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Past Questions — 2010
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, when the convention was ratified by a sufficient number of states. Therefore, 1947 is the correct year for its establishment. Option (a) 1950 is too late; Option (c) 1939 is before the Chicago Convention; and Option (d) 1929 is far too early.
For the movement of vehicles at the intersection of two roads, without any interference, the type of grade separation generally provided is
A)
delta
B)
clover leaf
C)
diamond interchange
D)
trumpet
The question asks for a grade separation that allows vehicles to move at the intersection of two roads 'without any interference'.
1. **Cloverleaf Interchange**: This is designed specifically for the intersection of two high-speed highways. It allows traffic to move from any direction to any other direction (including left and right turns) using a combination of overpasses, underpasses, and loop ramps. Because there are no traffic signals or stop signs required for the movements, it provides the highest level of 'non-interference' or continuous flow.
2. **Diamond Interchange**: While common, it typically involves at-grade intersections at the ends of the ramps, meaning vehicles must stop or yield (interference) to cross the minor road.
3. **Trumpet Interchange**: This is used where one road terminates into another (T-junction), not for the intersection of two continuous roads.
4. **Delta Interchange**: This is a simplified form of a T-junction interchange and does not provide full, non-interfering movement for two intersecting roads.
Therefore, the cloverleaf is the standard grade separation for providing continuous, non-interfering movement at the intersection of two roads.
The road foundation for modern highways construction was developed by
A)
Telford
B)
Macadam
C)
Tresguet
D)
Telford and Macadam simultaneously
The development of road foundations evolved through several key pioneers in the 18th and 19th centuries.
1. **Thomas Telford (Option a):** Telford is credited with developing the first systematic road foundation. His method involved placing a heavy foundation of large, hand-set stones (broken stones) at the bottom, which were then layered with smaller stones, creating a solid, stable base that could support heavy loads and provide effective drainage. This is considered the precursor to the modern engineered road foundation.
2. **John Loudon McAdam (Option b):** Macadam improved upon previous methods by focusing on the 'wearing course.' He argued that the natural soil (subgrade) could support the load if it was kept dry. He eliminated the heavy stone foundation used by Telford and instead used layers of small, angular broken stones that compacted under traffic to form a dense, water-resistant surface. While revolutionary, his method focused more on the surface/pavement than the deep foundation.
3. **Pierre-Marie-Jérôme Tresguet (Option c):** Tresguet was an early pioneer who used a foundation of large stones, but his methods were less widely adopted and refined than Telford's in the context of the evolution toward modern highway engineering.
Therefore, when referring specifically to the development of the 'road foundation' (the structural base), Telford's contribution is the most significant.
Model of river is
A)
simple model
B)
undistorted model
C)
distorted model
D)
all the above
In fluid mechanics, model laws are used to scale prototypes. A model is 'undistorted' if the scale ratio is the same for all linear dimensions (length, width, and depth). However, for river models, if an undistorted scale is used, the depth of the water in the model becomes extremely small, leading to excessive viscous effects (surface tension and boundary layer thickness) that dominate the flow and make the model unrealistic. To maintain a reasonable depth and ensure that the flow remains turbulent and representative of the prototype, the vertical scale (depth) is kept different from the horizontal scale (length and width). This practice of using different scales for different dimensions is known as 'distortion'. Therefore, river models are typically distorted models to ensure the validity of the hydraulic simulation.
The parameters (friction factor f, Reynolds number Re, roughness number D/k) plot diagram is called
A)
Moody’s diagram
B)
Stanton-Pannel diagram
C)
Reynolds diagram
D)
(a) and (b)
The plot relating the Darcy friction factor (f), the Reynolds number (Re), and the relative roughness (k/D or D/k) is most commonly known as the Moody's diagram. However, the Moody diagram is actually a synthesis of earlier experimental data and theoretical work. The Stanton-Pannel diagram (developed by Stanton and Pannel) was one of the primary precursors and equivalent representations used to determine the friction factor for turbulent flow in pipes based on the same parameters. In many advanced fluid mechanics contexts and older technical textbooks, both terms are recognized as referring to the graphical representation of these specific dimensionless parameters. Therefore, since both (a) and (b) describe this specific plot, option (d) is the most comprehensive answer.
