Question 1

Discharge equivalence of an ogee weir Under free-flow (non-drowned) conditions, the discharge over an ogee weir is effectively the same as that over which type of weir?

Accepted Answer

Introduction / Context: Ogee crests are shaped to match the lower nappe of a sharp-crested weir to minimize separation and maintain accurate discharge characteristics. Hence, their discharge relation mirrors that of sharp-crested weirs when flow is not submerged. Given Data / Assumptions: Free overflow (no submergence from downstream water level). Standard ogee profile correctly shaped for approach velocity. Head measured over the crest as in sharp-crested calibrations. Concept / Approach: Because an ogee is designed to conform to the nappe trajectory, it behaves hydraulically like a sharp edge for free overflow. Thus, Q ∝ H^(3/2) with a similar coefficient of discharge, subject to approach and aeration conditions. Step-by-Step Solution: Assume free overflow over ogee crest.Apply sharp-crested weir equation Q = C_d * b * sqrt(2 g) * H^(3/2) (adjusted for end contractions if relevant).Note that correct crest aeration preserves this relationship. Verification / Alternative check: Empirical calibrations show close agreement of discharge coefficients between ogee and sharp-crested weirs under free flow. Why Other Options Are Wrong: V-notch and Cipoletti use different head–discharge relations; drowned weirs involve submergence corrections; broad-crested weirs have different flow regimes and coefficients. Common Pitfalls: Applying free-flow formula when downstream submergence exists; neglecting approach velocity corrections. Final Answer: Sharp-crested weir

Question 2

Error propagation for a triangular (V-notch) weir For a triangular notch (V-notch), discharge varies as H^(5/2), where H is the head over the crest. If there is a +1% error in measuring H, the approximate percentage error in computed discharge Q is:

Accepted Answer

Introduction / Context: Knowing how measurement errors propagate into discharge estimates helps set instrumentation accuracy. For a V-notch weir, Q depends strongly on head, so small head errors can produce larger percentage errors in Q. Given Data / Assumptions: Q ∝ H^(5/2) for a triangular notch under free flow. Small relative error in head measurement: dH/H = +1%. Linearized (differential) error propagation is adequate. Concept / Approach: For Q ∝ H^n, the relative error in Q is n times the relative error in H: dQ/Q ≈ n * dH/H. Here, n = 5/2 = 2.5. Step-by-Step Solution: Write Q = k * H^(5/2).Take logarithms and differentiate: dQ/Q = (5/2) * dH/H.For dH/H = 0.01 ⇒ dQ/Q ≈ 2.5 * 0.01 = 0.025 = 2.5%. Verification / Alternative check: More exact finite-difference check: ((H * 1.01)^(2.5) − H^(2.5)) / H^(2.5) ≈ 2.5% for small errors, confirming the differential result. Why Other Options Are Wrong: 1.25% and 1.5% correspond to lower exponents; 2.0% assumes square dependence; 5.0% doubles the correct factor. Common Pitfalls: Using the rectangular-weir exponent (3/2) accidentally; mixing absolute and relative errors. Final Answer: 2.50%

Question 3

In fluid mechanics, identify which of the following typical real-world flows is most likely not laminar. Consider practical Reynolds numbers and usual sizes/velocities in field or laboratory conditions.

