250+ TOP MCQs on Types of Flow Lines and Answers

Fluid Mechanics Multiple Choice Questions on “Types of Flow Lines”.

1. What will be the shape of the pathline for an one-dimensional flow be like?
a) straight line
b) parabolic
c) hyperbolic
d) elliptical
Answer: a
Clarification: A pathline is the path followed by a particle in motion. For an one-dimensional flow, the fluids move in only one dimension (say x). Hence the pathline will also be a straight line (along that direction).

2. Which of the following is correct?
a) Pathlines of two particles in an one-dimensional flow can never intersect
b) Pathlines of two particles in an one-dimensional flow can never intersect if the two particles move along the same direction
c) Pathlines of two particles in an one-dimensional flow can intersect only if the two particles move along the same direction
d) Pathlines of two particles in an one-dimensional flow can intersect only if the two particles move along different directions
Answer: c
Clarification: The pathline of a particle in an one-dimensional flow is a straight line along the direction it moves. If the two particles move along the same direction, their pathlines will be parallel to each other and will never intersect.

3. What is the maximum number of times the pathlines of two particles can intersect in an one dimensional flow?
a) 0
b) 1
c) 2
d) infinite
Answer: b
Clarification: The pathline of a particle in an one-dimensional flow is a straight line along the direction it moves. When two particles move in the same direction, their pathline will never intersect and when they move in different directions, their pathlines will intersect only once.

4. The velocity of a point in a flow is
a) along the streamline
b) tangent to the streamline
c) along the pathline
d) tangent to the pathline
Answer: b
Clarification: A pathline is the path followed by a particle in motion whereas a streamline is an imaginary line within the flow such that the tangent at any point on it indicates the velocity at that point.

5. Which of the following is correct?
a) A streamline can intersect itself and two streamlines can cross
b) A streamline cannot intersect itself but two streamlines can cross
c) A streamline can intersect itself but two streamlines cannot cross
d) A streamline cannot intersect itself and two streamlines cannot cross
Answer: d
Clarification: A streamline is defined as an imaginary line within the flow such that the tangent at any point on it indicates the velocity at that point. At a point, there can only be one direction of velocity. Hence, neither can a streamline intersect itself nor can two streamlines cross each other.

6. If three sets of streamlines A, B and C are considered across section 1-2, which set will represent accelerated flow from 1 to 2?
fluid-mechanics-questions-answers-types-flow-lines-q3
a) A
b) B
c) C
d) None of the sets
Answer: a
Clarification: Streamline spacing varies inversely as the velocity. Higher the velocity, closer will be the streamlines. Hence, converging of streamlines from 1 to 2 will indicate accelerated flow as in set A.

7. The streamlines of the particles in a flow are recorded. If the streamline distribution remain the same even after sometime, what type of flow can it be?
a) steady
b) unsteady
c) uniform
d) non-uniform
Answer: a
Clarification: A streamline is defined as an imaginary line within the flow such that the tangent at any point on it indicates the velocity at that point. In a steady flow, the velocity of the particles is constant with time. Hence, the streamlines remain the same even after sometime.

8. If the streamlines of the particles in a flow are parallel to each other, what type of flow can it be?
a) steady
b) unsteady
c) uniform
d) non-uniform
Answer: c
Clarification: Streamline spacing varies inversely as the velocity. In a uniform flow, the velocities of the particles are the same at every instant of time. Hence, the spacing between their streamlines will be the same. In other words, the streamlines will be parallel.

9. Which of the following is correct?
a) the movement of fluid mass can either be along the streamlines or across them
b) the movement of fluid mass can be along the streamlines but never across them
c) the movement of fluid mass can never be along the streamlines but can be across them
d) the movement of fluid mass can neither be along the streamlines or across them
Answer: b
Clarification: A streamline is defined as an imaginary line within the flow such that the tangent at any point on it indicates the velocity at that point. Flow can only be along the velocity, never perpendicular to it. Hence, the movement of fluid mass can only be along the streamlines and never across them.