If the degree of the curve (specified length 30m) is 153º, the radius of the curve is approximately
A)
573m
B)
382m
C)
1910m
D)
none of the above
1. Understanding the Definition: The 'degree of a curve' (D) is defined as the angle subtended at the center of the curve by an arc of a specified length (L). In this problem, the specified length L = 30m and the degree D = 153º.
2. Formula: The relationship between the radius (R), the arc length (L), and the central angle (D in degrees) is given by the formula:
L = (π * R * D) / 180
Rearranging to solve for R:
R = (L * 180) / (π * D)
3. Calculation:
L = 30 m
D = 153º
R = (30 * 180) / (3.14159 * 153)
R = 5400 / 480.66
R ≈ 11.23 m
4. Analysis of Options:
The calculated radius is approximately 11.23 meters. Comparing this to the given options:
a. 573m (Incorrect)
b. 382m (Incorrect)
c. 1910m (Incorrect)
Since the calculated value does not match any of the provided numerical options, the correct choice is 'none of the above'. Note: It is highly likely there is a typo in the question's degree value (e.g., if D was 1.53º, R would be 1123m; if D was 15.3º, R would be 112.3m), but based on the text provided (153º), the result is 11.23m.
Difference FB and BB of a line without local attraction is
A)
100º
B)
270º
C)
180º
D)
200º
In surveying, the Fore Bearing (FB) is the bearing of a line measured in the direction of the progress of the survey, and the Back Bearing (BB) is the bearing of the same line measured in the opposite direction. Mathematically, the relationship between the Fore Bearing and Back Bearing of a line is given by: Back Bearing = Fore Bearing ± 180°. Therefore, the absolute difference between the FB and BB of a line is |FB - BB| = 180°. This relationship holds true provided there is no 'local attraction' (interference from nearby magnetic objects) affecting the compass needle. If local attraction exists, the difference will deviate from 180°. Since the question explicitly states 'without local attraction', the difference is exactly 180º.
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 super-elevated (banked) to counteract centrifugal force for fast-moving vehicles, slow-moving vehicles may experience a tendency to slide inward toward the center of the curve due to gravity. To prevent this inward sliding and to avoid inconvenience to slow-moving vehicles, the super-elevation (e) is limited. According to standard design guidelines (such as IRC), the maximum value of the centrifugal ratio (which corresponds to the maximum super-elevation e = V² / gR) is generally restricted to 0.07 (7%) for plain terrain or 0.10 (10%) for hilly terrain to ensure stability for slow vehicles.
Among the given options, 1/8 (which is 0.125) is the closest standard theoretical limit often cited in textbooks to represent the upper bound of the centrifugal ratio to maintain safety and comfort for slow-moving traffic, whereas 1/2, 1/4, and 1 are far too high and would cause slow vehicles to slide inward significantly.
Laplace equation in 3-Dimensional flow through soil with general notations is
A)
∂²φ/∂x² + ∂²φ/∂y² + ∂²φ/∂z² = 0
B)
∂²h/∂x² + ∂²h/∂y² + ∂²h/∂z² = 0
C)
∂u/∂x + ∂v/∂y + ∂w/∂z = 0
D)
none of the above
In soil mechanics, the flow of water through a porous medium is governed by Darcy's Law. For a steady-state, incompressible flow through a homogeneous and isotropic soil, the continuity equation leads to the Laplace equation. The Laplace equation describes the distribution of the total hydraulic head (h) in the medium.
1. **Derivation**: According to Darcy's Law, the velocity components are v_x = -k(∂h/∂x), v_y = -k(∂h/∂y), and v_z = -k(∂h/∂z).
2. **Continuity Equation**: For steady flow, the net flow into a control volume must be zero: ∂v_x/∂x + ∂v_y/∂y + ∂v_z/∂z = 0.
3. **Substitution**: Substituting the velocity components into the continuity equation gives: ∂/∂x(-k ∂h/∂x) + ∂/∂y(-k ∂h/∂y) + ∂/∂z(-k ∂h/∂z) = 0.
4. **Simplification**: Assuming the coefficient of permeability (k) is constant (isotropic and homogeneous), we divide by -k to get: ∂²h/∂x² + ∂²h/∂y² + ∂²h/∂z² = 0.
Analysis of options:
- Option (a) uses φ, which typically represents a potential function or stream function, but the standard representation for flow nets in soil mechanics is based on the hydraulic head (h).
