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Past Questions — 2010
Practical use of Bernoulli’s equation is applied to
A)
venturimeter
B)
orifice meter
C)
nozzle meter
D)
all the above
Bernoulli's equation states that for an incompressible, non-viscous fluid in steady flow, the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant along a streamline. This principle is the fundamental basis for flow measurement devices that create a pressure drop to determine flow velocity.
1. Venturimeter: It uses a converging section to increase velocity and decrease pressure. The pressure difference between the inlet and the throat is measured and used to calculate the flow rate based on Bernoulli's principle.
2. Orifice meter: Similar to the venturimeter, it creates a constriction (orifice plate) that causes a pressure drop. The relationship between the pressure difference and the flow rate is derived from Bernoulli's equation (with a discharge coefficient to account for losses).
3. Nozzle meter: This device uses a converging section (nozzle) to accelerate the fluid, creating a pressure drop that is measured to determine the flow rate, again applying the principles of Bernoulli's equation.
Since all three devices rely on the conversion of pressure energy into kinetic energy to measure flow rate, they are all practical applications of Bernoulli's equation.
In laminar boundary layer, thickness of boundary layer δ varies with longitudinal distance x from leading edge as
A)
x-1/2
B)
x1/2
C)
x
D)
x2
In fluid mechanics, specifically for a laminar boundary layer over a flat plate, the growth of the boundary layer thickness (δ) is governed by the Blasius solution. The boundary layer thickness is defined as the distance from the wall where the velocity reaches 99% of the free-stream velocity (U∞). The formula for the boundary layer thickness in laminar flow is given by: δ ≈ 5 * x / sqrt(Re_x), where Re_x is the Reynolds number at distance x. Since Re_x = (ρ * U∞ * x) / μ, we can substitute this into the equation: δ ∝ x / sqrt(x) = x^(1 - 1/2) = x^(1/2). Therefore, the thickness of the laminar boundary layer varies with the square root of the longitudinal distance x from the leading edge. Option (a) is incorrect as it suggests an inverse relationship; option (c) suggests a linear relationship (which occurs in some specific non-Newtonian or different flow regimes); and option (d) suggests a quadratic relationship, which is physically incorrect for this scenario.
Pressure rise within the pipe due to water hammer depends on
A)
velocity of flow
B)
time of valve closure
C)
elastic properties of fluid and pipe materials
D)
all the above
Water hammer Δp = rho*a*Vo depends on flow velocity, closure time, and elasticity of fluid and pipe, so all factors.
For night landing, the thresholds are lighted
A)
white
B)
yellow
C)
green
D)
red
In airport lighting systems, specific colors are used to guide pilots during night landings or low-visibility conditions. The runway threshold lights are designed to mark the beginning of the runway available for landing. According to international aviation standards (ICAO and FAA), threshold lights are green. These lights indicate the start of the landing surface to the approaching pilot. In contrast, the runway end lights (which mark the end of the runway for a landing aircraft or the start for a departing aircraft) are red. White lights are typically used for the runway edge lights to define the lateral limits of the runway. Yellow lights are commonly used for taxiway centerlines or runway guard lights. Therefore, for night landing, the threshold lights are green.
To avoid inconvenience to slow- moving vehicles, the maximum value of the centrifugal ratio on roads is generally taken as
A)
1/2
B)
1/4
C)
1/8
D)
1
In highway engineering, the centrifugal ratio is defined as the ratio of the centrifugal acceleration to the acceleration due to gravity (g). It is expressed as: Centrifugal Ratio = V² / (gR), where V is the speed of the vehicle and R is the radius of the curve. When a road is banked (super-elevated), fast-moving vehicles are stabilized by the banking. However, slow-moving vehicles may experience a tendency to slide inward (down the slope) due to gravity if the super-elevation is too steep. To prevent this inward sliding and ensure the comfort and safety of slow-moving vehicles, the centrifugal ratio is limited. According to standard transportation engineering practice and IRC (Indian Roads Congress) guidelines, the maximum value of the centrifugal ratio is generally restricted to 1/8 to avoid this inconvenience.