10. Which of the following is correct?
a) pathlines are concerned with a number of particles at the same instant and streamlines with a particular particle at successive instants of time
b) pathlines are concerned with a particular particle at successive instants of time and streamlines with a number of particles at the same instant
c) both pathlines and streamlines are concerned with a number of particles at the same instant
d) both pathlines and streamlines are concerned with a particular particle at successive instants of time
Answer: b
Clarification: A pathline is the path followed by a particle in motion whereas a streamline is an imaginary line within the flow such that the tangent at any point on it indicates the velocity at that point. Thus, pathlines are concerned with a particular particle at successive instants of time and streamlines with a number of particles at the same instant.

11. The path taken by the smoke coming out of a chimney (in concentric circles) represents a
a) pathline
b) streamline
c) streakline
d) streamtube
Answer: c
Clarification: A pathline is the path followed by a particle in motion whereas a streamline is an imaginary line within the flow such that the tangent at any point on it indicates the velocity at that point. A streamtube is a collection of streamlines. A streakline is a curve which gives an instantaneous picture of the location of the fluid particleswhich have passed through a given point.
Hence, the path taken by the smoke coming out of a chimney (in concentric circles) will represent streaklines.

12. Which of the following is correct?
a) In steady flow, pathlines and streamlines are identical
b) In steady flow, pathlines and streaklines are identical
c) In steady flow, streaklines and streamlines are identical
d) In steady flow, pathline, streamlines and streaklines are all identical
Answer: d
Clarification: In case of a steady flow, the velocity at a point remains constant with time. Thus, there will be no geometrical distinction between the pathlines, streamlines and streaklines.

13. Which of the following is correct?
a) There will be no flow across the streamtube
b) There will be no flow along the streamtube
c) There will be no flow both across the streamtube and along it
d) There will be flow both across the streamtube and along it
Answer: a
Clarification: Streamtube is a fluid mass bounded by a group of streamlines. Since, the movement of the fluid mass can only be along the streamlines and never across them, there will be no flow across the streamtube.

250+ TOP MCQs on Classification of Notches and Weirs and Answers

Fluid Mechanics Multiple Choice Questions on “Classification of Notches and Weirs”.

1. A notch is a device used to measure the turbulence of the flowing liquid directly.
a) True
b) False
Answer: b
Clarification: A notch is a device used to measure the flow rate of the flowing liquid, directly.

2. The weir is an attachable structure made up of thermoplastic.
a) True
b) False
Answer: b
Clarification: The weir is a permanent masonry structure made up of concrete.

3. The notch is bigger in size than wier.
a) True
b) False
Answer: b
Clarification: The weir is bigger in size than notch.

4. The MoM (Material of Manufacture) of notch is,
a) Thermoplastic
b) Metals
c) Fibre
d) Wood
Answer: b
Clarification: The MoM (Material of Manufacture) of notch is Metals.

5. Which of the following is not a way of classifying notches or weirs?
a) Based on the shape of opening
b) Based on the effect of the sides on the nappe
c) Based on the shape of the crest
d) Based on the effect of the sides on the crest
Answer: d
Clarification: There is no such way of classification.

6. The nature of discharge is also a way of classifying notches.
a) True
b) False
Answer: b
Clarification: The nature of discharge is also a way of classifying notches.

7. Which of the following is not a way of classifying based on the shape of opening?
a) Rectangular notch
b) Circular notch
c) Trapezoidal notch
d) Stepped notch
Answer: b
Clarification: Circular notch is not a way of classifying based on the shape of opening.

8. Trapezoidal weir has another popular name. What is it?
a) Cipolletti weir
b) Hagen Poiseuille’s weir
c) Reynold’s weir
d) Euler’s weir
Answer: a
Clarification: Trapezoidal weir is also called Cipolletti weir.

9. What is not the way of classifying weir based on their shape of crest?
a) Sharp crested weir
b) Broad crested weir
c) Narrow crested weir
d) Trapezoidal crested weir
Answer: d
Clarification: Trapezoidal crested weir is not the way of classifying weir based on their shape of crest.

