← Legal Metrology
Past Questions
The first Indian railway was laid in
A)
1775
B)
1804
C)
1825
D)
1853
The first passenger railway line in India was opened on April 16, 1853. It ran between Bori Bunder (Mumbai) and Thane, covering a distance of approximately 34 kilometers. The train was hauled by three locomotives named Sahib, Sindh, and Sultan.
Analysis of other options:
- 1775: This predates the invention of the steam locomotive (developed by Richard Trevithick in 1804).
- 1804: This is the year the first steam locomotive was successfully run in the UK, not India.
- 1825: This marks the opening of the Stockton and Darlington Railway in England, the first public railway in the world, but not in India.
Stream gauging is the method of measurement of
A)
rainfall
B)
runoff
C)
discharge
D)
evapotranspiration
Stream gauging is the process of measuring the volume of water flowing through a river channel or stream per unit of time, which is technically defined as 'discharge' (typically measured in cubic meters per second, m³/s, or cubic feet per second, cfs).
Here is why the other options are incorrect:
- a. Rainfall: Measured using rain gauges (pluviometers).
- b. Runoff: While stream gauging is used to determine runoff at a specific point, 'runoff' refers to the total amount of precipitation that reaches the stream. Stream gauging specifically measures the instantaneous or average flow rate (discharge).
- d. Evapotranspiration: Measured using lysimeters or calculated via the Penman-Monteith equation, involving atmospheric and soil data, not stream flow measurements.
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).
1. Let R be the radius of the curve.
2. Let φ (phi) be the deflection angle (also known as the intersection angle or external angle).
3. In the triangle formed by the center of the curve (O), the point of intersection (PI), and the point of curve (PC), the angle at the center is equal to the deflection angle φ.
4. The line from the center to the PI bisects the deflection angle, creating a right-angled triangle where the angle at the center is φ/2.
5. Using trigonometry in this right triangle:
tan(φ/2) = Opposite / Adjacent = Tangent Length (T) / Radius (R).
6. Rearranging the formula gives: T = R tan(φ/2).
Therefore, option (c) is the correct mathematical relationship for the tangent length of a simple curve.
Major loss that occurs in pipe flow is given by
A)
Darcy’s equation
B)
Reynolds equation
C)
Euler’s equation
D)
Navier-Stokes equation
In fluid mechanics, head loss in a pipe is categorized into two types: Major Loss and Minor Loss.
1. Major Loss: This is the pressure loss due to friction between the flowing fluid and the pipe wall. It is calculated using the Darcy-Weisbach equation: h_f = (f * L * v^2) / (2 * g * D), where 'f' is the friction factor, 'L' is the length of the pipe, 'v' is the velocity, 'g' is acceleration due to gravity, and 'D' is the diameter. Therefore, Darcy's equation is the correct answer.
2. Why other options are incorrect:
- Reynolds equation (or Reynolds Number): This is used to determine the flow regime (laminar, transitional, or turbulent) based on inertial and viscous forces, not to calculate head loss.
- Euler’s equation: This describes the motion of an inviscid (frictionless) fluid, meaning it specifically ignores the losses that the question is asking about.
- Navier-Stokes equation: These are the fundamental partial differential equations that describe the motion of viscous fluid substances. While they form the basis for deriving flow behavior, they are not the specific 'equation' used to calculate major head loss in practical pipe flow applications.
The main function of sleepers is
A)
to hold rails at correct gauge
B)
to support rails
C)
to distribute load from rails to ballast
D)
all the above
In railway engineering, sleepers (also known as ties) are the transverse supports placed under the rails. Their primary functions are as follows:
1. **Maintaining Gauge (Option a):** Sleepers hold the rails at the correct distance from each other (the gauge), ensuring that the track does not spread under the lateral pressure of the train wheels.
2. **Supporting Rails (Option b):** They provide a firm base to support the rails, preventing them from sagging and maintaining the longitudinal alignment of the track.
3. **Load Distribution (Option c):** The rails transmit the heavy concentrated wheel loads to the sleepers, which then distribute this load over a wider area of the ballast. This prevents the rails from sinking into the formation and protects the subgrade from excessive pressure.
Since all three functions are essential and primary roles of the sleepers, the correct answer is 'all the above'.
In order to have a continuous flow through a siphon, no portion of the pipe be higher than
A)
10 m
B)
10.33 m
C)
5.5 m
D)
7.6 m
A siphon works on the principle of atmospheric pressure pushing liquid up into the tube. For a continuous flow to occur, the pressure at the highest point (the summit) of the siphon must not drop below the vapor pressure of the liquid. If the pressure drops to the vapor pressure, cavitation occurs, and the liquid column breaks, stopping the flow.
