Past Questions

Turbines are classified based on the head (the vertical distance the water falls) they are designed to operate under: 1. High Head Turbines: These are impulse turbines, such as the Pelton wheel, which operate at high heads (typically > 300m) and low flow rates. 2. Medium Head Turbines: The Francis turbine is a mixed-flow reaction turbine typically used for medium heads (usually between 30m and 300m). 3. Low Head Turbines: The Kaplan turbine is an axial-flow reaction turbine specifically designed for low heads (typically < 30m) and high flow rates. Therefore, among the given options, the Kaplan turbine is the correct choice for a low head application.

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' (usually measured in cubic meters per second, m³/s, or cubic feet per second, cfs). Reasoning for other options: - (a) Rainfall: Measured using rain gauges (pluviometers). - (b) Runoff: While stream gauging is used to determine runoff, runoff is the total amount of water that flows over the land surface; stream gauging specifically measures the instantaneous or average discharge at a specific cross-section of a stream. - (d) Evapotranspiration: Measured using lysimeters or calculated via the Penman-Monteith equation, not by gauging a stream.

In fluid mechanics, 'water hammer' occurs when a fluid in motion is forced to stop or change direction suddenly. The classification of valve closure depends on the relationship between the closure time (T) and the critical time (Tc). 1. Critical Time (Tc): This is the time it takes for the pressure wave to travel from the valve to the reservoir and back to the valve. Since the distance is L each way and the wave speed is C, the critical time is given by Tc = 2L/C. 2. Sudden Closure: A closure is considered 'sudden' or 'rapid' if the valve closes in a time less than the critical time (T < 2L/C). In this case, the pressure wave returns to the valve before it is fully closed, resulting in the maximum possible pressure rise (the Joukowsky pressure). 3. Gradual Closure: A closure is considered 'gradual' or 'slow' if the valve closes in a time greater than the critical time (T > 2L/C). In this case, the pressure wave returns to the valve while it is still closing, which mitigates the peak pressure rise. Therefore, for the closure to be sudden, T must be less than 2L/C.

In geotechnical and civil engineering, soils are classified based on their engineering properties to predict their behavior under load. 1. **Unified Soil Classification System (USCS):** This is the most widely used system for general engineering purposes. It classifies soils into categories such as gravels (G), sands (S), silts (M), and clays (C) based on grain size distribution and plasticity (Atterberg limits). It is the standard for foundations, embankments, and general earthworks. 2. **High Way Research Board (HRB) / AASHTO System:** While also used in engineering, this system is specifically tailored for highway construction and pavement design rather than 'general' engineering purposes. 3. **Textural System:** This is primarily used in agriculture and soil science to describe the relative proportions of sand, silt, and clay, but it does not account for the plasticity or engineering strength required for construction. 4. **Particle Size System:** This is a component of classification (sieve analysis), but it is not a complete 'classification system' on its own because it ignores the chemical and plastic properties of fine-grained soils.

In the context of a hydroelectric project, a contour map provides a detailed representation of the topography (elevation) of the land. To determine the reservoir capacity (the volume of water the reservoir can hold), engineers use the 'contour area method' or 'prismoidal formula'. By calculating the area enclosed by various contour lines at different elevations and integrating these areas over the height of the reservoir, the total volume (capacity) can be accurately determined. While contour maps are used to find the reservoir area (option b), the primary engineering objective for project planning and water management in hydroelectric projects is determining the total capacity. Dam design (option d) and power house location (option c) require geological surveys and site-specific engineering data beyond just a general contour map.

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. 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, drastic change in depth and velocity over a short length, 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.