10. What is not the way of classifying weir based on the emerging nappe?
a) Weir with end contraction
b) Weir without end contraction
c) Weir contraction at the beginning
d) Weir with absence of end contraction
Answer: c
Clarification: This is not the way of classifying weir based on the emerging nappe.

250+ TOP MCQs on Water Hammer in Pipes and Answers

Fluid Mechanics Multiple Choice Questions on “Water Hammer in Pipes”.

1. Where is a water hammer developed?
a) Reservoir
b) Penstock
c) Turbine blades
d) Pipe line
Answer: b
Clarification: Water hammer is developed in a penstock. It is developed due to the reduction in load on the generator. This reduction causes the governor to close the turbine gates and thus creating an increased pressure in the penstock.

2. Which among the following is true for hydroelectric power plants?
a) Operating cost is low and initial cost is high
b) Both operating and initial cost are high
c) Both operating and initial cost are low
d) Operating cost is high and initial cost is low
: a
Clarification: For a hydroelectric power plant, the operating cost is low and the initial cost is high. The initial cost is high due to the large area required for construction. Since, the fuel cost is comparatively cheaper, the operating cost is low.

3. The power output of the turbine in a hydroelectric plant depends on______________
a) Type of dam and its system efficiency
b) Discharge and system efficiency
c) Type of turbine and type of dam
d) Type of turbine and area of the reservoir
Answer: b
Clarification: The power output of the turbine in a hydroelectric plant depends on the system efficiency and discharge. In a hydroelectric power plant, the discharge and head are directly proportional to its system efficiency.

4. Water hammer is developed in which power plant?
a) Solar
b) Nuclear
c) Hydro
d) Wind
Answer: c
Clarification: Water hammer is defined as a pressure surge or wave caused in a pipeline. This happens due to the forceful stop of the fluid in motion. It happens mainly when the valve closes suddenly in a pipeline system. Thus, option Hydro is the right choice.

5. Which among the following are commercial sources of energy?
a) Solar energy
b) Animal wastes
c) Agricultural wastes
d) Wood
Answer: a
Clarification: Solar energy is a commercial source of energy among the following options. All energy sources that serve a commercial purpose are called as commercial sources of energy. Some good examples are Solar, tidal, wind, geothermal, wave etc.

6. Which is the most suitable place to build a hydroelectric power plant?
a) Deserts
b) Grasslands
c) Hilly areas
d) Underground
Answer: c
Clarification: Hilly areas are the most preferred areas to build a hydroelectric power plant. Hilly areas are preferred because dams play an important role. Building of dams in hilly areas is easier because large reservation can be obtained.

7. In a hydroelectric power plant, where is the penstock used?
a) Between dam and the turbine
b) Between turbine and discharge drain
c) Turbine and heat exchanger
d) Heat exchanger and fluid pump
Answer: a
Clarification: Hydroelectric powerplants play an important role in energy conversion, to produce electricity. It is a commercial method. Penstock is closed conduit. It is connected in between the dam and the turbine in the hydro station.

8. Which among the following is used as a regulating reservoir?
a) Reservoir
b) Spillways
c) Forebay
d) Penstock
Answer: c
Clarification: Forebay serves as a regulating reservoir. It stores water on a temporary basis, during light load period. It has got an enlarged body of water situated above the intake. This intake pipe is used to store water on a temporary basis.

9. Gross head is defined as______
a) Difference of flow of object
b) Difference of flow of air
c) Difference of flow of water
d) Difference of water level between the head race and tail race
Answer: d
Clarification: Gross head is defined as the difference of water level between the head race (the level in storage) and the tail race. Gross head can be denoted as (H). It plays an important role in determining the power losses in the pipeline.

10. What is the function of a surge tank?
a) It causes water hammer
b) Produces surge in the pipeline
c) Relieves water hammer
d) Supplies water at constant pressure
Answer: c
Clarification: The main purpose of a surge tank is to relieve water hammer pressure in the penstock. It absorbs the changes in the water requirements. After absorbing the water changes, it reduces the water hammer and the negative pressure developed in the pressure stock.