- Option (b) is the standard Laplace equation for the total hydraulic head (h) in 3D flow.
- Option (c) is the general continuity equation for velocity vectors (u, v, w), not the Laplace equation.
Out of the following sources of water, which one is not used for water supply as surface source?
A)
Rivers and streams
B)
Lakes and ponds
C)
Underground water storage
D)
Storage reservoir
In environmental engineering and water supply systems, water sources are broadly classified into two categories: Surface Water and Groundwater.
1. Surface Water: This refers to water that is available on the surface of the earth. Examples include:
- Rivers and streams (Option a): Flowing surface water.
- Lakes and ponds (Option b): Standing surface water.
- Storage reservoirs (Option d): Man-made structures designed to collect and store surface runoff.
2. Groundwater: This refers to water that has percolated through the soil and is stored in the pores and fractures of underground rock formations (aquifers).
Since 'Underground water storage' refers to groundwater, it is not a surface source. Therefore, it is the correct answer to the question asking which source is NOT used as a surface source.
Uniform or normal flow in open channel is a condition when
A)
force causing the flow is larger than force of resistance
B)
force causing the flow is less than force of resistance
C)
force causing the flow is equal to force of resistance
D)
none of the above
In open channel flow, 'Uniform Flow' (also known as Normal Flow) occurs when the depth, velocity, and cross-section of the flow remain constant along the length of the channel. From a force balance perspective, the flow is driven by the component of gravity acting in the direction of the bed slope (the force causing the flow). This driving force is opposed by the frictional resistance exerted by the channel boundaries (the force of resistance). For the flow to be uniform, there must be no net acceleration of the fluid particles; therefore, the driving force must exactly balance the resisting force. If the driving force were larger (Option a), the flow would accelerate (non-uniform). If the resisting force were larger (Option b), the flow would decelerate (non-uniform). Thus, the condition for normal flow is that the force causing the flow is equal to the force of resistance.
A rectangular open channel of depth y and width B is economic or efficient if
A)
y = 2B
B)
B = 2y
C)
y = 1.5B
D)
B = 1.5y
In fluid mechanics, an 'economic' or 'most efficient' channel section is one that provides the maximum discharge for a given cross-sectional area, slope, and roughness. This occurs when the wetted perimeter (P) is minimized for a given area (A), as this reduces frictional resistance.
For a rectangular channel:
1. Area (A) = B * y
2. Wetted Perimeter (P) = B + 2y
To find the minimum perimeter for a constant area, we express B in terms of A and y: B = A/y.
Substitute B into the perimeter equation: P = (A/y) + 2y.
To minimize P, we take the derivative with respect to y and set it to zero:
dP/dy = -A/y² + 2 = 0
Therefore, A/y² = 2
Since A = B * y, we substitute it back: (B * y) / y² = 2
B / y = 2
B = 2y
Thus, the most efficient rectangular section is one where the width (B) is twice the depth (y), or equivalently, the hydraulic radius (R = A/P) is equal to half the depth (y/2).
Pitot tube is an instrument to measure
A)
pressure of flow
B)
discharge of liquid
C)
velocity of flow
D)
total energy of flowing liquid
A Pitot tube is a pressure-measuring instrument used to calculate the fluid flow velocity. It works on the principle of Bernoulli's equation by converting the kinetic energy of the moving fluid into potential energy (pressure). When the tube is placed facing the flow, the fluid is brought to a complete stop at the tip (stagnation point), creating 'stagnation pressure'. By measuring the difference between this stagnation pressure and the static pressure of the fluid, the local velocity of the flow can be calculated using the formula: v = sqrt(2(P_stagnation - P_static) / rho), where rho is the density of the fluid.
Why other options are incorrect:
- (a) Pressure of flow: While it measures pressure, its primary purpose is to use that pressure to determine velocity. Static pressure is measured by a static port, not a Pitot tube alone.
- (b) Discharge of liquid: Discharge (flow rate) is the product of velocity and cross-sectional area. While a Pitot tube can help find discharge if the area is known, it directly measures velocity, not discharge.
- (d) Total energy: Total energy includes internal energy and potential energy due to height, which a Pitot tube does not measure.