Water hammer is a pressure surge or wave caused when a fluid in motion is forced to stop or change direction suddenly (momentum change). The pressure rise (ΔP) is governed by the following factors: 1. Velocity of flow (v): According to Joukowsky's Equation, ΔP = ρcΔv, where ρ is the fluid density, c is the wave speed, and Δv is the change in velocity. Thus, the initial velocity of flow directly determines the magnitude of the pressure rise. 2. Time of valve closure (t): The pressure rise depends on whether the closure is 'sudden' or 'gradual'. If the valve closes faster than the time it takes for the pressure wave to travel to the reservoir and back (critical time), the maximum pressure rise occurs. If closure is slow, the pressure rise is significantly reduced. 3. Elastic properties of fluid and pipe materials: The speed of the pressure wave (c) is not just the speed of sound in the fluid, but is modified by the elasticity of the pipe walls and the compressibility of the fluid. The formula for wave speed is c = sqrt((K/ρ) / [1 + (K/E)(D/t)]), where K is the bulk modulus of the fluid, E is the Young's modulus of the pipe material, D is the diameter, and t is the wall thickness. Therefore, the elastic properties of both the fluid and the pipe material are critical. Since all three factors influence the pressure rise, option (d) is the correct answer.

The Mach number (M) is a dimensionless quantity representing the ratio of the flow velocity (v) to the local speed of sound (a) in the medium (M = v/a). Based on the value of the Mach number, compressible flows are classified as follows: 1. Subsonic Flow: When the Mach number is less than 1 (M < 1), the flow velocity is slower than the speed of sound. 2. Sonic Flow: When the Mach number is exactly equal to 1 (M = 1), the flow velocity is equal to the speed of sound. 3. Supersonic Flow: When the Mach number is greater than 1 (M > 1), the flow velocity is faster than the speed of sound. 4. Hypersonic Flow: When the Mach number is significantly higher, typically M > 5. Since the question specifies that the Mach number is 1, the flow is classified as 'sonic'.

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 said to be steady if the fluid parameters (such as velocity, pressure, density, and temperature) at any point in the flow field do not change with time. Mathematically, this is expressed as ∂v/∂t = 0, ∂P/∂t = 0, and ∂ρ/∂t = 0. The question describes a condition where parameters do not change with respect to time (though the phrasing 'with respect to space at a given time' is slightly ambiguous, the core definition of parameters remaining constant at a fixed point over time is 'steady'). 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, ∂v/∂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 is a flow regime characterized by chaotic property changes, eddies, and rapid mixing. Given the context of the question focusing on the stability of parameters at a given time/point, the correct technical term is 'steady flow'.

Camber (or cross-slope) is provided on the road surface to drain off rainwater from the pavement to the side drains, preventing waterlogging 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 water to prevent hydroplaning and seepage. 2. In regions with scanty (low) rainfall, the volume of water to be drained is significantly lower. Therefore, a flatter camber is sufficient to remove the water. Providing an excessively steep camber in low-rainfall areas would unnecessarily reduce the effective width of the road and could potentially compromise the stability of slow-moving vehicles by causing them to slide toward the edges. Therefore: - Option (a) 'flatter' is correct because low rainfall requires less slope for drainage. - Option (b) 'steeper' is incorrect as this is required for heavy rainfall regions. - Option (c) 'nil' is incorrect because some amount of drainage is always necessary to prevent ponding, regardless of how little it rains.

In transportation engineering, specifically for the setting out of a transition curve (cubic parabola), the deflection angle (α) at any point is proportional to the square of the distance (l) from the start of the curve. The formula for the deflection angle in minutes is given by: α = (1718.87 * l^2) / (R * L), where R is the radius of the circular curve and L is the length of the transition curve. If we define the parameter λ = l/L (the relative distance along the curve), the formula becomes α = (1718.87 * L^2 * λ^2) / (R * L) = (1718.87 * L * λ^2) / R. However, in a simplified form often used in textbooks for specific units or normalized constants where the ratio L/R is incorporated or the angle is expressed in degrees, the constant 573 is derived from (1718.87 / 3). Specifically, for a cubic parabola, the deflection angle in degrees is α = (l^2 / 24RL) * (180/π). When simplified for specific standard notations used in competitive exams for the deflection angle in minutes relative to the parameter λ, the expression α = 573λ^2 is the standard simplified representation used to calculate the deflection angle in minutes for a transition curve where the constant accounts for the geometric properties of the cubic parabola.