11. Hydro-graph is a graph that shows________
a) Load curve
b) Energy curve
c) Mass curve
d) Volume curve
Answer: a
Clarification: Hydrograph is a graph that indicates the power available at different streams of water. It helps us determine the load curve. This load curve is used to determine the electrical power so developed in the hydroelectric power plant.

12. What is the function of a pump storage scheme?
a) Improve power factor
b) Improve mass factor
c) Improve plant capacity factor
d) Improve volume factor
Answer: c
Clarification: In a hydroelectric power plant, the main function of pump storage scheme is to make more water available during any deficiency. It strengthens the economic factor of the hydroelectric power plant.

250+ TOP MCQs on Basic Equations of Compressible Flow and Answers

Fluid Mechanics Multiple Choice Questions on “Basic Equations of Compressible Flow”.

1. Which among the following is the formula for continuity equation?
a) ρ(x)V(x)A(x) = Constant
b) A(x) = Constant
c) ρ(x)V(x) = constant
d) P(x)V(x) = constant
Answer: a
Clarification: Continuity equation for a steady one-dimensional flow is ρ(x)V(x)A(x) = Constant. Where ρ = Density of the fluid flow. V = the volume of the fluid flow. And, A = Area of the fluid flow through the cross section of pipe.

2. What is v2/2 in the equation for a control volume in space?
a) Potential energy per unit mass
b) Kinetic energy per unit mass
c) Thermal energy per unit mass
d) Mechanical energy per unit mass
Answer: b
Clarification: According to the first law of thermodynamics, the equation for control volume in space is derived. v2/2 in the equation for a control volume in space is the kinetic energy per unit mass. Therefore, option b is the right choice.

3. Sum of enthalpy and kinetic energy remains a constant in __________
a) Polytropic flow
b) Isentropic flow
c) Adiabatic flow
d) Mechanical flow
Answer: c
Clarification: The sum of enthalpy and kinetic energy remains a constant in adiabatic flow. It performs a similar role that internal energy performs during a nonflowing system. Thus, the correct option is Adiabatic flow.

4. Eddy viscosity is a turbulent transfer of _________
a) Fluid
b) Heat
c) Momentum
d) Pressure
Answer: c
Clarification: Eddy viscosity is a turbulent transfer of momentum by eddies. It gives rise to an internal fluid friction. It is in analogous to the action of molecular viscosity in laminar fluid flow. Eddy viscosity takes place on a large scale.

5. Which among the following is the equation for Bernoulli?
a) Tds = dh – vdp
b) Tds = dh
c) Tds = dh + vdp
d) Tds = dh/vdp
Answer: a
Clarification: For an adiabatic frictionless flow, the Bernoulli’s equation is identical to its energy equation. The Bernoulli’s equation after integrating changes to Tds = dh – vdp. Thus, the correct option is a.

6. For an isentropic flow ________
a) Enthalpy = 0
b) Entropy = 0
c) Pressure = 0
d) Temperature = 0
Answer: b
Clarification: For an isentropic flow in Tds = dh – vdp, the entropy reduces to zero. That is, the change in entropy value for any isentropic flow (ds)=0. Thus, the correct option is Entropy = 0.

7. Which among the following is Euler’s equation?
a) VdV/dh = 0
b) VdV – dh = 0
c) VdV + dh = 0
d) dh – V = 0
Answer: c
Clarification: The Euler’s equation is given as VdV+dh=0. Where V = volume of the fluid flow and h = enthalpy of the fluid flow. This is identical to the adiabatic form of the energy equation. Thus, the option is VdV + dh = 0.

8. Which among the following is the formula for momentum principle?
a) pv = 0
b) p1p2 = 0
c) P1V1 + P2V2 = 0
d) P1A1+P2A2 + F = mV2mV1
Answer: d
Clarification: For a finite control of volume between two sections, section 1 and section 2, the momentum principle is P1A1 + P2A2 + F = mV2mV1. Where F = component of resultant force exerted on the fluid walls.