Hydrologic routing is based on
A)
storage continuity equation
B)
momentum equation
C)
energy equation
D)
none of the above
Hydrologic routing is the process of predicting the shape of a flood wave (hydrograph) as it moves downstream through a river reach or a reservoir. The fundamental principle governing this process is the Law of Conservation of Mass, which in hydrology is expressed as the Storage Continuity Equation. The general equation is: I - O = dS/dt, where 'I' is the inflow rate, 'O' is the outflow rate, and 'dS/dt' is the rate of change of storage within the system.
- Option (b) Momentum equation: This is used in hydraulic routing (Saint-Venant equations) to describe the physics of flow velocity and pressure, but general hydrologic routing simplifies this by focusing on storage.
- Option (c) Energy equation: This (Bernoulli's principle) is used to determine head losses and flow profiles in pipes or open channels, not for routing hydrographs.
- Option (d) is incorrect because option (a) is the established basis for hydrologic routing.
The father of soil mechanics is
A)
Karl Terzaghi
B)
Fellenius
C)
Kray
D)
Henkel
Karl Terzaghi (1883–1963) is universally recognized as the 'Father of Soil Mechanics'. He revolutionized the field of geotechnical engineering by publishing his seminal work, 'Erdbaumechanik' (Theoretical Soil Mechanics), in 1925. His most significant contribution was the development of the 'Principle of Effective Stress', which explains how the load is shared between the soil skeleton and the pore water, providing the theoretical foundation for calculating settlement and stability in soils.
Regarding the other options:
- Fellenius: Known for his contributions to slope stability analysis (the Fellenius method).
- Henkel (likely referring to Rankine or similar theorists in context): While various engineers contributed to soil pressure and shear strength, they did not establish the field as a whole.
- Kray: Not a recognized primary figure in the foundational establishment of soil mechanics.
Flow net is utilized for determination of
A)
hydrostatic pressure
B)
seepage
C)
exit gradient
D)
seepage pressure
A flow net is a graphical representation consisting of flow lines (paths taken by water particles) and equipotential lines (lines of equal total head). It is primarily used in soil mechanics to determine the quantity of seepage (discharge) occurring through a porous medium, such as under a dam or through a levee. The formula for seepage discharge is q = k H (Nf / Nd), where k is hydraulic conductivity, H is the total head loss, Nf is the number of flow channels, and Nd is the number of potential drops. While flow nets can also be used to calculate the exit gradient (the hydraulic gradient at the downstream end), their fundamental and primary utility is the determination of the total seepage flow. In the context of standard competitive examinations for Civil Engineering, 'seepage' is the most comprehensive and primary answer.
When flow in open channel is critical state of flow, Froude’s number Fr is given by
A)
Fr > 1
B)
Fr = 1
C)
Fr < 1
D)
Fr = -1
In open channel flow, the Froude number (Fr) is a dimensionless parameter used to characterize the flow regime based on the ratio of inertial forces to gravitational forces. It is defined as Fr = V / √(gD), where V is the flow velocity, g is the acceleration due to gravity, and D is the hydraulic depth.
There are three distinct states of flow based on the Froude number:
1. Subcritical Flow (Tranquil flow): Fr < 1. In this state, the flow is slow and deep, and disturbances can travel upstream.
2. Supercritical Flow (Rapid flow): Fr > 1. In this state, the flow is fast and shallow, and disturbances cannot travel upstream.
3. Critical Flow: Fr = 1. This is the transitional state where the specific energy is at a minimum for a given discharge.
Since the question asks for the Froude number when the flow is in a 'critical state', the correct value is exactly 1.
In deriving unsteady flow equations in groundwater flow, the assumptions are
A)
aquifer is homogeneous, isotropic and of infinite extent
B)
before pumping piezometric head is horizontal
C)
rate of pumping is assumed to be zero
D)
well diameter is small so storage in well is neglected
E)
all the above
The question refers to the fundamental assumptions used in deriving the Theis equation (1935), which is the basis for unsteady (transient) flow analysis in groundwater hydraulics.