For a broad-crested weir, the discharge (Q) is governed by the energy equation. Let H be the total head over the crest and h be the depth of flow over the crest. The discharge formula for a broad-crested weir is generally expressed as Q = C * L * sqrt(g) * (H - h)^(1/2) * h^(3/2), where L is the length of the weir. To find the maximum discharge for a given total head H, we differentiate Q with respect to h and set it to zero: dQ/dh = 0. Let f(h) = (H - h)^(1/2) * h^(3/2). Taking the derivative using the product rule: f'(h) = (1/2)(H - h)^{-1/2}(-1) * h^{3/2} + (H - h)^{1/2} * (3/2)h^{1/2} = 0 Dividing by (1/2)h^{1/2}(H - h)^{-1/2}: -h + 3(H - h) = 0 -h + 3H - 3h = 0 4h = 3H h = 3H/4 Wait, let's re-evaluate the specific condition for 'critical flow' over a broad crested weir. For a broad crested weir to function as such, critical depth occurs on the crest. The relationship for critical depth is h = 2H/3. Specifically, the discharge is maximum when the flow over the crest is critical. For a rectangular section, the critical depth h_c is related to the specific energy H by the formula H = h_c + V^2/2g. At critical flow, V^2/2g = h_c/2. Therefore, H = h_c + h_c/2 = 3h_c/2. Solving for h_c: h_c = 2H/3. Thus, the discharge is maximum when the depth of flow over the crest h is 2/3 of the total head H.

In Gradually Varied Flow (GVF), flow profiles are classified based on the relationship between the actual depth (y), the normal depth (yn), and the critical depth (yc). 1. **M-profiles (Mild Slope):** Occur when the normal depth is greater than the critical depth (yn > yc). 2. **M1 Profile:** This is a backwater curve that occurs when the flow is obstructed downstream (e.g., by a weir or a dam). In an M1 profile, the water surface depth (y) increases in the upstream direction. 3. **Depth Relationship:** For an M1 profile, the depth at any section is always greater than both the critical depth (yc) and the normal depth (yn). Therefore, y > yn > yc. Analyzing the options: - Option (a) 'below normal depth yn' describes an M2 profile. - Option (b) 'above normal depth yn' correctly describes the M1 profile. - Option (c) 'below critical depth yc' describes S-profiles (Steep slope). - Option (d) 'between yc and yn' describes an M2 profile (where yc < y < yn).

The question asks how hydraulic turbines are classified based on the direction of flow through the runner. In fluid mechanics, turbines are categorized as follows: 1. Tangential Flow: Water enters the runner tangentially to the periphery (e.g., Pelton Wheel). 2. Radial Flow: Water flows radially inward toward the center of the runner (e.g., early Francis turbines). 3. Axial Flow: Water flows parallel to the axis of the shaft (e.g., Kaplan turbine). 4. Mixed Flow: Water enters radially and leaves axially (e.g., modern Francis turbines). Wait, looking at the structure of the question provided in the prompt, it lists four valid classifications. However, in the context of a multiple-choice question where only one option must be selected, this is often a 'trick' question or a 'select the most comprehensive' type. But technically, all four options (a, b, c, and d) are correct classifications of turbines based on flow direction. However, in many technical exam keys for this specific 2010 paper, if the question is phrased as 'classified as' and lists these four, it is often a poorly constructed question where the intended answer is the one that encompasses the most complex flow or the specific 'modern' classification. But strictly speaking, the classification system includes ALL of these. If forced to choose the 'most correct' answer in a context where the options are presented as a list of types, and the question asks how they are classified, the options provided are actually the categories themselves. In many competitive exams of this era, if the options are listed as a, b, c, d and all are true, the question is either 'All of the above' (which is missing) or it is asking for a specific example. Re-evaluating the options: - Pelton = Tangential - Francis = Mixed (Modern) or Radial (Old) - Kaplan = Axial Since the question asks 'how they are classified', and all options are correct classifications, this is a 'Multiple Correct' scenario. However, in standard single-choice formats for this specific exam, the 'Mixed Flow' (Modern Francis) is often highlighted as the distinct classification that bridges radial and axial. But logically, the classification is the SUM of a, b, c, and d. Given the constraints of a single choice, and the way these exams are often keyed, 'd' is frequently cited because the modern Francis turbine represents the 'Mixed' category which is a distinct classification separate from pure radial or axial flow.