Capacity of reservoir is usually determined by
A)
mass curve of rainfall
B)
mass curve of inflow
C)
depth-area duration curve
D)
intensity duration frequency curve
The capacity of a reservoir is determined based on the need to store excess water during periods of high inflow and release it during periods of low inflow to meet a specific demand. The 'Mass Curve of Inflow' (also known as the cumulative inflow curve) is a plot of the cumulative volume of water entering the reservoir over time. By plotting the cumulative demand (cumulative outflow) against the cumulative inflow, the maximum difference between the two curves represents the required storage capacity of the reservoir to ensure that the demand is met even during the driest periods.
Why other options are incorrect:
- a. Mass curve of rainfall: Rainfall is a component of inflow, but reservoir capacity is based on the actual streamflow (inflow) reaching the site, which accounts for runoff coefficients and losses.
- c. Depth-area duration curve: This is used to determine the relationship between the water level (depth) and the surface area of the reservoir, which helps in calculating the volume for a given depth, but it does not determine the required capacity based on demand.
- d. Intensity duration frequency (IDF) curve: This is used in urban drainage and storm sewer design to estimate peak rainfall intensity for a given duration and return period, not for long-term reservoir storage capacity.
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. A river flowing through a flood plain is generally in its 'lower course' or 'mature/old stage'.
Analyzing the options:
1. '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 valley.
2. 'Delta stage' refers specifically to the mouth of the river where it enters a larger body of water, not the general flood plain area.
3. 'Sub-mountain stage' refers to the transition from mountainous terrain to plains (upper course), which is the opposite of a developed flood plain.
Since none of the provided technical terms (trough, delta, or sub-mountain) correctly describe the general stage of a river in a flood plain, the correct option is 'none of the above'. The correct terminology would typically be the 'Lower Course' or 'Old Age Stage'.
Hydrograph is a graphical representation of
A)
surface runoff against time
B)
ground water flow against time
C)
rainfall against time
D)
discharge of river against time
A hydrograph is a fundamental tool in hydrology defined as a graph showing the rate of flow (discharge) versus time past a specific point in a river, channel, or catchment.
Step-by-step reasoning:
1. **Definition**: The term 'hydro' refers to water and 'graph' refers to a plot. In hydrology, a hydrograph specifically plots the discharge (Q) on the y-axis and time (t) on the x-axis.
2. **Analysis of Options**:
- **Option a (surface runoff against time)**: While surface runoff contributes to the hydrograph, the hydrograph represents the total discharge at a gauging station, which includes both surface runoff and baseflow (groundwater contribution).
- **Option b (ground water flow against time)**: This describes a baseflow hydrograph, which is only one component of the total hydrograph.
- **Option c (rainfall against time)**: This is called a 'Hyetograph', not a hydrograph.
- **Option d (discharge of river against time)**: This is the precise definition. The discharge (usually measured in m³/s or cfs) of a stream is plotted against time to analyze the response of a watershed to a rainfall event.
Therefore, the most comprehensive and accurate answer is the discharge of the river against time.
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 derivation of the unsteady flow equations (specifically the Theis equation), which is the foundation for analyzing transient groundwater flow in aquifers. The derivation relies on several simplifying assumptions to make the partial differential equation solvable:
1. **Aquifer Properties (Option a):** The aquifer is assumed to be homogeneous (same properties everywhere), isotropic (same properties in all directions), and of infinite radial extent to avoid boundary effects.
2. **Initial Conditions (Option b):** It is assumed that before pumping begins, the piezometric surface (water table or potentiometric surface) is horizontal and the head is uniform throughout the aquifer.
3. **Pumping Rate (Option c):** While the well is pumping, the derivation often considers the 'instantaneous' start of pumping. However, in the context of the mathematical simplification of the governing equation, the rate of pumping (Q) is treated as a constant source/sink term, and the derivation focuses on the response to this change from a zero-state (initial equilibrium).
4. **Well Geometry (Option d):** The diameter of the well is assumed to be negligible compared to the radius of influence, meaning the volume of water stored within the well casing itself is ignored in the overall mass balance of the aquifer.
Since all these assumptions are standard for the derivation of the Theis unsteady flow equation, option 'e' is the correct choice.
If R is the radius of a simple curve and φ is the angle of deflection, its tangent length is
A)
R sin(φ/2)
B)
R cot(φ/2)
C)
R tan(φ/2)
D)
R cos(φ/2)
In surveying, for a simple circular curve, the tangent length (T) is the distance from the Point of Curve (PC) to the Point of Intersection (PI). Let R be the radius of the curve and φ (phi) be the deflection angle (also known as the intersection angle or external angle).
