Question 1

Bernoulli's equation: identify the assumptions used in its basic form  Consider steady flow along a streamline for an ideal fluid.  Which set of assumptions is inherent in the standard Bernoulli relation?

Accepted Answer

Concept/Approach Bernoulli's equation is derived for inviscid (no losses), steady, incompressible flow along a streamline, with only gravity as body force and using one-dimensional (section-averaged) velocity at the cross-section. Final Answer All of the above

Question 2

Centre of buoyancy: validate the definition  Statement: “The centre of buoyancy is the centre of area of the immersed body.”  Decide whether the statement is correct.

Accepted Answer

Concept/Approach The centre of buoyancy is the centroid (centre of gravity) of the displaced volume of fluid, not the centre of area of the body's immersed surface. Final Answer Disagree

Question 3

Fluid kinematics: name the type of flow with no change of volume or density  During the motion, the fluid's volume and density remain constant everywhere.  Choose the correct term for this flow.

Accepted Answer

Concept/Approach If density does not change during motion, the flow is called incompressible. Uniform and steady describe spatial and temporal constancy of velocity, not density. Final Answer Incompressible flow

Question 4

Head loss due to an obstruction in a pipe: validate the given relation  Statement: “The loss of head due to an obstruction in a pipe is twice the loss of head at its entrance.”  Decide whether the statement is correct.

Accepted Answer

Concept/Approach Entrance loss for a sharp-edged entrance is commonly taken as Ke = 0.5, giving he = 0.5 × (v2 / 2g). Loss due to an obstruction depends on its geometry and blockage ratio; its coefficient is not universally a fixed multiple of the entrance loss. Final Answer Disagree

Question 5

Siphon spillway: discharge–head relation  Let a be the flow area at the throat and H be the effective head. Cd denotes the coefficient of discharge and g is gravitational acceleration.  Choose the correct proportional form for the discharge through …

Accepted Answer

Concept/Approach For free-flow (weir-like) siphon action, discharge varies as area × velocity with velocity ≈ √(2gH) and effective head dependence H^(3/2) for weir-type flow. Relation Q = Cd × a × √(2g) × H^(3/2) (up to geometry-dependent constants). Final Answer Cd × a × √(2g) × H^(3/2)

Question 6

Hydrostatics terminology: name the point defined by displaced liquid volume  The point defined as the centre of gravity of the volume of liquid displaced by an immersed body is called what?  Choose the correct term.

Accepted Answer

Concept/Approach Centre of buoyancy is the centroid of the displaced fluid volume; the centre of pressure is where the resultant hydrostatic force acts on a surface; the metacentre is a stability-related point for floating bodies. Final Answer Centre of buoyancy

Question 7

Free nappe over a sharp-crested weir: pressure condition beneath the nappe  For a ventilated, freely falling nappe (free nappe case), determine the pressure condition.  Choose the correct statement.

Accepted Answer

Concept/Approach A free nappe is ventilated on its underside, allowing atmospheric air to enter. Hence the pressure beneath the nappe equals atmospheric pressure. If not ventilated, sub-atmospheric (negative gauge) pressure may develop and the nappe can cling to the crest, which is not the free-nappe case. Final Answer The pressure below the nappe is atmospheric

Question 8

Maximum efficiency for power transmission through a pipe  For power transmitted hydraulically through a pipeline with frictional head loss, what is the maximum possible transmission efficiency (at the condition for maximum power at the outlet)? Choo…

Accepted Answer

Given data Power transmitted through a pipe with head loss due to friction. Concept/Approach For a pipeline delivering power, the power at the outlet is P ∝ Q (H − h_f), with head loss h_f ∝ Q^2. Differentiating w.r.t. flow rate shows maximum power occurs when h_f = H/3. The corresponding efficiency is η = (H − h_f)/H = (H − H/3)/H = 2/3 = 66.67%. Final Answer 66.67%

Question 9

Depressed nappe over a weir: pressure condition below the nappe  A depressed nappe forms when air cannot freely circulate beneath the falling sheet of water (nappe). Identify the correct pressure condition beneath the nappe.

Accepted Answer

Concept/Approach A depressed nappe occurs when air is not properly ventilated below the nappe, creating sub-atmospheric (negative gauge) pressure beneath it. If vented, the pressure would be atmospheric and the nappe would be free, not depressed. Final Answer the pressure below the nappe is negative

Question 10

Metric unit conversion: volume occupied by 1 litre of water  One litre is defined as one cubic decimetre (1 dm³). Select the correct equivalent volume in cubic centimetres (cm³).

Accepted Answer

Step-by-step 1 litre = 1 dm³.1 dm = 10 cm ⇒ 1 dm³ = (10 cm)³ = 1000 cm³. Final Answer 1000 cm3

Question 11

Total hydrostatic thrust on a vertical wall (per unit length)  A vertical wall retains a single liquid of specific weight w up to height H on one side. Find the total pressure (resultant hydrostatic force) on the wall per unit length.