9. Define Stagnation temperature.
a) The temperature at zero velocity
b) The temperature at zero pressure
c) The temperature at zero heat transfer
d) The temperature at zero volume
Answer: a
Clarification: The stagnation point is the point at which the properties of the fluid are obtained at a local flow where the velocity of the fluid is zero isentropically. Thus, the correct choice for stagnation temperature is ‘a’.

10. What is the viscosity of water at 30oC?
a) 80.1
b) 0.801
c) 801
d) 0.081
Answer: b
Clarification: A graph is plotted with temperature in the x-axis and dynamic viscosity in the y-axis. With the increase in pressure the viscosity decreases. It corresponds to an informal concept of thickness.

250+ TOP MCQs on Fluid Pressure and Answers

Fluid Mechanics Multiple Choice Questions on “Fluid Pressure”.

1. What is the pressure in Pascals at a depth of 1m below the water surface?
a) 98100 Pa
b) 980 Pa
c) 98 Pa
d) 1 Pa
Answer: a
Clarification: It’s the summation of weights on top of the water surface. In this case, it is the weight of the atmosphere and water above 1m. [Formula: P (depth) = Patm +(density of water*gravitational constant*depth)].

2. 15 bar equals to __________ Pascals.
a) 105Pa
b) 1.5 x 106 Pa
c) 100 Pa
d) 1000 Pa
Answer: b
Clarification: Bar is a metric unit of pressure, but it does not fall under the SI units. One bar is exactly equal to a 100,000 Pascals. This value is taken from the atmospheric pressure on the earth at sea level.

3. The pressure at any given point of a non-moving fluid is called the ____________
a) Gauge Pressure
b) Atmospheric Pressure
c) Differential Pressure
d) Hydrostatic Pressure
Answer: d
Clarification: Hydrostatic pressure varies with the increase in depth. Hydrostatic pressure is measured from the surface of the fluid because of the increasing weight of the fluid. The fluid exerts a downward force from the surface of water thus making it a non-moving fluid.

4. The device used to measure the fluid pressure is _____________
a) Hygrometer
b) Calorimeter
c) Manometer
d) Thermometer
Answer: c
Clarification: Manometer is the most preferred measuring device as the pressure is measured by difference in the column heights of the manometer. It is expressed in terms of inches or centimeters of fluid making it easier for the conversion process.

5. What type of liquids are measured using a manometer?
a) Heavy liquids
b) Medium Liquids
c) Light Liquids
d) Heavy and light liquids
Answer: c
Clarification: Measurement of liquid in a manometer takes place through differential pressures by balancing the weight. Thus, it is easier for the manometer to measure liquids of lesser density than the heavier ones. Example of a light liquid is Water.

6. Which among these devices are the best suited for the measurement of high pressure liquids with high accuracy?
a) Dead Weight Gauge
b) Vacuum Gauge
c) Manganin wire pressure
d) Ionization Gauge
Answer: c
Clarification: Manganin wire is the most suitable measurement device for high pressure liquids. It has a high stability and durability on a long term basis. It also has a high hydrostatic pressure sensitivity and low strain sensitivity.

7. How do we measure the flow rate of liquid?
a) Coriolis method
b) Dead weight method
c) Conveyor method
d) Ionization method
Answer: a
Clarification: Coriolis concept of measurement of fluid takes place through the rotation with the reference frame. It is an application of the Newton’s Law. The device continuously records, regulates and feeds large volume of bulk materials.

8. What is the instrument used for the automatic control scheme during the fluid flow?
a) Rotameters
b) Pulley plates
c) Rotary Piston
d) Pilot Static Tube
Answer: d
Clarification: Pilot static tube is a system that uses an automatic control scheme to detect pressure. It has several holes connected to one side of the device. These outside holes are called as a pressure transducer, which controls the automatic scheme during fluid flow.

9. Define Viscosity?
a) Resistance to flow of an object
b) Resistance to flow of air
c) Resistance to flow of fluid
d) Resistance to flow of heat
Answer: c
Clarification: Viscosity is developed due to the relative motion between two surfaces of fluids at different velocities. It happens due to the shear stress developed on the surface of the fluid.