1. The maximum theoretical height a column of water can be supported by atmospheric pressure is calculated using the formula: h = P_atm / (ρ * g).
2. Standard atmospheric pressure (P_atm) is approximately 101,325 Pa (N/m²).
3. The density of water (ρ) is approximately 1000 kg/m³ and acceleration due to gravity (g) is 9.81 m/s².
4. Calculation: h = 101,325 / (1000 * 9.81) ≈ 10.33 meters.
Therefore, no portion of the pipe can be higher than 10.33 m above the free surface of the liquid; otherwise, the vacuum created would cause the water to boil/vaporize at room temperature, breaking the siphon effect.
Manning’s equation is used in open channel to estimate
A)
average velocity
B)
average depth
C)
average slope
D)
average discharge
Manning's equation is an empirical formula used in fluid mechanics and hydraulics to calculate the average flow velocity of water in an open channel. The formula is expressed as: V = (1/n) * R^(2/3) * S^(1/2), where 'V' is the average velocity, 'n' is the Manning roughness coefficient, 'R' is the hydraulic radius (area divided by wetted perimeter), and 'S' is the slope of the energy grade line (usually the bed slope for uniform flow). While the average discharge (Q) can be calculated using this equation by multiplying the velocity by the cross-sectional area (Q = A * V), the equation itself is fundamentally designed to solve for the average velocity. Options b and c are parameters used as inputs to the equation, not the primary value estimated by the formula.
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.) 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/elevation head (z). The Hydraulic Grade Line (H.G.L.) is defined as the line representing the sum of the pressure head and the datum head (HGL = P/γ + z). Therefore, the difference between the T.E.L. and the H.G.L. is the velocity head (v²/2g). While the H.G.L. includes the elevation, in the context of pipe flow analysis, it is primarily used to represent the piezometric head (pressure head relative to a datum). Among the given options, 'pressure head' is the most accurate representation of what the H.G.L. tracks, as it excludes the kinetic energy (velocity head) component of the total energy. Option (a) is incorrect because energy head refers to the T.E.L. Option (c) is incorrect because friction head loss is the slope/drop of the H.G.L. along the pipe, not the line itself.
For determination of average precipitation in a catchment, best method is
A)
arithmetical method
B)
isohytel mean method
C)
Theissen polygon method
D)
none of the above
To determine the average precipitation over a catchment area, three primary methods are commonly used:
1. **Arithmetical Mean Method**: This is the simplest method, calculating the average of all rain gauge readings. It is only accurate if the gauges are uniformly distributed and the terrain is flat with no significant variation in rainfall.
2. **Thiessen Polygon Method**: This method assigns a weight to each gauge based on the area it represents. It is more accurate than the arithmetical mean because it accounts for non-uniform distribution of gauges, but it assumes that rainfall varies linearly between stations.
3. **Isohyetal Method**: This method involves drawing lines of equal precipitation (isohyets) on a map. It is considered the most accurate (best) method because it accounts for both the distribution of the rain gauges and the actual topographic variations (orographic effects) of the terrain, which the other two methods ignore.
Since the Isohyetal method incorporates the most spatial information and handles complex terrain most effectively, it is recognized as the best method for determining average precipitation.
The field capacity of a soil depends upon
A)
capillary tension in soil
B)
porosity of soil
C)
both (a) and (b)
D)
neither (a) nor (b)
Field capacity is defined as the amount of soil moisture or water content held in the soil after excess water has drained away and the rate of infiltration has decreased. It is the upper limit of the available water capacity for plants.
1. Capillary Tension (a): Field capacity is fundamentally governed by the balance between the force of gravity (pulling water down) and the capillary forces (holding water in the soil pores). The strength of capillary tension depends on the size of the pores; smaller pores exert higher capillary tension, allowing the soil to retain more water against gravity.
2. Porosity of Soil (b): Porosity refers to the total volume of void space in the soil. Since water is stored within these pores, the total volume available for water storage (and thus the field capacity) is directly related to the soil's porosity and the distribution of pore sizes (texture).
Because field capacity is a result of how much space is available (porosity) and how strongly the water is held in those spaces (capillary tension), both factors are critical. Therefore, option (c) is the correct choice.
Stagnation point is the point in flowing fluid where
A)
pressure is zero
B)
where velocity is zero
C)
total energy is maximum
D)
momentum of flow is zero
In fluid mechanics, a stagnation point is defined as a point in a flow field where the local velocity of the fluid is zero. This typically occurs when a flowing fluid hits a solid boundary perpendicularly (such as the nose of an aircraft or the center of a Pitot tube), causing the fluid to come to a complete stop. At this point, the kinetic energy of the fluid is converted into pressure energy, resulting in the 'stagnation pressure'.