Accepted Answer

Introduction / Context: Whether a flow is laminar or turbulent depends mainly on the Reynolds number Re = (ρ * V * L) / μ, where ρ is density, V is velocity, L is a characteristic length (for pipes, diameter D), and μ is dynamic viscosity. Many small-scale or very slow flows are laminar, while large, fast pipe flows are typically turbulent. Given Data / Assumptions: Typical municipal or industrial water pipelines carry significant discharge with pipe diameters from tens to hundreds of millimetres and average velocities near 1–3 m/s. Measuring instruments for oil often use very small passages and low velocities. Plant xylem conduits are microscopic; blood vessels have small diameters and pulsatile but moderate velocities. Groundwater seepage occurs through tiny pores with very low velocities. Concept / Approach: Laminar flow in a pipe is likely when Re < 2000; turbulence dominates for Re > 4000. For water pipelines, taking D ≈ 0.1–1.0 m and V ≈ 1 m/s with ν ≈ 1e-6 m^2/s gives Re ≈ 10^5–10^6, far into the turbulent regime. Small passages and low speeds strongly reduce Re, favouring laminar flow in instruments, plants, and porous media. Step-by-Step Solution: Estimate Re in water pipe: Re ≈ (V * D) / ν ≈ (1 m/s * 0.1 m) / (1e-6 m^2/s) ≈ 1e5 → turbulent.Oil in instruments: small D and higher μ (lower ν) with low V → Re commonly well below 2000 → laminar.Plant xylem and groundwater: micro-scale channels with minute velocities → extremely low Re → laminar/creeping flow.Blood in arteries: although pulsatile and sometimes transitional in large arteries, typical mean Re remains in laminar to transitional range, not fully turbulent. Verification / Alternative check: Empirical experience in water distribution shows roughness-dependent head losses consistent with turbulent correlations (Darcy–Weisbach with turbulent f or Hazen–Williams), confirming turbulence prevalence in pipelines. Why Other Options Are Wrong: Oil in instruments: designed for laminar operation and precise metering.Rise in plants: capillary/xylem flow at very low Re → laminar.Blood in arteries: generally laminar except under special conditions.Groundwater beds: Darcy’s law assumes laminar seepage. Common Pitfalls: Assuming all biological flows are turbulent; most are laminar due to scale. Ignoring viscosity differences between oil and water. Final Answer: Flow in water pipe lines

Question 4

Which governing equation set is applicable to unsteady (time-varying) flow in open channels? Choose the most appropriate theoretical framework used in open-channel hydraulics.

Accepted Answer

Introduction / Context: Open-channel flows such as river floods, dam-break waves, and surges are often unsteady and nonuniform. Their transient behaviour is described by depth-averaged equations that capture time variation and spatial gradients of depth and discharge. Given Data / Assumptions: Free-surface flow dominated by gravity (shallow water assumption). One-dimensional depth-averaged modelling is acceptable over channel reaches. Time dependence must be represented explicitly. Concept / Approach: The Saint-Venant (shallow-water) equations comprise continuity and momentum partial differential equations with source terms for bed slope, friction, and external inputs. They generalize gradually varied flow to unsteady conditions and are the standard basis of flood routing and surge simulation. Step-by-Step Solution: Continuity: ∂A/∂t + ∂Q/∂x = q_l (lateral inflow per unit length).Momentum: ∂Q/∂t + ∂(βQ^2/A)/∂x + gA ∂y/∂x = gA(S0 − Sf) + external forces.These equations allow wave celerity, backwater effects, and reflections to be modelled.Numerical schemes (e.g., finite volume) integrate them for hydrographs and stage predictions. Verification / Alternative check: Special cases recover steady GVF (when ∂/∂t = 0) or kinematic waves (when inertia is neglected). Hence they correctly subsume many open-channel formulae as limits. Why Other Options Are Wrong: Chezy/Manning: empirical steady uniform relations; do not model time dependence or spatial storage.Bernoulli: steady inviscid along a streamline; not a full unsteady channel model.Darcy–Weisbach: pipe head loss, not open-channel unsteady theory. Common Pitfalls: Applying steady uniform formulas to floods or surges. Neglecting friction/source terms in the momentum equation. Final Answer: Saint-Venant equations (unsteady continuity and momentum for shallow water)

Question 5

The magnitude of water hammer pressure rise in a pipeline depends on several factors. Which comprehensive choice correctly lists the influencing parameters?