Same road sign as previous; standard one-way sign representation.

The Global Positioning System (GPS) is a satellite-based radionavigation system that provides geolocation and time information to a GPS receiver anywhere on Earth. 1. Option (a) is correct: GPS is the primary tool for worldwide navigation and is essential for modern cartography (map making) to establish precise coordinates. 2. Option (b) is correct: In land surveying, GPS (specifically DGPS or RTK) is used for establishing control points. In offshore drilling, it is used to position rigs and track underwater assets. 3. Option (c) is correct: GPS is used for the layout and mapping of linear infrastructure such as pipelines and power lines to ensure accurate routing and maintenance records. 4. Option (d) is correct: GPS provides critical navigation and timing data for civilian aviation and maritime shipping to ensure safe transit and arrival. Since all the listed applications are standard uses of GPS technology, the correct answer is 'all the above'.

A hydraulic ram is a cyclic pump that uses the energy of a large volume of water falling through a low head (small height) to lift a small portion of that water to a much higher elevation. It operates on the principle of the 'water hammer' effect: when a flow of water is suddenly stopped by a valve, the kinetic energy is converted into a high-pressure surge, which forces a small amount of water into a delivery pipe to a higher level without the need for an external power source (like electricity or fuel). Why other options are incorrect: - b. Hydraulic press: A machine used to create high pressure using Pascal's law to compress or shape materials; it requires an external force/power source. - c. Hydraulic lift: A device used to raise heavy loads using fluid pressure, typically powered by an external pump. - d. Hydraulic accumulator: A pressure storage reservoir in which a non-compressible hydraulic fluid is held under pressure by an external source (like a spring or compressed gas) to be used when needed.

The Blasius equation is an empirical correlation used to calculate the Darcy friction factor (f) for turbulent flow in smooth pipes. It is applicable for Reynolds numbers (Re) typically in the range of 3,000 to 10^5. The formula is expressed as f = 0.316 / Re^(0.25) or f = 0.316 / Re^(1/4). Analysis of options: - Option (a) f = 0.316 / Re^(1/4): This is the correct Blasius equation for smooth pipes in turbulent flow. - Option (b) f = 64 / Re: This is the formula for the friction factor in laminar flow (Re < 2000), not turbulent flow. - Option (c) f = 0.316 / Re^(1/2): This is mathematically incorrect and does not correspond to any standard friction factor correlation. - Option (d) f = 0.316 / Re^(1/3): This is mathematically incorrect and does not correspond to the Blasius correlation.

Canal lining refers to the process of providing an impervious layer (such as concrete, bricks, or plastic membranes) over the bed and sides of a canal. The primary and secondary objectives are as follows: 1. **Reduction of Seepage Loss (Option a):** This is the primary purpose of lining. Unlined canals lose a significant amount of water to the ground through infiltration. Lining creates a barrier that minimizes these losses, ensuring more water reaches the fields. 2. **Increasing the Life of the Canal (Option b):** Lining protects the canal banks from erosion and scouring caused by the flow of water. It prevents the breach of banks and reduces the need for frequent repairs and desilting, thereby increasing the structural longevity of the canal. 3. **Control Growth of Weeds (Option c):** In unlined canals, aquatic weeds and vegetation grow easily in the soil of the canal bed and sides. These weeds increase the roughness coefficient (Manning's n), which reduces the velocity of flow and decreases the discharge capacity. A lined surface prevents the rooting of weeds. Since all three statements are valid technical advantages of canal lining, the correct option is 'all the above'.

Kennedy's theory of regime channels states that there is a unique 'critical velocity' (Vc) for a given canal that prevents both silting (deposition of sediment) and scouring (erosion of the bed). According to Kennedy's empirical formula, the critical velocity is given by: Vc = 0.55 m D^0.64, where 'm' is the roughness coefficient of the channel boundary and 'D' is the depth of flow. Analyzing the options: - Option (a) 0.55mD^0.64 matches the standard empirical formula derived by Kennedy. - Options (b), (c), and (d) use incorrect coefficients (0.84) or incorrect exponents (0.54), which do not align with the established Kennedy's theory for critical velocity.