1. **Option (a):** The aquifer is assumed to be homogeneous (same properties everywhere), isotropic (same properties in all directions), and of infinite radial extent to simplify the differential equation.
2. **Option (b):** It is assumed that the initial state of the aquifer is in equilibrium, meaning the piezometric surface (water table or potentiometric surface) is horizontal before pumping begins.
3. **Option (c):** While the well is pumping at a constant rate 'Q', the derivation of the governing differential equation often considers the change in storage. However, in the context of the 'initial state' or the boundary conditions used to solve the partial differential equation, the system starts from a zero-pumping state. (Note: In some textbooks, this is phrased as the pumping rate being constant, but the baseline for the drawdown calculation is the pre-pumping state).
4. **Option (d):** The well is treated as a 'line source'. This means the diameter of the well is considered negligible compared to the radius of influence, allowing the storage within the well casing itself to be ignored.
Since all these assumptions are standard for the derivation of the Theis unsteady flow equation, option (e) is the correct choice.
Hardy-Cross method is used to the problems of
A)
boundary layer problem
B)
pipe network
C)
solution of water hammer problem
D)
none of the above
The Hardy-Cross method is an iterative technique used in fluid mechanics and hydraulic engineering to solve for the flow rates and pressure drops in a complex network of pipes (pipe networks). It is based on two fundamental principles: 1) The Law of Conservation of Mass (Kirchhoff's First Law), which states that the sum of flows entering a junction must equal the sum of flows leaving it. 2) The Law of Conservation of Energy (Kirchhoff's Second Law), which states that the algebraic sum of head losses around any closed loop in the network must be zero.
Analysis of other options:
- Option (a) Boundary layer problems are typically solved using the Prandtl boundary layer equations or numerical methods like CFD (Computational Fluid Dynamics).
- Option (c) Water hammer problems involve transient flow and pressure surges, which are solved using the Method of Characteristics (MOC) or other differential equation solvers for unsteady flow.
- Option (d) is incorrect as option (b) is the established application of the Hardy-Cross method.
Base flow is separated from hydro graph by
A)
straight line method
B)
fixed base method
C)
variable slope method
D)
all the above
Base flow separation is the process of dividing a total streamflow hydrograph into two components: the direct runoff (surface runoff) and the base flow (groundwater contribution). Because the exact point where surface runoff ends and base flow begins is not physically observable, several empirical methods are used:
1. **Straight Line Method**: A straight line is drawn from the start of the rising limb to the point on the recession limb where the hydrograph becomes linear. This is the simplest but least accurate method.
2. **Fixed Base Method**: This method assumes that the base flow remains constant during the period of direct runoff. A horizontal line is drawn from the point where the recession limb becomes linear back to the start of the rise.
3. **Variable Slope Method**: This is a more sophisticated approach where the base flow is assumed to increase gradually during the period of direct runoff, following a curve or a series of slopes to better reflect the actual groundwater response.
Since all three methods (a, b, and c) are recognized techniques for separating base flow from a hydrograph, the correct option is 'all the above'.
The dimension of dynamic viscosity in M-L-T system is
A)
ML-1T-1
B)
M-1L-1T
C)
M-1LT-1
D)
ML-1T2
To find the dimensions of dynamic viscosity (μ), we can use Newton's Law of Viscosity:
τ = μ * (du/dy)
Where:
- τ (Shear Stress) = Force / Area. Dimensions: [MLT⁻²] / [L²] = [ML⁻¹T⁻²]
- du/dy (Velocity Gradient) = Change in velocity / Change in distance. Dimensions: [LT⁻¹] / [L] = [T⁻¹]
Rearranging the formula for dynamic viscosity (μ):
μ = τ / (du/dy)
Substituting the dimensions:
μ = [ML⁻¹T⁻²] / [T⁻¹]
μ = [ML⁻¹T⁻²] * [T¹]
μ = [ML⁻¹T⁻¹]
In the M-L-T system, this is written as ML⁻¹T⁻¹.