Accepted Answer

Introduction / Context: Water hammer is a transient pressure surge caused by rapid changes in flow velocity, such as sudden valve closures or pump trips. Correct design requires understanding all parameters that influence the peak pressure rise and wave speed. Given Data / Assumptions: Rigid/elastic pipe containing a slightly compressible liquid (e.g., water). Valve or pump manoeuvres can be fast or slow relative to wave travel time. Reflections occur at boundaries (valves, reservoirs, elbows). Concept / Approach: The Joukowsky relation Δp = ρ * a * ΔV shows that surge magnitude depends on fluid density ρ, wave speed a, and velocity change ΔV. The wave speed a itself depends on liquid compressibility and pipe wall elasticity: a = sqrt( K / ρ / (1 + (K * D)/(E * e)) ), where K is bulk modulus, E is pipe Young’s modulus, D pipe diameter, e wall thickness. Step-by-Step Solution: Faster closure → larger instantaneous ΔV → larger Δp.Longer pipeline → longer wave travel time 2L/a governs whether closure is “rapid” and affects reflection interactions.Stiffer pipe (higher E) → higher wave speed a → larger Δp for the same ΔV.Less compressible liquid (higher K) → higher a → larger Δp. Verification / Alternative check: Method of characteristics simulations confirm that closure schedule, pipe length, and material properties all alter peak and subsequent oscillations. Why Other Options Are Wrong: Any single-factor answer is incomplete; all listed factors contribute materially to surge magnitude. Common Pitfalls: Assuming “rigid column” without accounting for elasticity, which underestimates peak pressure. Ignoring reflections and timing relative to 2L/a. Final Answer: All of the above

Question 6

To avoid interruption of flow in a siphon due to air accumulation at the highest point, where should the small air vessel (air release/vent) be provided?

Accepted Answer

Introduction / Context: A siphon conveys liquid over a rise by maintaining a continuous column under sub-atmospheric pressure at the summit. Air can exsolve from water or be drawn in through small leaks, collecting at the top and breaking the siphon if not vented. Given Data / Assumptions: Closed conduit with a summit (highest point) above both reservoirs. Risk of air pocket formation at the crown due to low pressure. Objective: maintain continuity of the water column. Concept / Approach: Air pockets naturally migrate to and collect at the highest point. Providing an air vessel or automatic air-release/air-admittance device at the summit purges trapped air (or admits air for controlled shutdown), preventing vapor lock and loss of prime. Step-by-Step Solution: Identify the point of minimum absolute pressure: the summit.Install a small air vessel/vent at this crown location.Periodically or automatically discharge accumulated air to keep the conduit liquid-full. Verification / Alternative check: Field practice and siphon design guidelines consistently show air-release valves at summits; CFD and model tests confirm air entrapment zones align with the geometric high point. Why Other Options Are Wrong: Inlet/outlet: not the locus of trapped air accumulation.Arbitrary point: ineffective unless it coincides with the crown. Common Pitfalls: Omitting air release on long siphons with multiple local high points. Failing to provide vacuum-break for safe shutdown, leading to column separation. Final Answer: At the summit (crown) of the siphon

Question 7

The classical linear relation between shear stress and velocity gradient in a Newtonian fluid (viscosity law) was proposed by which scientist?

Accepted Answer

Introduction / Context: For many common fluids (water, air, light oils), the shear stress τ is proportional to the rate of strain (velocity gradient) du/dy. This linear proportionality defines Newtonian behaviour and introduces the key material property called dynamic (absolute) viscosity μ. Given Data / Assumptions: Simple shear between parallel plates is the reference configuration. Small enough rates of deformation to remain within Newtonian regime. Concept / Approach: Newton’s law of viscosity states τ = μ * (du/dy). Here μ is a constant for a Newtonian fluid at a given temperature and pressure. Non-Newtonian fluids do not follow this linear law (μ depends on shear rate). Step-by-Step Solution: Recognize the linear τ–(du/dy) constitutive equation.Attribute the proposal to Isaac Newton, who formalized the proportionality.Identify μ as dynamic (absolute) viscosity with SI units Pa·s (N·s/m^2). Verification / Alternative check: Textbooks and rheology references define Newtonian fluids via this relation. Bernoulli contributed to energy principles, Chezy/Bazin to open-channel empirical formulas, Helmholtz to vortex dynamics—not the viscosity law. Why Other Options Are Wrong: Bernoulli: energy/pressure–velocity relation, not constitutive law.Chezy and Bazin: channel resistance relations.Helmholtz: vorticity and fluid kinematics. Common Pitfalls: Confusing dynamic viscosity μ with kinematic viscosity ν = μ/ρ. Applying Newton’s law to non-Newtonian fluids without checking rheology. Final Answer: Newton

Question 8

Classify the type of flow: Which of the following describes a steady but non-uniform flow scenario?