Analysis of other options:
- Option (a): Pressure is not zero; in fact, pressure is typically at its maximum (stagnation pressure) at this point.
- Option (c): Total energy remains constant along a streamline (according to Bernoulli's principle for inviscid flow); it is not 'maximum' at the stagnation point, but rather the kinetic energy is converted to pressure energy.
- Option (d): While the velocity is zero (and thus momentum per unit volume is zero), the term 'momentum of flow' usually refers to the global property of the stream, and the defining characteristic of a stagnation point is specifically the zero velocity vector.
The causes of solid waste pollution are
A)
population increase
B)
affluence
C)
growth of technology
D)
all the above
Solid waste pollution is driven by several socio-economic and demographic factors:
1. Population Increase: As the number of people increases, the total volume of waste generated per unit of area increases proportionally, putting pressure on waste management systems.
2. Affluence: Higher income levels lead to increased consumption patterns. Affluent societies tend to purchase more packaged goods, luxury items, and disposable products, which significantly increases the amount of waste produced per capita.
3. Growth of Technology: While technology can help manage waste, it also creates new types of pollution. The rapid obsolescence of electronic devices (e-waste) and the invention of non-biodegradable materials like plastics and synthetic polymers are direct results of technological growth.
Since all three factors contribute significantly to the increase in solid waste, option 'd' is the correct choice.
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. **Identify Given Data**:
- Weight of the liquid (W) = 9 N
- Volume of the liquid (V) = 1 litre
2. **Convert Units to SI**:
- The standard unit for volume in Fluid Mechanics is cubic meters (m³).
- 1 m³ = 1000 litres
- Therefore, 1 litre = 1/1000 m³ = 0.001 m³
3. **Apply Formula for Specific Weight**:
- Specific weight (γ) is defined as the weight per unit volume of a substance.
- Formula: γ = Weight / Volume
- γ = 9 N / 0.001 m³
4. **Calculate Result**:
- γ = 9 * 1000 N/m³ = 9000 N/m³
Comparing this result to the options:
- Option (a) 900 N/m³ is incorrect (off by a factor of 10).
- Option (b) 9000 N/m³ matches our calculation.
- Option (c) 90 N/m³ is incorrect.
- Option (d) 9 N/m³ is incorrect (this is the weight of 1 litre, not the weight per cubic meter).
Air vessel is essential in
A)
centrifugal pump
B)
reciprocating pump
C)
air lift pump
D)
submersible pump
An air vessel is a closed chamber containing compressed air at the top and liquid at the bottom, used specifically in reciprocating pumps. Its primary functions are: 1) To reduce the acceleration head (pulsations) of the liquid, ensuring a more uniform and continuous flow at the delivery end. 2) To reduce the friction losses in the pipeline by smoothing out the velocity fluctuations. 3) To protect the pump and piping from hydraulic shocks (water hammer). In contrast, centrifugal pumps provide a continuous flow by nature and do not require air vessels. Air lift pumps operate on the principle of density difference using injected air, and submersible pumps are typically centrifugal or helical in design, neither of which utilizes an air vessel for flow smoothing.
Rankine’s theory of active earth pressure assumptions are
A)
soil mass is homogenous, dry and cohesion less
B)
ground surface may be horizontal or inclined
C)
back of the wall is vertical and smooth
D)
all the above
Rankine's Theory of Earth Pressure is based on several simplifying assumptions to derive the active and passive pressure coefficients.
1. **Soil Properties (Option a):** Rankine assumed the soil is homogeneous (uniform properties throughout), dry (or saturated, but the basic theory starts with dry/cohesionless soil), and cohesionless (c = 0). This allows the use of the internal friction angle (φ) as the primary strength parameter.
2. **Ground Geometry (Option b):** The theory is applicable whether the ground surface is horizontal or inclined at an angle (β) to the horizontal.
3. **Wall Interface (Option c):** A critical assumption is that the back of the wall is perfectly smooth (no friction between the wall and the soil) and vertical. This ensures that the failure plane is planar and the resultant pressure acts horizontally.
Since all three statements (a, b, and c) are fundamental assumptions of Rankine's theory, the correct option is 'd'.
If F is the drag force, u is the free upstream velocity around a submerged body of projected area A and ρ is the density of the fluid then drag coefficient Cd is
A)
F / (ρu^2 A)
B)
F / (ρu^2 A/2)
C)
F / (ρu^2 A^2)
D)
none of the above
The drag force (F) acting on a body moving through a fluid (or a fluid flowing past a stationary body) is defined by the drag equation. The formula is: F = Cd * (1/2 * ρ * u^2) * A, where:
- F is the drag force
- Cd is the dimensionless drag coefficient
- ρ (rho) is the density of the fluid
- u is the free upstream velocity
- A is the projected frontal area of the body.
