, such as the flow of blood in arteries, the operation of a carburetor in an internal combustion engine, and even in the flight of a frisbee. It is a fundamental principle in understanding and analyzing fluid flow and is widely used in engineering and physics.

Mercury is used in the barometer because:
  • a)
    it is a perfect fluid
  • b)
    its volume changes with temperature
  • c)
    it is a liquid metal
  • d)
    it gives less height of column for high pressure
Correct answer is option 'D'. Can you explain this answer?

Dishani Desai answered
Mercury is used in the barometer because it is a high-density fluid which gives less height of column for high pressures. A barometer using water, for instance, would need to be 13.6 times taller than a mercury barometer to obtain the same pressure difference. This is because mercury is 13.6 times denser than water.

Friction drag is generally larger than the pressure drag in _______.
  • a)
    Flow past a sphere
  • b)
    Flow past a cylinder
  • c)
    Flow past an airfoil
  • d)
    Flow past a thin sheet
Correct answer is option 'C'. Can you explain this answer?

Flow past an airfoil
Friction drag is generally larger than pressure drag in flow past an airfoil due to the complex flow patterns and separation that occur around the airfoil shape. When air flows over an airfoil, the boundary layer near the surface of the airfoil experiences shear stress, resulting in friction drag. This friction drag is caused by the viscosity of the air and the resistance it exerts on the surface of the airfoil.

Pressure drag
On the other hand, pressure drag is related to the pressure difference between the front and rear of the airfoil. This pressure difference creates resistance to the flow of air and contributes to the overall drag force experienced by the airfoil. In flow past an airfoil, the pressure drag is generally less significant compared to the friction drag.

Effect of shape
The shape of an airfoil, with its curved surfaces and varying thickness, contributes to the development of turbulent boundary layers and separation points, which in turn increase the friction drag. The pressure distribution around an airfoil also plays a role in determining the overall drag characteristics.

Conclusion
Overall, in flow past an airfoil, the friction drag is typically larger than the pressure drag due to the complex flow phenomena and boundary layer effects associated with the airfoil shape. Understanding these drag components is essential for optimizing the design and performance of airfoil shapes in various engineering applications.

An accumulator is a device to store
  • a)
    Sufficient quantity of liquid to compensate the change in discharge 
  • b)
    Sufficient energy to derive the machine when the normal energy source does not function
  • c)
    Sufficient energy in case of machines which work intermittently to supplement the discharge from the normal source
  • d)
    Liquid which otherwise would have gone to waste
Correct answer is option 'C'. Can you explain this answer?

Sravya Tiwari answered
Explanation:

An accumulator is a device used in hydraulic systems to store and release energy. It acts as a supplementary energy source in case of machines that work intermittently or require additional energy to supplement the discharge from the normal source.

1. Purpose of an Accumulator:
- The main purpose of an accumulator is to store energy in the form of pressurized fluid (usually hydraulic fluid) and release it when needed.
- It helps in maintaining a steady and constant fluid pressure in the hydraulic system, compensating for any fluctuations in demand or supply.

2. Working Principle:
- The accumulator consists of a cylindrical chamber divided into two sections by a movable piston or bladder.
- One section is filled with hydraulic fluid, while the other section is filled with an inert gas (usually nitrogen) under pressure.
- When the hydraulic system is operating, the hydraulic fluid enters the accumulator, compressing the gas and storing energy.
- When the system requires additional energy, the compressed gas expands, forcing the stored hydraulic fluid back into the system.

3. Types of Accumulators:
There are different types of accumulators, including:
- Piston Accumulator: It uses a piston to separate the gas and fluid chambers.
- Bladder Accumulator: It uses a flexible bladder to separate the gas and fluid chambers.
- Diaphragm Accumulator: It uses a diaphragm to separate the gas and fluid chambers.

4. Use in Intermittent Machines:
- Intermittent machines, such as presses, require a high amount of energy during specific operations but operate intermittently.
- The accumulator helps supply the required energy during peak demand periods when the normal energy source may not be sufficient.
- It ensures that the machine operates smoothly and efficiently without overloading the primary power source.

5. Supplementing Discharge:
- In some machines, the discharge from the normal energy source may not be sufficient to meet the desired output or performance.
- The accumulator acts as a supplement by providing additional energy to meet the high-demand periods.
- It helps in improving the overall performance and efficiency of the machine.

In conclusion, an accumulator is a device that stores energy in hydraulic systems and releases it when needed. It is used in machines that work intermittently or require additional energy to supplement the discharge from the normal energy source. By providing supplementary energy, the accumulator ensures smooth operation and improved performance of the machines.

Bernoulli’s equation is applied to
  • a)
    Venturimeter
  • b)
    Orifice meter
  • c)
    Pitot tube meter
  • d)
    All of the above
Correct answer is option 'D'. Can you explain this answer?

Kavya Mehta answered
Bernoulli's equation states that the summation of pressure head, kinetic head and datum/potential head is constant for steady, incompressible, irrotational and non-viscous flow. In other words an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy i.e. the total energy of a flowing system remain constant until external force is applied. So Bernoulli’s equation refers to conservation of energy.
All flow measuring devices like Venturimeter, Orifice meter, Pitot tube meter works on the Bernoulli’s theorem.