Accepted Answer

Introduction / Context: Flow classification distinguishes whether properties vary with time (steady vs unsteady) and whether they vary in space along the streamline or cross-section (uniform vs non-uniform). Correct classification helps select appropriate equations and coefficients. Given Data / Assumptions: Steady means ∂()/∂t = 0 at a fixed point. Uniform means spatial invariance along the flow direction (properties do not change with x). Constant discharge implies time-invariant volumetric flow rate Q. Concept / Approach: In a duct with changing cross-section, keeping Q constant forces the mean velocity to change with area A(x) because V = Q/A. Thus the flow is non-uniform (varies with position) but steady (no time variation). Step-by-Step Solution: Option (b): Expanding tube, Q = constant → V decreases with x → spatial variation present → non-uniform; Q constant → steady.Option (a): Decreasing rate over time → unsteady.Option (c): Increasing rate over time → unsteady and non-uniform.Option (d): Increasing rate over time → unsteady (even if geometry is uniform).Option (e): Reservoir emptying → unsteady outflow. Verification / Alternative check: For (b), continuity gives dV/dx ≠ 0 with dV/dt = 0, which is the definition of steady, non-uniform flow. Why Other Options Are Wrong: (a), (c), (d), (e) all involve time variation of Q or head → unsteady. Common Pitfalls: Equating “uniform” with “constant Q”. Uniform refers to spatial uniformity, not discharge alone. Ignoring geometry changes when assessing uniformity. Final Answer: An expanding tube carrying a constant discharge rate

Question 9

A small fluid element can undergo which fundamental types of motion as it moves within a continuum?

Accepted Answer

Introduction / Context: Fluid kinematics describes motion without invoking forces. A differential fluid element in flow may change position, orientation, and shape. Recognizing these modes aids in understanding vorticity, strain rates, and velocity gradients. Given Data / Assumptions: Continuum hypothesis holds (properties are smoothly varying). Fluid element is infinitesimal, allowing linearization of velocity field. Concept / Approach: The local velocity gradient tensor decomposes into symmetric (rate-of-strain/deformation) and antisymmetric (rigid-body rotation) parts, plus the velocity vector itself accounts for translation. Hence, general motion combines translation, rotation, and distortion simultaneously. Step-by-Step Solution: Translation: element moves bodily with velocity vector V(x,t).Rotation: antisymmetric component corresponds to half the vorticity vector; causes spinning.Distortion: symmetric component produces extension, compression, and shear—changing shape/volume (for compressible flows). Verification / Alternative check: Any general linear velocity field V = A·x can be split into V = (Ω × x) + E·x, where Ω relates to rotation and E is the rate-of-strain tensor; adding a constant velocity gives translation. Why Other Options Are Wrong: Single-mode answers ignore the full kinematic decomposition; real flows commonly exhibit all three simultaneously. Common Pitfalls: Confusing particle rotation with streamline curvature; curvature can exist without local rigid-body spin. Assuming incompressible flow implies no distortion; shear deformation still occurs. Final Answer: All of the above (translation, rotation, and distortion)

Question 10

In Newton’s viscosity relation τ = μ (du/dy), the symbol μ represents which property of the fluid?

Accepted Answer

Introduction / Context: Precise terminology matters in fluid mechanics. Newton’s law of viscosity defines a proportionality constant between shear stress and velocity gradient. This constant has standard names and units that distinguish it from other viscosity measures. Given Data / Assumptions: Shear stress τ is proportional to du/dy for Newtonian fluids. SI units are used unless otherwise stated. Concept / Approach: In τ = μ (du/dy), μ is the dynamic (also called absolute) viscosity, with SI unit Pa·s (N·s/m^2). The kinematic viscosity is ν = μ/ρ with units m^2/s. Vague terms like “simple viscosity” or just “viscosity” can cause confusion in calculations and unit checks. Step-by-Step Solution: Identify the equation as Newton’s law of viscosity.Recognize μ as a property independent of the shear rate for Newtonian fluids.Select the precise term “dynamic viscosity”. Verification / Alternative check: Dimensional analysis: [μ] = [τ]/[du/dy] = (N/m^2) / (s^-1) = N·s/m^2 = Pa·s, confirming dynamic viscosity, not kinematic viscosity. Why Other Options Are Wrong: “Viscosity” and “simple viscosity” are imprecise; “absolute viscosity” is acceptable but the best standard term is dynamic viscosity.“All of the above” would imply every label is equally correct, which is misleading. Common Pitfalls: Mixing ν and μ in formulas (e.g., Reynolds number uses ν). Assuming μ is constant for non-Newtonian fluids. Final Answer: Dynamic viscosity