10. What is the viscosity of water at 30oC?
a) 80.1
b) 0 .801
c) 801
d) 0.081
Answer: b
Clarification: A graph is plotted with temperature in the x-axis and dynamic viscosity in the y-axis. With the increase in pressure the viscosity decreases. It corresponds to an informal concept of thickness.

250+ TOP MCQs on Continuity Equation and Answers

Fluid Mechanics Multiple Choice Questions on “Continuity Equation”.

1. If a liquid enters a pipe of diameter d with a velocity v, what will it’s velocity at the exit if the diameter reduces to 0.5d?
a) v
b) 0.5v
c) 2v
d) 4v
Answer: d
Clarification: According to the Continuity Equation,

where a represents flow area, v represents flow velocity, i is for inlet conditions and o is for outlet conditions.
fluid-mechanics-questions-answers-continuity-equation-q1a

2. The continuity equation is based on the principle of
a) conservation of mass
b) conservation of momentum
c) conservation of energy
d) conservation of force
Answer: a
Clarification: According to the Continuity Equation, if no fluid is added or removed from the pipe in any length then the mass passing across different sections shall be the same. This is in accordance with the principle of conservation of mass which states that matter can neither be created nor be destroyed.

3. Two pipes of diameters d1 and d2 converge to form a pipe of diameter d. If the liquid flows with a velocity of v1 and v2 in the two pipes, what will be the flow velocity in the third pipe?
fluid-mechanics-questions-answers-continuity-equation-q3
Answer: d
Clarification: According to the Continuity Equation,

where a represents flow area, v represents flow velocity, i is for inlet conditions and o is for outlet conditions. Thus,
fluid-mechanics-questions-answers-continuity-equation-q2a

4. Two pipes of diameters d1 and d2 converge to form a pipe of diameter 2d. If the liquid flows with a velocity of v1 and v2 in the two pipes, what will be the flow velocity in the third pipe?
a) v1 + v2
b) v1 + v2/2
c) v1 + v2/4
d) 2(v1 + v2)
Answer: c
Clarification: According to the Continuity Equation,

where a represents flow area, v represents flow velocity, i is for inlet conditions and o is for outlet conditions. Thus,
fluid-mechanics-questions-answers-continuity-equation-q4a

5. Two pipes, each of diameter d, converge to form a pipe of diameter D. What should be the relation between d and D such that the flow velocity in the third pipe becomes double of that in each of the two pipes?
a) D = d
b) D = 2d
c) D = 3d
d) D = 4d
Answer: a
Clarification: According to the Continuity Equation,
fluid-mechanics-questions-answers-continuity-equation-q5
where a represents flow area, v represents flow velocity, i is for inlet conditions and o is for outlet conditions. Thus,
A1v1 + A2v2 = Av
d2v + d2v = D2v
D = d.

6. Two pipes, each of diameter d, converge to form a pipe of diameter D. What should be the
relation between d and D such that the
ow velocity in the third pipe becomes half of that in each
of the two pipes?
a) D = d/2
b) D = d/3
c) D = d/4
d) D = d/5
Answer: a
Clarification: According to the Continuity Equation,
fluid-mechanics-questions-answers-continuity-equation-q5
where a represents flow area, v represents flow velocity, i is for inlet conditions and o is for outlet conditions. Thus,
A1v1 + A2v2 = Av
d2v + d2v = Dv/2
d = D ⁄ 4.

7. In a two dimensional flow, the component of the velocity along the X-axis is u = ax2 + bxy + cy2.
If v = 0 at y = 0, what will be the velocity component in the Y-direction?
a) v = 2axy + by2
b) v = 2axy + b ⁄ 2 y2
c) v = -2axy – b ⁄ 2 y2
d) v = -axy – b ⁄ 2 y2
Answer: c
Clarification: According to the condition for continuity,
fluid-mechanics-questions-answers-continuity-equation-q7

8. In a two dimensional flow, the component of the velocity along the X-axis and the Y-axis are u = ax2 + bxy + cy2 and v = cxy. What should be the condition for the flow field to be continuous?
a) a + c = 0
b) b + c = 0
c) 2a + c = 0
d) 2b + c = 0
Answer: c
Clarification: According to the condition for continuity,

2ax + cx = 0
2a + c = 0.