The velocity potential which follow the equation of continuity is ________ 
  • a)
    x2y
  • b)
    x2- y2
  • c)
    cos x
  • d)
    x2 + y2
Correct answer is option 'B'. Can you explain this answer?

Yash Das answered
The equation of continuity is a fundamental principle in fluid mechanics that states that the mass flow rate of an incompressible fluid remains constant along a streamline. In other words, the rate at which mass enters a given region must equal the rate at which mass leaves that region.

The velocity potential is a scalar field that can be used to describe the motion of a fluid. It is defined as the scalar function ϕ such that the velocity vector field V is the gradient of ϕ, i.e., V = ∇ϕ. The velocity potential is useful because it simplifies the equations of motion for an incompressible fluid.

The equation of continuity can be expressed in terms of the velocity potential as follows:

∇·V = ∇·(∇ϕ) = ∇²ϕ = 0

This is the Laplace equation for the velocity potential. In two dimensions, this equation reduces to:

(∂²ϕ/∂x²) + (∂²ϕ/∂y²) = 0

Now, let's analyze the given options:

a) x²y: This does not satisfy the Laplace equation, as the second derivative with respect to x is non-zero.

b) x² - y²: This does satisfy the Laplace equation, as the second derivatives with respect to x and y cancel each other out.

c) cos x: This does not satisfy the Laplace equation, as it is not a harmonic function.

d) x²y²: This does not satisfy the Laplace equation, as the second derivative with respect to y is non-zero.

Therefore, the correct option is b) x² - y², as it satisfies the Laplace equation and hence represents a velocity potential that follows the equation of continuity.

Kinematic viscosity of water in comparison to mercury is _____.
  • a)
    Higher
  • b)
    Lower
  • c)
    Same
  • d)
    Higher/lower depending on temperature
Correct answer is option 'A'. Can you explain this answer?

The dynamic viscosity of mercury (1.52 cp) is greater than water (0.894 cp). The kinematic viscosity is the dynamic viscosity divided by the density. Mercury is a lot denser than water, so its kinematic viscosity is lower than the kinematic viscosity of water.

The force exerted by the jet on fixed plate shown in the figure below is equal to:
  • a)
    aV2 sin θ
  • b)
    ρav2 sin θ
  • c)
    ρav2 cos θ
     
  • d)
    aV2 tan θ
Correct answer is option 'B'. Can you explain this answer?

Divya Banerjee answered
Let us apply the impulse-momentum equation in the direction normal to the plate 
Fn=ρaV(Vsinθ−0)=ρaV2sinθFx=Fnsinθ=ρV2sinθ×sinθ=ρaV2sin2θFy=Fncosθ=ρV2sinθ×cosθ=ρaV2sin2θcosθ

Which one of the following is true about ideal fluid?
  • a)
    It is compressible 
  • b)
    It is incompressible
  • c)
    It has high shear force
  • d)
    It has high value of viscosity
Correct answer is option 'B'. Can you explain this answer?

Ideal fluid is Incompressible and it has zero value of shear force. Ideal fluid does not actually exist in nature, but sometimes used for fluid flow problems. An ideal fluid is a fluid that has several properties including the fact that it is :
Incompressible – the density is constant
Irrotational – the flow is smooth, no turbulence
Nonviscous – (Inviscid) fluid has no internal friction

Which of the following is CORRECT about the viscosity of gas?
  • a)
    Inversely proportional to the temperature
  • b)
    Increases with an increase in the temperature
  • c)
    Independent of pressure
  • d)
    Independent of temperature
Correct answer is option 'B'. Can you explain this answer?

The correct answer is option 'B': Viscosity of gas increases with an increase in temperature.

Viscosity is the measure of a fluid's resistance to flow. It is a property that determines the internal frictional resistance of a gas to flow when subjected to shear stress. The viscosity of a gas is influenced by various factors, including temperature and pressure.

Effect of Temperature on Viscosity:
When the temperature of a gas increases, the viscosity also increases. This is because as the temperature rises, the kinetic energy of the gas molecules also increases. The increased kinetic energy causes the gas molecules to move faster and collide with each other more frequently and with greater force. These collisions result in increased intermolecular interactions and stronger bonds between the gas molecules, leading to an increase in viscosity.

Explanation:
1. Gas Molecules and Kinetic Energy:
- Gas molecules are in constant random motion due to their kinetic energy.
- The kinetic energy of gas molecules is directly related to temperature. As temperature increases, the kinetic energy of the gas molecules also increases.
- This increased kinetic energy causes the gas molecules to move faster and collide more frequently.

2. Collisions and Intermolecular Interactions:
- When gas molecules collide, they exert forces on each other.
- These collision forces are responsible for the internal frictional resistance within the gas, which determines its viscosity.
- At higher temperatures, the increased kinetic energy of the gas molecules leads to more frequent and stronger collisions.
- These collisions result in increased intermolecular interactions and stronger bonds between the gas molecules.

3. Increased Viscosity:
- The increased intermolecular interactions and stronger bonds between gas molecules at higher temperatures result in an increase in viscosity.
- The gas molecules experience greater resistance to flow due to the increased intermolecular forces.
- This increased resistance leads to a higher viscosity of the gas.

Conclusion:
In summary, the correct option is 'B': Viscosity of gas increases with an increase in temperature. This is because the increased kinetic energy of gas molecules at higher temperatures leads to more frequent and stronger collisions, resulting in increased intermolecular interactions and higher viscosity.

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