Question 11

An ideal fluid in theoretical fluid mechanics is defined by which combination of properties?

Accepted Answer

Introduction / Context: Many fundamental flow theorems (e.g., Bernoulli’s equation in its simplest form) are derived for an “ideal fluid.” Knowing the precise definition prevents misuse of inviscid formulas in situations where viscosity or compressibility matters. Given Data / Assumptions: Idealization for analytical convenience, not a real substance. Used in potential flow theory and elementary Bernoulli applications. Concept / Approach: An ideal fluid is inviscid (μ = 0) and incompressible (density constant). With μ = 0, there is no viscous shear; with constant density, the continuity equation simplifies and pressure–velocity relationships are tractable. Step-by-Step Solution: State “non-viscous” (inviscid) → neglect shear stresses.State “incompressible” → ρ = constant, acoustic effects ignored.Thus, the correct pair is: incompressible and non-viscous. Verification / Alternative check: Potential flow solutions assume irrotational, inviscid, incompressible flow. Low-speed water flows are often modelled as nearly incompressible, but never exactly inviscid in reality—hence the term “ideal”. Why Other Options Are Wrong: Incompressible and viscous: describes many real liquids, but not “ideal”.Compressible and non-viscous: used in some aerodynamics models, but not the textbook “ideal fluid” in basic hydraulics.Compressible and viscous: most general real fluid; far from “ideal”.“Inviscid only”: omits the incompressibility part of the classical definition. Common Pitfalls: Applying ideal inviscid results near walls where boundary layers dominate. Neglecting compressibility at high Mach numbers in gases. Final Answer: Incompressible and non-viscous (inviscid)

Question 12

Flow in circular pipes: criterion for turbulent regime  In internal flow through a straight circular pipe, the flow is classified as turbulent when the Reynolds number (based on pipe diameter) satisfies which condition?

Accepted Answer

Introduction / Context: Classifying pipe flow as laminar, transitional, or turbulent is fundamental for choosing head-loss correlations (e.g., Darcy–Weisbach with appropriate f) and for predicting mixing and heat transfer. The Reynolds number Re encapsulates the ratio of inertial to viscous forces and serves as the key indicator. Given Data / Assumptions: Straight, circular pipe of constant diameter. Re based on diameter: Re = (rho * V * D) / mu. Fully developed internal flow assumptions. Concept / Approach: Empirical evidence from Osborne Reynolds’ dye experiments shows three regimes: laminar (Re < about 2100), transitional (roughly 2100–3000), and turbulent (Re > about 3000). These thresholds are widely used in engineering design. Step-by-Step Solution: Identify the regime from the numerical range of Re.If Re > 3000, inertial effects dominate and disturbances amplify → turbulent flow.Therefore, the turbulent condition corresponds to “more than 3000.” Verification / Alternative check: Head-loss behavior: in turbulent flow, the friction factor depends weakly on Re and on relative roughness, unlike the f = 64/Re relation of laminar flow. Why Other Options Are Wrong: Less than 2100 → laminar, not turbulent. Between 2100 and 3000 → transitional regime, not purely turbulent. “None of these” is incorrect because a standard threshold exists. Common Pitfalls: For noncircular ducts, use hydraulic diameter; near entrances or fittings the thresholds can shift due to disturbances. Final Answer: more than 3000

Question 13

Internal (re-entrant) mouthpiece: effect of length on jet behavior  For an internal (re-entrant) mouthpiece fitted to a tank wall, which statements about jet behavior versus mouthpiece length (relative to its diameter) are correct?