1. In a simple curve, the angle subtended by the arc at the center is equal to the deflection angle φ.
2. The tangent length T is calculated using the geometry of the right-angled triangle formed by the radius, the tangent, and the line connecting the center of the circle to the point of intersection (PI).
3. In this triangle, the angle at the center is φ/2.
4. Using trigonometry: tan(φ/2) = Opposite / Adjacent = T / R.
5. Rearranging for T, we get: T = R tan(φ/2).
Comparing this to the options:
- Option (a) R sin(φ/2) is incorrect as it does not represent the tangent length.
- Option (b) R cot(φ/2) is the reciprocal of the correct formula.
- Option (c) R tan(φ/2) is the mathematically correct formula for tangent length.
- Option (d) R cos(φ/2) is incorrect.
Hydraulic grade line (H.G.L.) in pipe flow represents
A)
energy head
B)
pressure head
C)
friction head loss
D)
all the above
In fluid mechanics, the Total Energy Line (T.E.L.) and the Hydraulic Grade Line (H.G.L.) are used to describe the energy profile of a fluid flowing through a pipe.
1. **Total Energy Line (T.E.L.)**: This represents the total head of the fluid, which is the sum of the pressure head (P/γ), the velocity head (v²/2g), and the datum head (z).
T.E.L. = (P/γ) + (v²/2g) + z
2. **Hydraulic Grade Line (H.G.L.)**: This represents the sum of the pressure head and the datum head. It is essentially the T.E.L. minus the velocity head.
H.G.L. = (P/γ) + z
While the H.G.L. technically includes the elevation (datum head), in the context of pipe flow analysis and standard multiple-choice questions of this type, it is used to represent the 'piezometric head' or the 'pressure head' relative to a datum.
Comparing the options:
- Option (a) 'energy head' refers to the T.E.L.
- Option (b) 'pressure head' (specifically the piezometric head) is what the H.G.L. represents.
- Option (c) 'friction head loss' is the difference in energy between two points along the T.E.L., not the line itself.
- Option (d) is incorrect as only (b) is applicable.
If 1 litre of liquid weighs 9N, its specific weight is
A)
900 N/m3
B)
9000 N/m3
C)
90 N/m3
D)
9 N/m3
Step-by-step calculation:
1. **Understand the Definition**: Specific weight (γ) is defined as the weight per unit volume of a substance. The formula is:
Specific Weight (γ) = Weight (W) / Volume (V).
2. **Identify Given Values**:
- Weight (W) = 9 N
- Volume (V) = 1 litre
3. **Unit Conversion**: To find the answer in N/m³ (the standard SI unit for specific weight), we must convert litres to cubic metres (m³).
- 1 m³ = 1000 litres
- Therefore, 1 litre = 1/1000 m³ = 0.001 m³
4. **Calculate Specific Weight**:
γ = 9 N / 0.001 m³
γ = 9 * 1000 N/m³
γ = 9000 N/m³
Comparing this result to the options:
- Option (a) 900 N/m³ is incorrect (calculation error by factor of 10).
- Option (b) 9000 N/m³ is correct.
- Option (c) 90 N/m³ is incorrect.
- Option (d) 9 N/m³ is incorrect (this is the weight per litre, not per cubic metre).
Symon’s rain gauge is
A)
non-recording gauge
B)
tipping bucket gauge
C)
flat recording gauge
D)
weighing type gauge
Symons' rain gauge is the standard non-recording rain gauge used by the India Meteorological Department (IMD). It consists of a cylindrical vessel with a funnel that collects rainwater into a bottle. The water is manually measured using a graduated cylinder at specific intervals (usually every 24 hours).
Why other options are incorrect:
- b. Tipping bucket gauge: This is a recording gauge that uses a mechanism to tip a bucket once a specific amount of rain is collected, sending an electrical pulse to a logger.
- c. Flat recording gauge: This refers to recording gauges (like the floating type) that use a pen and a rotating drum to create a chart of rainfall over time.
- d. Weighing type gauge: This is a recording gauge that weighs the collected rain in a bucket and converts the weight into depth on a chart.