Analyzing the options:
- Option (a) ML-1T-1: Correct.
- Option (b) M-1L-1T: Incorrect dimensions.
- Option (c) M-1LT-1: Incorrect dimensions.
- Option (d) ML-1T2: Incorrect dimensions.
If D is the duty in ha/cumec, B is the base period of a crop in days, Δ is the depth of water in metre, the relationship among them are
A)
D = 8.64 Δ / B
B)
D = 8.64 B / Δ
C)
Δ = 8.64 B / D
D)
none of the above
Standard duty relation Δ=8.64B/D meters, so D=8.64B/Δ.
Euler’s equation for motion of fluids is given by (Where Z is the datum head, p is the pressure intensity; V is the average velocity and ρ is the density of fluid)
A)
dρ/dp + gdZ + VdV = 0
B)
dp/ρ + gdZ + VdV = 0
C)
dρ/p + gdZ + VdV = 0
D)
ρdp + gdZ + VdV = 0
Euler's equation of motion describes the motion of an inviscid (frictionless) fluid. It is derived from Newton's Second Law (F = ma). For a fluid element, the forces acting on it are the pressure force and the gravitational force.
1. The pressure gradient force per unit mass is given by: (dp / ρ) in the direction of flow.
2. The gravitational force per unit mass is given by: g dZ (where Z is the vertical elevation).
3. The acceleration of the fluid element is given by: V dV (convective acceleration).
Summing these forces according to the principle of conservation of momentum for a steady flow along a streamline, we get:
dp/ρ + g dZ + V dV = 0
This equation is the differential form of the Bernoulli equation. Integrating this equation for a steady, incompressible, frictionless flow leads to the Bernoulli equation: p/ρ + gZ + V²/2 = constant.
Comparing this to the options:
- Option (a) and (c) incorrectly place density (ρ) in the numerator of the pressure term.
- Option (d) incorrectly multiplies pressure by density instead of dividing it.
The most common foundation that can be laid in an open excavation by allowing natural slopes on all sides, is
A)
open or shallow foundation
B)
grillage foundation
C)
raft foundation
D)
deep foundation
Step-by-step reasoning: 1. Definition of Open Foundation: An open foundation (also known as a shallow foundation) is constructed by excavating the soil to a certain depth. If the soil is stable enough, the sides of the excavation are left as natural slopes (without the need for shoring or piling) to reach the required bearing stratum. 2. Analysis of Options: (a) Open/Shallow foundations are specifically characterized by being laid in open excavations where the load is transferred to the soil at a shallow depth. (b) Grillage foundations are used for heavy loads on soft soil, typically involving steel beams, and are not defined by the 'natural slope' excavation method. (c) Raft foundations are used when the soil bearing capacity is low or loads are very high, covering the entire area of the structure; while they can be shallow, the 'open excavation with natural slopes' is the primary definition of a basic open foundation. (d) Deep foundations (like piles or caissons) are used when the surface soil is weak and require specialized machinery (boring/driving) rather than simple open excavation with natural slopes. 3. Conclusion: The description provided in the question is the textbook definition of an open or shallow foundation.
The stages of river in flood plain is called
A)
trough stage
B)
delta stage
C)
sub-mountain stage
D)
none of the above
In hydrology and fluvial geomorphology, the 'stages' of a river typically refer to the water level relative to a datum or the longitudinal profile of the river. The river is generally divided into three main stages or courses: the Upper Course (mountainous/youthful stage), the Middle Course (valley/mature stage), and the Lower Course (floodplain/old age stage).
Analyzing the options:
- 'Trough stage' is not a standard term for a river stage in a flood plain; a trough usually refers to a low point in a wave or a depression in topography.
- 'Delta stage' refers specifically to the mouth of the river where it enters a larger body of water, which is a specific feature of the lower course, not the general term for the stage in the flood plain.
- 'Sub-mountain stage' refers to the transition from mountains to plains (upper to middle course), which is the opposite of the flood plain area.