Accepted Answer

Introduction / Context: Mouthpieces are short tubes attached to orifices. An internal (re-entrant or Borda’s) mouthpiece projects into the tank. Depending on its length-to-diameter ratio, the jet may either contract and pass through without wetting the wall (running free) or expand to contact the wall (running full), changing the discharge coefficient. Given Data / Assumptions: Internal (re-entrant) mouthpiece with sharp entry. Length-to-diameter ratio varied from about 1 to about 3. Steady head, incompressible flow, negligible air effects. Concept / Approach: Short re-entrant mouthpieces cause a vena contracta inside the tube; the core jet remains detached from the wall (running free). As length increases, boundary layers grow and the jet expands, touching the wall, so the mouthpiece runs full. Texts commonly cite transitions near L ≈ D (free) and L ≈ 3D (full). Step-by-Step Solution: Case L ≈ D: Flow separates just at the sharp edge; jet contracts and does not wet the wall → running free.Case L ≈ 3D: Boundary layer growth and pressure recovery make the jet expand to contact the wall → running full with jet diameter ≈ tube diameter.Therefore, both statements are valid. Verification / Alternative check: Discharge coefficients differ: running-free coefficients are lower than running-full values, matching qualitative behavior observed in experiments on Borda’s mouthpieces. Why Other Options Are Wrong: Choosing only one misses the documented length effects. “Neither” contradicts established mouthpiece behavior. Common Pitfalls: Confusing internal (re-entrant) with external mouthpieces; ignoring end contractions and length-scale effects. Final Answer: both (a) and (b)

Question 14

Hydraulic mean depth for pipes not running full (open-channel condition)  For a circular conduit flowing partially full (i.e., as an open channel), the hydraulic mean depth m is defined as which of the following?

Accepted Answer

Introduction / Context: When a circular pipe does not run full, it behaves as an open channel. In open-channel hydraulics, two related geometric parameters are used: hydraulic radius R = A / P (area over wetted perimeter) and hydraulic mean depth m = A / T (area over top width). Understanding the correct definition is essential for using Chezy or Manning equations in partially filled conduits. Given Data / Assumptions: Partially full circular conduit (free surface present). A = cross-sectional flow area. P = wetted perimeter (in contact with water). T = top width of the free surface. Concept / Approach: By definition for open-channel flow: hydraulic mean depth m is the ratio of area to top width, m = A / T. Hydraulic radius R is a different but related parameter R = A / P. Students often confuse these two, but they are used in different empirical relations. Step-by-Step Solution: Identify the regime: pipe not running full → open-channel treatment.Recall definitions: m = A / T (mean depth), R = A / P (hydraulic radius).Select the option that matches m = A / T. Verification / Alternative check: For a very wide channel, T ≫ depth, so m approaches the actual flow depth, consistent with intuition that “mean depth” ≈ depth for wide channels. Why Other Options Are Wrong: m = r(θ − sin θ) is an expression (up to constants) related to sector geometry, not the general definition of m. m = A / P defines hydraulic radius R, not mean depth. m = P / A or any inverted form has wrong dimensions. Common Pitfalls: Using A / P when asked specifically for hydraulic mean depth; mixing up R and m in Manning/Chezy applications. Final Answer: m = A / T

Question 15

Projectile just reaches the top of a vertical column  A jet is projected at 45° from a point 40 m away from the foot of a vertical column and just reaches the top of the column. Assuming ideal projectile motion, what is the height of the column?

