Question 1

Broad-crested weir: formula for maximum discharge For a broad-crested weir of length L with head H over the crest and coefficient of discharge C_d, select the correct expression for maximum discharge.

Accepted Answer

Concept/Approach For free overflow over a broad-crested weir at maximum discharge condition, the theoretical constant is about 1.705; thus Q = 1.71 Cd L H3/2 (SI units when H in metres, Q in m3/s). Final Answer 1.71 Cd × L × H3/2

Question 2

Definition: flumed structure in open channels  A channel structure is termed “flumed” when its width, compared to the parent channel, satisfies which condition?  Choose the correct completion.

Accepted Answer

Concept/Approach A flume is a contraction (narrowed section) inserted into a channel; hence its width is less than the channel width. Final Answer Less than the width of the channel

Question 3

Orifices: coefficient of resistance (head-loss coefficient) — select the correct definition  Choose the ratio that defines the coefficient of resistance for an orifice.

Accepted Answer

Concept/Approach Coefficient of resistance (head-loss coefficient) Cr quantifies energy loss: Cr = hloss / h. Other coefficients: Cv = va/vth, Cc = ajet/aorifice, Cd = Qa/Qth. Final Answer Loss of head in the orifice divided by the available head.

Question 4

Error propagation for triangular notch (V-notch): effect of head-reading error on discharge  If the head over the notch apex is H, how much percentage error in discharge occurs for a 1% error in H?  Choose the correct value.

Accepted Answer

Concept/Approach For a triangular (V) notch, discharge Q ∝ H5/2. Step-by-step Relative error: dQ/Q = (5/2) × dH/H.For dH/H = 1% → dQ/Q = 2.5%. Final Answer 2.5%

Question 5

Pressure terminology: values below atmospheric  What is the name given to pressure less than atmospheric?  Choose the correct option.

Accepted Answer

Concept/Approach All three terms are commonly used for pressure below atmospheric when expressed as a gauge value: suction pressure, vacuum pressure, or negative gauge pressure. Final Answer All of these

Question 6

Use of bulk modulus in dimensionless numbers  The value of bulk modulus of a fluid (or equivalently speed of sound) is required to evaluate which engineering number?  Choose the correct option.

Accepted Answer

Concept/Approach Mach number M = V / c, where c = speed of sound = √(bulk modulus / density). Hence bulk modulus is essential for compressibility/sonic effects captured by Mach number. Final Answer Mach number

Question 7

Reynolds number for a ship: dependence on velocity and length  For a ship moving in water, consider Reynolds number Re = (V × L) / ν, where V is velocity, L is a characteristic length and ν is kinematic viscosity.  Complete the statement about how R…

Accepted Answer

Concept/Approach Reynolds number in external flows is Re = V L / ν. Holding ν fixed (same fluid and temperature), Re increases linearly with both V and L. Final Answer Proportional to both velocity and length

Question 8

Fluid mechanics: coefficient of discharge for an external mouthpiece  For a sharp-edged external mouthpiece (running free), identify the standard coefficient of discharge value used in calculations. Choose the correct numerical value.

Accepted Answer

Concept/Approach The coefficient of discharge Cd for an external mouthpiece (free discharge) is empirically established around 0.85–0.86 for water at normal conditions. This accounts for contraction and velocity effects at the mouthpiece. Final Answer 0.855

Question 9

Venturimeter: velocity at the throat versus at the inlet  In a venturimeter working under full-bore flow, compare the fluid velocity at the throat with the velocity at the inlet. Choose the correct relation.

Accepted Answer

Concept/Approach From continuity, Q = A V = constant. Because the throat area is smaller than the inlet area, the velocity must increase at the throat to maintain the same discharge. Final Answer Velocity at the throat is greater than at the inlet

Question 10

Laminar flow in a circular pipe: friction factor dependence on Reynolds number For viscous (laminar) flow in a pipe of uniform diameter, the Darcy friction factor varies as which function of the Reynolds number R_N? Choose the correct exp…

Accepted Answer

Concept/Approach For fully developed, laminar flow in a circular pipe, the Darcy friction factor is f = 64/Re. The head loss due to friction is then hf = f (L/D) (V²/(2g)). Final Answer 64/RN

Question 11

Coefficient of contraction for an orifice Define the coefficient of contraction C_c for a sharp-edged orifice in terms of areas. Choose the correct ratio.