Since none of the provided terms (a, b, or c) correctly define the general 'stage' of a river in its flood plain (which is correctly termed the 'Lower Course' or 'Old Age Stage'), the correct option is 'none of the above'.
When fluid parameters like velocity, density, pressure etc. do not change with respect to space at a given time, flow is called
A)
laminar
B)
steady
C)
turbulent
D)
uniform
In fluid mechanics, flow is classified based on how fluid properties change with respect to time and space.
1. **Steady Flow**: By definition, flow is called 'steady' if the fluid parameters (velocity, pressure, density, etc.) at any point in the flow field do not change with time. Mathematically, for any property $\phi$, $\frac{\partial \phi}{\partial t} = 0$. The question describes a scenario where parameters do not change with respect to time at a given point (though the phrasing 'with respect to space at a given time' is slightly ambiguous, the core definition of parameters remaining constant over time at a fixed location is the definition of steady flow).
2. **Uniform Flow**: Flow is 'uniform' if the velocity and other parameters do not change with respect to space (position) at a given instant of time. Mathematically, $\frac{\partial V}{\partial s} = 0$.
3. **Laminar Flow**: This refers to a flow regime where fluid particles move in smooth, parallel layers or streamlines without mixing.
4. **Turbulent Flow**: This refers to a flow regime characterized by chaotic property changes, eddies, and rapid mixing.
Given the context of the question focusing on the stability of parameters over time, the correct term is 'steady'.
In scanty rainfall region, the camber provided is
A)
flatter
B)
steeper
C)
nil
D)
none of the above
Camber (or cross-slope) is provided on the road surface to drain off rainwater from the pavement to the side drains, preventing water logging and protecting the road structure from moisture damage. The magnitude of the camber depends primarily on the intensity of rainfall and the type of pavement surface.
1. In regions with heavy rainfall, a steeper camber is required to ensure rapid drainage of large volumes of water.
2. In regions with scanty (low) rainfall, the volume of water to be drained is minimal. Therefore, a flatter camber is sufficient to remove the water.
Providing an excessively steep camber in low-rainfall areas would be disadvantageous as it would reduce the stability of vehicles (increasing the risk of overturning or sliding) and increase the wear and tear on the pavement edges.
Therefore:
- Option (a) 'flatter' is correct because low rainfall requires less slope for drainage.
- Option (b) 'steeper' is incorrect as this is used for heavy rainfall regions.
- Option (c) 'nil' is incorrect because some slope is always necessary to prevent ponding, even in dry regions.
International Civil Aviation Organisation (ICAO) was set up in Montreal in
A)
1950
B)
1947
C)
1939
D)
1929
The International Civil Aviation Organization (ICAO) is a specialized agency of the United Nations. It was established following the Convention on International Civil Aviation, which was signed in Montreal on December 7, 1944 (known as the Chicago Convention). However, the organization officially came into existence and began its operations on April 4, 1947, after the ratification of the convention by a sufficient number of states. Therefore, while the planning began in 1944, the formal setup/establishment date is 1947.
Analysis of options:
- 1950: Incorrect; the organization was already operational.
- 1947: Correct; the date the ICAO officially came into existence.
- 1939: Incorrect; this predates the Chicago Convention.
- 1929: Incorrect; this predates the Chicago Convention.
Bernoulli’s equation is obtained by integrating
A)
Navier-Stokes equation
B)
Reynolds equation
C)
Euler’s equation
D)
all the above
Bernoulli's equation is a statement of the conservation of energy for a flowing fluid. Mathematically, it is derived by integrating Euler's equation of motion along a streamline. Euler's equation describes the motion of an inviscid (frictionless), incompressible fluid. When Euler's equation is integrated under the assumptions of steady flow, incompressible fluid, and no friction (viscosity), it yields the Bernoulli equation: P + 1/2ρv² + ρgh = constant.
Why other options are incorrect:
- a. Navier-Stokes equations are the general equations of motion for viscous fluids. While Euler's equation is a special case of Navier-Stokes (where viscosity is zero), Bernoulli's equation specifically stems from the integration of the inviscid Euler's equation.