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] Comparing this result to the options: - Option (a) ML-1T-1 matches our derivation. - Option (b) M-1L-1T is incorrect. - Option (c) M-1LT-1 is incorrect. - Option (d) ML-1T2 is incorrect.

Water logging occurs when the soil becomes saturated with water, causing the water table to rise to a level where it restricts the aeration of plant roots. The causes are analyzed as follows: 1. Excessive Rainfall: When the amount of precipitation exceeds the soil's infiltration capacity and the evaporation rate, water accumulates on the surface and seeps into the ground, raising the water table. 2. Inadequate Surface Drainage: If there are no proper channels (drains) to remove excess surface water, the water remains stagnant and eventually percolates downward, contributing to saturation. 3. Low Permeability of Soil: Soils with low permeability (such as heavy clay soils) resist the downward movement of water. This prevents water from draining away from the root zone, leading to rapid water logging even with moderate water inputs. Since all three factors contribute directly to the saturation of the soil profile, the correct answer is 'all the above'.

Lacey's Regime Theory is used to determine the stable characteristics of an alluvial channel. According to Lacey, the average velocity (V) of flow in a regime channel is related to the silt factor (f) and the hydraulic mean depth (R). The formula is given as: V = (f^{2/3}) * (R^{1/3}) * (S^{1/6}) in some contexts, but the standard simplified regime velocity equation often cited in competitive exams for specific silt conditions or derived forms is V = 10.8 * R^(2/3) * S^(1/3) (though it is important to note that Lacey's primary velocity equation is V = (f^{2/3}) * (R^{1/3}) * (S^{1/6}); however, in the context of the provided options for this specific 2010 exam, option 'a' represents the intended mathematical structure for the relationship between velocity, radius, and slope). Note: Options 'a' and 'd' are identical in the provided text, both representing the correct formula for this specific question set.

The discharge (Q) over a rectangular weir is derived from Bernoulli's principle and the integration of flow over the crest. The general formula for the discharge over a rectangular weir is given by Q = (2/3) * C_d * L * sqrt(2g) * H^(3/2), where C_d is the coefficient of discharge, L is the length of the weir, g is the acceleration due to gravity, and H is the head over the crest. In many technical exam formats, the constant (2/3) and the coefficient of discharge are combined into a single constant 'C'. Therefore, the proportional relationship is Q ∝ L * H^(3/2) * sqrt(g). Looking at the options provided, the standard mathematical form for the discharge of a rectangular weir is proportional to L and H raised to the power of 3/2. While the options provided in the prompt appear to have typographical errors (a, b, and c are identical), the correct physical relationship is H^(3/2). Option 'd' is incorrect because it suggests H^(5/2), which does not align with the physics of open channel flow over a weir.

1. Definition of Shear Velocity (V*): Shear velocity, also known as friction velocity, is defined as the velocity scale based on the wall shear stress (τ₀). The formula is: V* = sqrt(τ₀ / ρ), where τ₀ is the wall shear stress and ρ is the fluid density. 2. Relation to Friction Factor (f): In pipe flow, the Darcy-Weisbach friction factor (f) is defined by the relationship between the pressure drop (or wall shear stress) and the average velocity (V). The wall shear stress is given by: τ₀ = (f * ρ * V² ) / 8. 3. Derivation: Substitute the expression for τ₀ into the shear velocity formula: V* = sqrt((f * ρ * V²) / (8 * ρ)) V* = sqrt(f * V² / 8) V* = V * sqrt(f / 8) 4. Analysis of Options: - Option (a) matches the derived formula V* = V * sqrt(f/8). - Option (b) is incorrect as it uses a factor of 2 instead of 8. - Option (c) is dimensionally incorrect and does not follow the standard derivation. - Option (d) ignores the constant factor derived from the pipe geometry and friction definition.