Accepted Answer

Definitions Cc = Avc / Ao (contraction)Cv = Vactual / Vtheoretical (velocity)Cd = Qactual / Qtheoretical = Cc Cv (discharge) Final Answer area of jet at vena contracta to the area of orifice

Question 12

Floating body stability: response to a small angular displacement  A floating body is given a small angular displacement and returns to its original position. Identify the equilibrium classification. Choose the correct option.

Accepted Answer

Concept/Approach A floating body is in stable equilibrium if, after a small angular displacement, a righting moment acts to restore it to the initial position. This typically requires the metacentre to lie above the centre of gravity (GM > 0). Final Answer stable equilibrium

Question 13

Power transmitted through a pipeline with head loss Let w be the specific weight (N/m³), Q the discharge (m³/s), H the supply head and h_f the frictional head loss. Select the correct expression for the power delivered at the outlet.

Accepted Answer

Concept/Approach Power delivered equals weight flow rate times the available head at the outlet: P = w Q Hout = w Q (H - hf). Head loss reduces the usable head. Final Answer w × Q × (H - hf)

Question 14

Examples of laminar (low Reynolds number) flow  Identify which of the following are classic examples of laminar flow regimes. Choose the correct option.

Accepted Answer

Concept/Approach Laminar flow occurs at low Reynolds numbers where viscous forces dominate. Porous-media groundwater flow (Darcy's law), creeping flow around tiny particles, and instrument oil flow are standard laminar cases. Final Answer all of these

Question 15

Dam stability checks: essential limit states  When assessing the stability of a gravity wall or dam, which conditions must be verified? Choose the correct option.

Accepted Answer

Concept/Approach Standard checks include: (i) no tensile stress at the base, (ii) adequate factor of safety against overturning, and (iii) adequate factor of safety against sliding. All must be satisfied. Final Answer all of these

Question 16

Venturimeter installation orientation  A venturimeter is used for measuring discharge in a full pipe. Select the correct statement regarding its installation orientation and location.

Accepted Answer

Concept/Approach A venturimeter can be installed in any orientation provided the pipe runs full and pressure tappings are correctly referenced. The discharge equation accounts for elevation if needed. Final Answer any direction and in any location

Question 17

Definition check: ideal fluid properties  An ideal fluid is defined by two key properties in continuum mechanics. Decide whether the statement is correct: "An ideal fluid is frictionless and incompressible." Choose the correct option.

Accepted Answer

Concept/Approach An ideal fluid has no viscosity (frictionless) and is incompressible. These assumptions underpin Euler's equations and Bernoulli's equation for inviscid flow. Final Answer True

Question 18

Head loss due to sudden enlargement in a pipe: write the correct formula  A pipeline of diameter d₁ along AB carries liquid and is suddenly enlarged at B to diameter d₂ for the downstream length BC. Assume steady incompressible flow with negligible …

Accepted Answer

Concept/Approach At a sudden enlargement, eddies form and energy is lost due to separation. The standard expression for the loss is based on the velocity change only. Step-by-step Head loss across enlargement = Loss of velocity head due to separationhe = (v₁ − v₂)² / (2g) Common pitfalls Do not use (v₁² − v₂²)/(2g); that would be the net change in velocity head, not the separation loss. Final Answer h = (v₁ − v₂)² / (2g)

Question 19

Rectangular notch (weir) discharge formula For a sharp-crested rectangular notch of width b with head H above the sill and coefficient of discharge C_d, select the correct standard expression for discharge.

Accepted Answer

Given data Width = b, head over sill = H, discharge coefficient = Cd. Concept/Approach Discharge over a sharp-crested rectangular notch is obtained by integrating elementary strips across the head. Result Q = (2/3) Cd b √(2g) H3/2 Final Answer (2/3) Cd b √(2g) H3/2

Question 20

External mouthpiece: pressure at vena contracta relative to atmosphere  In a free-discharging external mouthpiece, the absolute pressure head at the vena contracta is ____ the atmospheric pressure head by approximately 0.89 times the height of liqui…

Accepted Answer

Concept/Approach At the vena contracta of an external mouthpiece, the jet accelerates and the static pressure drops below atmospheric. Experiments show the pressure deficit is about 0.89h, where h is the liquid height above the vena contracta. Final Answer less than

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