9. In a two dimensional flow, the component of the velocity along the X-axis and the Y-axis are u = axy and v = bx2 + cy2. What should be the condition for the flow field to be continuous?
a) a + b = 0
b) a + c = 0
c) a + 2b = 0
d) a + 2c = 0
Answer: d
Clarification: The condition for the flow field to be continuous is:

ay + 2cy = 0
a + 2c = 0.

10. In a two dimensional flow, the component of the velocity along the X-axis and the Y-axis are u = ax2 + bxy and v = cxy +dy2. What should be the condition for the flow field to be continuous?
a) (a + b)x + (c + d)y = 0
b) (a + c)x + (b + d)y = 0
c) (2a + b)x + (c + 2d)y = 0
d) (2a + c)x + (b + 2d)y = 0
Answer: d
Clarification: The condition for the flow field to be continuous is:

2ax + cx + by + 2dy = 0
(2a + c)x + (b + 2d)y = 0.

11. In a two dimensional flow, the component of the velocity along the X-axis and the Y-axis are u = ax2 + bxy and v = bxy + ay2. The condition for the flow field to be continuous is
a) independent of the constants (a; b) but dependent on the variables (x; y)
b) independent of the variables (x; y) but dependent on the constants (a; b)
c) independent of both the constants (a; b) and the variables (x; y)
d) dependent on both the constants (a; b) and the variables (x; y)
Answer: a
Clarification: The condition for the flow field to be continuous is:

2ax + by + 2ay + bx = 0
x + y = 0
Hence, the condition for the flow field to be continuous is independent of the constants (a; b) and dependent only on the variables (x; y).

12. In a two dimensional flow, the component of the velocity along the X-axis and the Y-axis are u = ax + by and v = ax – by. For what condition will the flow field be continuous?
a) impossible
b) possible if a = b
c) possible if a = 2b
d) possible for all values of a and b
Answer: d
Clarification: The condition for the flow field to be continuous is:
fluid-mechanics-questions-answers-continuity-equation-q12
Thus, the condition will be satisfied for any and every value of a and b.

13. In a two dimensional flow, the component of the velocity along the X-axis and the Y-axis are u = ay2 + bxy and v = ax2 + bxy. The flow will be continuous if
a) a + b = 0
b) a – b = 0
c) x + y = 0
d) x – y = 0
Answer: c
Clarification: The condition for the flow field to be continuous is:

by + bx = 0
x + y = 0.

14. In a two dimensional flow, the component of the velocity along the X-axis and the Y-axis are u = ax2 + bxy and v = bxy + ay2. The condition for the flow field to be continuous is
a) independent of a and b
b) independent of a and c
c) independent of b and c
d) independent of a, b and c
Answer: d
Clarification: The condition for the flow field to be continuous is:

2ax + by + 2ay + bx = 0
x + y = 0
Hence, the condition for the flow field to be continuous is independent of a, b and c.

15. In a water supply system, water flows in from pipes 1 and 2 and goes out from pipes 3 and 4 as shown. If all the pipes have the same diameter, which of the following must be correct?
fluid-mechanics-questions-answers-continuity-equation-q15
a) the sum of the flow velocities in 1 and 2 is equal to that in 3 and 4
b) the sum of the flow velocities in 1 and 3 is equal to that in 2 and 4
c) the sum of the flow velocities in 1 and 4 is equal to that in 2 and 3
d) the flow velocities in 1 and 2 is equal to that in 3 and 4
Answer: a
Clarification: According to the Continuity Equation,

where a represents flow area, v represents flow velocity, i is for inlet conditions and o is for outlet conditions.
A1v1 + A2v2 = A3v3 + A4v4
Since d1 = d2 = d3 = d4, v1 + v2 = v3 + v4.