To find the expression for the drag coefficient (Cd), we rearrange the formula to solve for Cd:
Cd = F / (1/2 * ρ * u^2 * A)
This can be rewritten as: Cd = F / (ρu^2 A / 2).
Comparing this to the options:
- Option (a) F / (ρu^2 A) is incorrect because it misses the factor of 1/2 (dynamic pressure term).
- Option (b) F / (ρu^2 A/2) matches the derived formula exactly.
- Option (c) F / (ρu^2 A^2) is incorrect as the area A should be to the first power.
The convexity is provided to the carriage way between the crown and the edge of the pavement, is known as
A)
camber
B)
super-elevation
C)
height of the pavement
D)
none of the above
1. Definition of Camber: Camber is the transverse slope provided to the road surface. It is the convexity provided to the carriageway from the crown (the highest point of the road) to the edges.
2. Purpose: The primary objective of providing camber is to drain rainwater from the road surface to the side drains, preventing water logging and protecting the pavement from water penetration, which would otherwise weaken the subgrade.
3. Analysis of other options:
- Super-elevation (Option b): This is the transverse slope provided on horizontal curves to counteract centrifugal force, tilting the road inward toward the center of the curve. It is not for drainage across the entire carriageway but for stability during turning.
- Height of the pavement (Option c): This refers to the vertical distance of the pavement surface from a datum or the thickness of the pavement layers, which is unrelated to the convexity for drainage.
Therefore, the convexity provided between the crown and the edge is specifically termed as 'camber'.
Hydraulic jump is an example of
A)
steady gradually varied flow
B)
unsteady gradually varied flow
C)
rapidly varied flow
D)
uniform flow
A hydraulic jump occurs when a high-velocity supercritical flow transitions abruptly to a low-velocity subcritical flow, resulting in a sudden rise in the water surface level and significant energy dissipation through turbulence. In fluid mechanics, open channel flows are categorized based on how the depth changes over distance:
1. Uniform Flow: Depth remains constant along the channel.
2. Gradually Varied Flow (GVF): Depth changes slowly over a long distance (e.g., backwater curves).
3. Rapidly Varied Flow (RVF): Depth changes abruptly over a very short distance.
Since a hydraulic jump involves a sudden, abrupt change in depth and velocity over a short distance, it is a classic example of Rapidly Varied Flow (RVF). Options (a) and (b) are incorrect because the change is not gradual, and option (d) is incorrect because the depth is not constant.
In non-uniform steady gradually varied flow
A)
velocity varies gradually
B)
depth changes gradually
C)
discharge changes
D)
pressure changes gradually
In fluid mechanics, specifically open channel flow, flow is classified based on how parameters change with respect to time and space.
1. **Steady Flow**: The flow parameters (velocity, depth, etc.) at any point do not change with time. Therefore, the discharge (Q) remains constant throughout the reach, making option (c) incorrect.
2. **Non-Uniform Flow**: The flow parameters change from one section to another along the length of the channel.
3. **Gradually Varied Flow (GVF)**: This is a specific type of non-uniform flow where the depth of flow (y) changes slowly over a long distance. Because the depth changes gradually, the streamlines are nearly parallel, and the pressure distribution remains approximately hydrostatic.
Comparing the options:
- Option (a): While velocity does change, GVF is specifically defined by the gradual change in the water surface profile (depth).
- Option (b): This is the fundamental definition of GVF. The depth changes gradually over a long distance.
- Option (c): In steady flow, discharge is constant by definition.
- Option (d): While pressure changes, the defining characteristic of GVF is the gradual variation of the depth of flow.
Model of river is
A)
simple model
B)
undistorted model
C)
distorted model
D)
all the above
In fluid mechanics, model scaling is categorized based on the scale ratios used for different dimensions.
1. **Undistorted Models**: These are models where the scale ratio is the same for all linear dimensions (length, width, and depth). This maintains geometric similarity.
2. **Distorted Models**: These are models where different scale ratios are used for different dimensions (e.g., the horizontal scale is different from the vertical scale).
**Application to River Models**: Rivers are typically very wide and shallow. If an undistorted model were used (e.g., a 1:100 scale), the depth of the water in the model would become extremely small (often just a few millimeters), leading to excessive surface tension effects and viscous forces that would dominate the flow, making the model physically inaccurate (violating Froude scaling). To prevent this and ensure that the flow remains representative of the prototype, the vertical scale (depth) is intentionally made larger than the horizontal scale. This process is called 'distortion'. Therefore, models of rivers, harbors, and estuaries are almost always distorted models.