When the available data to make frequency analysis is not adequate, the method of flood analysis is done by
A)
regional flood-frequency analysis
B)
partial series analysis
C)
Stochastic method
D)
Gumbel flood frequency analysis
In hydrology, flood frequency analysis is used to predict the magnitude of a flood that will occur with a given return period. When the available data for a specific site (local data) is inadequate (short record length), the reliability of local frequency analysis (like Gumbel's method) decreases significantly. To overcome this, 'Regional Flood-Frequency Analysis' is employed. This method involves grouping several sites with similar physical and climatic characteristics (a homogeneous region) and combining their data to create a regional growth curve. This increases the sample size and provides a more statistically robust estimate for the site with missing or inadequate data.
Why other options are incorrect:
- b. Partial series analysis: This is used when only floods above a certain threshold are recorded, but it still relies on the available local record and is generally less robust than regional analysis for completely inadequate data.
- c. Stochastic method: This refers to a general class of probabilistic models; while flood analysis is stochastic, it is not a specific 'method' used specifically to solve the problem of inadequate data in the way regional analysis is.
- d. Gumbel flood frequency analysis: This is a standard local frequency analysis method. It requires a sufficient length of historical data to be accurate; if data is inadequate, Gumbel's method produces highly unreliable results.
River training works are necessary to
A)
direct the river flow in a desired path
B)
minimize the problems of flood and erosion
C)
control meandering and deposition
D)
all the above
River training works refer to various engineering measures adopted to control and guide the flow of a river.
1. Directing the river flow (Option a): Works such as guide banks and spurs are used to keep the river channel aligned and prevent it from shifting its course, ensuring the flow stays in a desired path (especially near bridges).
2. Minimizing flood and erosion (Option b): By stabilizing the banks through embankments (levees) and revetments, the risk of bank erosion is reduced, and the capacity of the channel is managed to mitigate flood risks to adjacent lands.
3. Controlling meandering and deposition (Option c): River training works help in preventing excessive meandering (which can lead to avulsion) and managing the deposition of sediment to maintain a required depth for navigation or flow efficiency.
Since all three objectives are primary goals of river training, the correct answer is 'all the above'.
If a spur is constructed at about 60º to 80º inclined upstream, it is called
A)
attracting spur
B)
deflecting spur
C)
repelling spur
D)
permeable spur
In river engineering, spurs (or groynes) are structures constructed transverse to the river flow to protect banks from erosion or to divert the current. They are classified based on the angle they make with the river bank:
1. **Attracting Spur**: These are inclined downstream (usually 60° to 80° to the bank, pointing downstream). They attract the flow toward the spur, which helps in protecting the bank but may cause erosion at the nose of the spur.
2. **Repelling Spur**: These are inclined upstream (usually 60° to 80° to the bank, pointing upstream). They repel the current away from the bank toward the center of the channel, thereby protecting the bank from erosion.
3. **Deflecting Spur**: These are constructed perpendicular to the bank (90°). They simply deflect the flow away from the bank.
4. **Permeable Spur**: This refers to the material used (e.g., timber piles) rather than the angle of inclination. They allow some water to pass through, reducing the turbulence at the nose.
Since the question specifies a spur inclined upstream at 60º to 80º, it is a repelling spur.
If V is the speed of the moving vehicle, R is the radius of the curve, g is the acceleration due to gravity, W is the width of the carriageway, the super-elevation is
A)
WV^2 / Rg
B)
W^2V / Rg
C)
W^2V^2 / Rg
D)
WV / Rg
Step-by-step derivation:
1. Super-elevation (e) is the raising of the outer edge of the pavement relative to the inner edge on a horizontal curve to counteract centrifugal force.
2. The formula for the rate of super-elevation (e) is given by: e = V^2 / (gR), where V is the speed, g is acceleration due to gravity, and R is the radius of the curve.
3. The rate of super-elevation (e) is defined as the ratio of the height difference (h) to the width of the carriageway (W). Therefore, e = h / W.
4. To find the actual super-elevation (the height 'h'), we rearrange the formula: h = e * W.
5. Substituting the value of e: h = (V^2 / gR) * W = WV^2 / Rg.
Comparing this result to the options:
- Option (a) WV^2 / Rg matches the derived formula.
- Option (b) W^2V / Rg is dimensionally incorrect.
- Option (c) W^2V^2 / Rg is dimensionally incorrect.
- Option (d) WV / Rg is dimensionally incorrect as speed must be squared to account for centrifugal force.