- b. Reynolds equation is used in lubrication theory to describe the pressure distribution in thin films of viscous fluids; it is not the basis for the general Bernoulli equation.
- d. Since only Euler's equation is the direct source of the integration for Bernoulli's principle, 'all the above' is incorrect.
Discharge over a broad crested weir is maximum when depth of flow h over the crest is related to the total head H by
A)
h = H/2
B)
h = H/3
C)
h = 2H/3
D)
h = 2H/5
For a broad-crested weir, the discharge (Q) is governed by the energy equation and the principle of critical flow. Let H be the total head over the crest and h be the depth of flow over the crest.
1. The specific energy (E) at the crest is equal to the total head H: H = h + v²/2g.
2. The discharge per unit width is q = v * h, so v = q/h.
3. Substituting v into the energy equation: H = h + q²/(2gh²).
4. To find the maximum discharge for a given total head H, we rearrange for q²: q² = 2gh²(H - h) = 2g(Hh² - h³).
5. To maximize q, we differentiate q² with respect to h and set it to zero: d(q²)/dh = 2g(2Hh - 3h²) = 0.
6. Solving for h: 2Hh = 3h² => h = 2H/3.
Thus, the discharge over a broad-crested weir is maximum when the depth of flow over the crest (h) is two-thirds of the total head (H). This corresponds to the condition of critical flow where the flow depth is h = 2/3 H.
A part of water from plants that goes in the sky to join the clouds is called
A)
evaporation
B)
transpiration
C)
interception
D)
none of the above
The question asks for the specific process by which water from plants enters the atmosphere.
1. **Transpiration (Option b):** This is the biological process where plants absorb water from the soil through their roots and release it as water vapor into the atmosphere through small pores in their leaves called stomata. This matches the description 'water from plants that goes in the sky'.
2. **Evaporation (Option a):** This is the physical process where liquid water from surfaces (like oceans, lakes, or soil) turns into water vapor due to heat. While it involves water going into the sky, it does not specifically refer to water coming 'from plants'.
3. **Interception (Option c):** This occurs when precipitation is caught by vegetation (leaves, branches) and evaporates back into the atmosphere before it ever reaches the soil. This is a process of catching rain, not the plant releasing its own internal water.
In hydrology, the combined process of evaporation and transpiration is referred to as 'Evapotranspiration'. However, since the question specifically highlights water coming 'from plants', the most accurate term is transpiration.
According to Kennedy’s theory, the critical velocity in metres in an irrigation canal which keeps the channel free from silting and scouring, is
A)
0.55mD0.64
B)
0.84mD0.64
C)
0.84mD0.54
D)
0.55mD0.54
Kennedy's formula Vc = 0.55*m*D^0.64 where m is critical velocity ratio and D depth.
The shape of the vertical curve is generally a
A)
Parabola
B)
Circle
C)
Hyperbola
D)
Spiral
In transportation engineering, vertical curves are used to provide a smooth transition between two different gradients (slopes). The most commonly used shape for these curves is the parabola for the following reasons: 1. Constant Rate of Change of Grade: A parabolic curve provides a constant rate of change of grade, which ensures a smooth transition and constant centrifugal acceleration for the vehicle. 2. Ease of Computation: The mathematical properties of a parabola make it very simple to calculate offsets and elevations at any point along the curve compared to a circular arc. 3. Comfort and Safety: It provides a gradual change in the vertical acceleration, ensuring passenger comfort and maintaining sight distance.
Why other options are incorrect:
- Circle: While circular arcs are used for horizontal curves, they are not used for vertical curves because the rate of change of grade is not constant, leading to abrupt changes in vertical acceleration (jerks) at the start and end of the curve.
- Hyperbola: Hyperbolic curves are mathematically complex and do not provide the constant rate of change of grade required for road design.
- Spiral: Transition spirals are used in horizontal alignment to transition from a straight path to a circular curve, not for vertical grade transitions.