Accepted Answer

Introduction / Context: Projectile kinematics is widely applied to free jets from nozzles. When a projectile “just reaches” an obstacle, the apex (maximum height) of the parabolic trajectory commonly coincides with the obstacle’s top for the critical case. Given Data / Assumptions: Launch angle θ = 45°. Horizontal distance from launch point to column foot = 40 m. Neglect air resistance. Critical case where the jet apex grazes the top of the column. Concept / Approach: For a projectile, the horizontal coordinate of the apex is x_apex = (u^2 * sin 2θ) / (2 g). For θ = 45°, sin 2θ = 1, so x_apex = u^2 / (2 g). The maximum height is H_max = (u^2 * sin^2 θ) / (2 g) = u^2 / (4 g) for θ = 45°. If the column is exactly at the apex, x_apex = 40 m and its height equals H_max. Step-by-Step Solution: Set x_apex = 40 m = u^2 / (2 g) ⇒ u^2 = 2 g * 40.Compute H_max = u^2 / (4 g) = (2 g * 40) / (4 g) = 20 m.Therefore, the column height is 20 m. Verification / Alternative check: Using the trajectory equation y = x tan θ − (g x^2) / (2 u^2 cos^2 θ) at x = 40 m with θ = 45° yields the same height. Why Other Options Are Wrong: 15 m and 30 m: Do not satisfy apex relations for θ = 45° at x = 40 m. 40 m and 60 m: Far exceed the maximum height given the apex location constraint. Common Pitfalls: Assuming the obstacle is not at the apex; forgetting sin 2θ = 1 at 45°; mixing metres with other units. Final Answer: 20 m

Question 16

Avoiding vaporisation (cavitation) at siphon summits  To avoid vaporisation in a pipeline crossing a ridge (i.e., at a siphon summit), the pipe centerline should be kept above the hydraulic gradient line by not more than approximately:

Accepted Answer

Introduction / Context: At high points in pressure pipelines (siphon summits), the static pressure may drop. If it falls below the vapor pressure head, vapor pockets form (cavitation/air binding), disrupting flow and damaging equipment. Designers therefore limit how far the summit rises above the hydraulic grade line (HGL). Given Data / Assumptions: Water at ordinary ambient temperatures. Allowance for minor losses and fluctuations. Rule-of-thumb limits applied in water-supply engineering. Concept / Approach: The vapor pressure head of water at room temperature corresponds to roughly 2–3 m of water column relative to absolute vacuum. Considering safety margins and dynamic effects, practice limits the summit’s elevation above the HGL to on the order of 6 m (often quoted around 6.0–6.5 m) to prevent local pressures from dropping to vapor pressure. Step-by-Step Solution: Identify allowable rise above HGL to keep piezometric head above vapor pressure head.Adopt the standard design guidance: about 6 m, commonly taken as ≈ 6.4 m in many problem sets.Therefore, select 6.4 m. Verification / Alternative check: More conservative designs choose ~6 m; the provided options include 6.4 m, aligning with typical textbook values. Why Other Options Are Wrong: 2.4 m: Too conservative; unnecessary for most systems. 10.0 m: Risks cavitation for ordinary temperatures. 5.0 m: Possible but not the standard value usually cited in exam contexts. Common Pitfalls: Ignoring temperature dependence of vapor pressure; neglecting transient (water hammer) depressions that can further reduce pressure at the summit. Final Answer: 6.4 m

Question 17

Factors affecting atmospheric pressure  Atmospheric pressure at a location varies primarily with which of the following?

Accepted Answer

Introduction / Context: Atmospheric pressure is the force per unit area exerted by the weight of the air column above the point of measurement. It is an important boundary condition in many hydraulic problems (e.g., cavitation, siphons, barometers). Given Data / Assumptions: Standard meteorological behaviors. No extreme phenomena (e.g., hurricanes) beyond typical variability. Concept / Approach: Pressure decreases with altitude as there is less overlying air mass. Temperature changes modify air density; warmer air expands (lower density) reducing pressure aloft, while cooler air increases density. Weather systems (highs/lows) reflect large-scale variations in atmospheric mass distribution, shifting local pressure up or down. Step-by-Step Solution: Altitude: higher elevation → lower atmospheric pressure.Temperature: warming generally lowers density, affecting pressure fields.Weather: synoptic-scale highs/lows directly change surface pressure. Verification / Alternative check: Barometric readings demonstrate daily and seasonal variations due to these factors; aviation altimeters require corrections for all three. Why Other Options Are Wrong: Any single-factor choice ignores other well-established contributors. Common Pitfalls: Assuming only altitude matters; forgetting temperature/pressure corrections used in fluid property tables. Final Answer: all of the above

Question 18

Attractive forces between fluid molecules  The tendency of molecules within the same fluid to attract each other is known as:

Accepted Answer

Introduction / Context: Molecular forces govern many interfacial and bulk fluid phenomena. Distinguishing cohesion and adhesion is vital for understanding capillarity, wetting, droplet formation, and surface tension. Given Data / Assumptions: Simple liquids, no complex surfactant effects. Standard definitions from fluid mechanics and physical chemistry. Concept / Approach: Cohesion refers to attraction between like molecules (e.g., water–water). Adhesion refers to attraction between unlike molecules (e.g., water–glass). Surface tension is a macroscopic manifestation of cohesive forces at an interface. Capillary action results from the interplay between adhesion (liquid–solid) and cohesion (liquid–liquid) plus gravity. Step-by-Step Solution: Identify the asked phenomenon: attraction among molecules of the same fluid → cohesion.Relate others: adhesion (unlike substances), surface tension (effect), capillarity (resulting behavior). Verification / Alternative check: Contact-angle behavior: water wets clean glass (adhesion > cohesion at interface), mercury does not (cohesion dominates), illustrating the concepts. Why Other Options Are Wrong: Capillarity is the consequence of cohesion and adhesion in small tubes. Surface tension is a bulk effect of cohesive forces across an interface, not the fundamental inter-molecular attraction name. Adhesion describes unlike molecules. Common Pitfalls: Using “surface tension” interchangeably with “cohesion”; ignoring the role of adhesion in wetting. Final Answer: cohesion

Question 19

Atmospheric pressure expressed as an equivalent water column  Standard atmospheric pressure at sea level is approximately equal to what head of water?

Accepted Answer

Introduction / Context: Barometric (atmospheric) pressure is often converted into an equivalent head of a fluid for hydraulic calculations and for calibrating manometers and barometers. Given Data / Assumptions: Standard atmosphere ≈ 101325 Pa. Water at about 4–20°C with density near 1000 kg/m^3. Concept / Approach: Hydrostatic relation: p = rho * g * h ⇒ h = p / (rho * g). Substituting p ≈ 101325 Pa, rho ≈ 1000 kg/m^3, g ≈ 9.81 m/s^2 gives a water head around 10.33 m; many textbooks use 10.3 m. Step-by-Step Solution: Compute h = 101325 / (1000 * 9.81) ≈ 10.33 m.Rounded engineering value → 10.30 m (option provided). Verification / Alternative check: In mercury, this corresponds to about 760 mm Hg because mercury is ~13.6 times as dense as water. Why Other Options Are Wrong: 9.81 m: numerically close but underestimates standard atmosphere. 5.0 m and 7.5 m: far too low. Common Pitfalls: Forgetting to use consistent units; using seawater density without noting salinity. Final Answer: 10.30 m

Question 20

Kinetic energy correction factor (α) for different regimes  Which of the following statements regarding the kinetic energy correction factor α in internal flow are true?

Accepted Answer

Introduction / Context: The kinetic energy correction factor α accounts for non-uniform velocity profiles when converting average velocity into kinetic energy per unit weight in the energy equation. It multiplies V^2/(2g) to correct for profile shape. Given Data / Assumptions: Fully developed flow in circular pipes for the canonical values. Definition: α = (1/A ∫ v^3 dA) / (V^3), where V is area-mean velocity. Concept / Approach: In laminar pipe flow, the parabolic profile makes α exactly 2. In turbulent flow, the flatter profile makes α close to 1; typical measured values lie near 1.03–1.06, and engineers often take α = 1 for simplicity unless very high accuracy is required. Step-by-Step Solution: Laminar: compute α from parabolic profile → α = 2.Turbulent: flatter profile → α slightly above 1 (≈ 1.03–1.06).Engineering practice often sets α = 1 for turbulent calculations. Verification / Alternative check: Energy equation with correction: z + p/(rho g) + α V^2/(2g) + h_pump − h_loss = const; choice of α is standard in textbooks. Why Other Options Are Wrong: Each individual statement (a), (b), (c) is correct; hence “all the above” is the best choice. Common Pitfalls: Confusing momentum correction factor β with α; using α = 2 in turbulent cases or α = 1 in laminar cases. Final Answer: all the above

Hydraulics Questions