Accepted Answer

Concept/Approach Pressure varies hydrostatically: p = w y at depth y. Resultant thrust per unit width is the area under the triangular pressure diagram. Step-by-step calculation F = ∫0H w y dy = w [y²/2]0H = w H²/2. Final Answer wH2/2

Question 12

Instrument selection: what a manometer measures best  A manometer is used for measuring pressure by balancing a column of fluid. Which range is it best suited for?

Accepted Answer

Concept/Approach Manometers (U-tube, differential, micro-manometers) measure pressure or pressure differences via liquid columns and are most suitable for low to modest pressures. High pressures are commonly measured with elastic gauges (e.g., Bourdon tubes). Atmospheric pressure specifically is measured by a barometer. Final Answer low pressure

Question 13

Stability of floating bodies and metacentric height (GM)  Two floating bodies A and B have metacentric heights GM of 1 m and 1.5 m respectively. Compare their stability and choose the correct statement.

Accepted Answer

Concept/Approach For small heel angles, the initial stability of a floating body increases with metacentric height GM. Larger GM ⇒ stronger righting moment for the same heel. Step-by-step GMB = 1.5 m > GMA = 1 m ⇒ B has greater initial stability. Final Answer The body B is more stable than body A

Question 14

Discharge over a right-angled (90°) V-notch  Given head H measured above the notch apex. Identify the exponent of H and the standard form of the discharge relation (up to proportionality).

Accepted Answer

Concept/Approach For a triangular (V) notch, the theoretical discharge is proportional to H5/2. For a right-angled notch (θ = 90°): Q = (8/15) Cd √(2g) H5/2. Final Answer Cd √(2g) × H5/2

Question 15

Basic fluid property: weight per unit volume  The weight per unit volume of a liquid at a standard temperature and pressure is called what?

Accepted Answer

Definitions Specific weight (γ) = weight per unit volume (N/m³).Mass density (ρ) = mass per unit volume (kg/m³).Specific gravity = ratio of a substance’s density to that of water (dimensionless). Final Answer specific weight

Question 16

Meaning of one-dimensional (1-D) flow in fluid mechanics  Select the statement that best describes one-dimensional flow.

Accepted Answer

Concept/Approach In 1-D flow, all primary flow properties are assumed to vary along a single spatial coordinate (one direction). The pathline may be curved locally; the key modeling assumption is the single predominant direction of variation. Final Answer takes place in one direction

Question 17

Time to empty a tank with an orifice at the bottom (uniform cross-section)  A tank of uniform area A holds liquid to height H1 and drains through a bottom orifice of area a (ideal Torricelli outflow). Find the total time required to empty the tank c…

Accepted Answer

Given data Uniform tank area A, initial head H1, orifice area a. Concept/Approach Torricelli outflow (ideal): v = √(2gH), discharge Q = a √(2gH). Continuity for falling head: A (−dH/dt) = a √(2gH). Step-by-step calculation dH/√H = − (a/A) √(2g) dtIntegrate H from H1 to 0: 2√H1 = (a/A) √(2g) · tt = (2A/a) √(H1/(2g)) = (A/a) √(2H1/g). Common pitfalls Missing the square-root dependence on head or forgetting to separate variables before integrating. Final Answer (A/a) × √(2H1/g)

Question 18

Siphon application: connecting two reservoirs across a ridge  A siphon (inverted U-shaped closed conduit) is used when two reservoirs are at different levels and a high ridge lies between them. State whether the statement is correct.  Choose the cor…

Accepted Answer

Concept/Approach A siphon conveys liquid from a higher reservoir to a lower one across an intermediate high point without pumping, provided the siphon remains full and the summit pressure stays above vapour pressure. Final Answer Agree

Question 19

Open-channel flow: definition of specific energy  Specific energy at a section is defined relative to the channel bed (datum through the bottom). Identify the correct description.

Accepted Answer

Concept/Approach Specific energy E in open channels is the energy per unit weight of fluid, referenced to the channel bed: E = y + v2/(2g) where y is depth and v is mean velocity. Final Answer Specific energy is the total energy measured with respect to the datum through the channel bottom.

Question 20

Power transmission through a pipe with nozzle: nozzle diameter for maximum power  A pipe of diameter D and length l carries water to a nozzle of diameter d at its end. The Darcy friction factor for the pipe is f (Darcy–Weisbach form). Find the nozzl…

Accepted Answer

Given data Pipe diameter D, length l; nozzle diameter d; Darcy friction factor f. Total head available = H (constant). Concept/Approach Head relation: H = hf + Vj2/(2g) with hf = (4 f l / D) × v2/(2g) and continuity v = (a/A) × Vj = (d2/D2) × Vj. Thus H = [1 + (4 f l / D) × (d4/D4)] × Vj2/(2g). Power delivered by jet: P ∝ a Vj3 ∝ d2[1 + k d4]-3/2 with k = 4 f l / D5. Step-by-step optimization Differentiate ln P: 2/d − (3/2) × (4k d3)/(1 + k d4) = 0→ 2(1 + k d4) = 6k d4 → d4 = 1/(2k) = D5/(8 f l)→ (d/D)4 = D/(8 f l) ⇒ d/D = ( D / (8 f l) )1/4. Final Answer d / D = ( D / (8 f l) )1/4

Hydraulics and Fluid Mechanics Questions