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. It is used to determine the friction factor for fluid flow in pipes across laminar, transitional, and turbulent regimes. However, historically and technically, the Stanton-Pannel diagram is another name for a similar plot used to represent the same relationship between these parameters. Therefore, both 'Moody's diagram' and 'Stanton-Pannel diagram' refer to this specific graphical representation of fluid friction. Option (c) is incorrect because the Reynolds diagram typically refers to different concepts or the general study of flow regimes, not specifically the friction factor plot.
The final setting of the plates of theodolite when taking a foresight is achieved by using the
A)
upper clamps screw
B)
upper tangent screw
C)
lower clamp screw
D)
lower tangent screw
In the operation of a transit theodolite, the process of sighting a target (whether it is a backsight or a foresight) involves two main steps: coarse adjustment and fine adjustment.
1. Coarse Adjustment: The upper clamp screw is loosened, and the telescope is rotated approximately toward the target. Once the telescope is nearly aligned, the upper clamp screw is tightened to lock the upper plate to the telescope.
2. Fine Adjustment (Final Setting): To achieve precise alignment with the target, the 'upper tangent screw' (also known as the slow-motion screw) is used. This screw allows for very small, controlled movements of the telescope, ensuring the cross-hairs are exactly centered on the target.
Why other options are incorrect:
- Upper clamp screw (a): This is used to lock or unlock the telescope for coarse rotation; it cannot provide the precision required for 'final setting'.
- Lower clamp screw (c): This locks the entire instrument (lower plate) to the tripod head; it is used during the initial centering and leveling, not for sighting a specific point.
- Lower tangent screw (d): This is used for the fine adjustment of the lower plate relative to the tripod, typically used during the initial orientation of the instrument, not for the final sighting of a foresight target.
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 in 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. Mathematically, for 3-dimensional flow, it is expressed as the sum of the second-order partial derivatives of the hydraulic head with respect to the spatial coordinates (x, y, and z) equaling zero: ∂²h/∂x² + ∂²h/∂y² + ∂²h/∂z² = 0.
Analysis of options:
- Option (a) uses φ, which typically denotes a potential function or stream function. While Laplace equations can be written for potential functions, in the specific context of soil mechanics flow nets and seepage, the primary variable is the hydraulic head (h).
- Option (b) is the standard form of the Laplace equation for 3D seepage in soil mechanics.
- Option (c) represents the Continuity Equation (divergence of velocity equals zero) for an incompressible fluid, not the Laplace equation.
- Option (d) is incorrect as option (b) is the standard representation.
Ground water occurs in different zones below ground level (GL). The zone just below the GL is
A)
zone of aeration
B)
capillary fringe
C)
unconfined aquifer
D)
pressure or confined aquifer
In hydrology, the subsurface is divided into distinct zones based on the saturation of the soil/rock pores.
1. **Zone of Aeration (Unsaturated Zone):** This is the layer immediately below the ground level (GL) and extending down to the water table. In this zone, the pore spaces contain both air and water. Because it is the topmost layer of the subsurface, it is the zone 'just below the GL'.
2. **Capillary Fringe:** This is a thin transition layer located immediately above the water table. Water is drawn upward from the water table by capillary action. While it is part of the aeration zone in a broad sense, it is specifically located at the bottom of that zone, not just below the GL.
3. **Unconfined Aquifer (Phreatic Zone):** This is the zone below the water table where all pore spaces are completely filled with water (saturated). It is located below the zone of aeration.
4. **Confined Aquifer (Pressure Aquifer):** This is a saturated zone trapped between two impermeable layers (aquitards/aquicludes), usually located much deeper in the subsurface.
Therefore, the zone immediately following the ground surface is the zone of aeration.
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 (Option b):** This is designed 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) without the need for traffic signals or stopping. The use of loop ramps and directional ramps ensures that there is no crossing of traffic streams (no interference), making it the ideal choice for continuous flow.
2. **Diamond Interchange (Option c):** While it provides grade separation for the main roads, the ramps typically intersect with the minor road at grade, requiring traffic signals or stop signs. This introduces 'interference'.
3. **Trumpet Interchange (Option d):** This is used where one road terminates into another (a T-junction), not for the intersection of two continuous roads.
4. **Delta Interchange (Option a):** This is a variation of a T-junction interchange and does not serve the purpose of a full four-way intersection of two roads without interference.
Therefore, the cloverleaf is the standard grade separation provided to eliminate interference at the intersection of two major roads.