ICAR AIEEA-PG — Agricultural Engineering & Technology (Major Subject Group 10) · India · National Testing Agency for ICAR
Original practice questions written to the published syllabus · not past papersFluids at rest and in motion, pipe flow and open channels: the base of irrigation, drainage, pumping and conservation structures.
In the exams: GATE AG Section 4 (hydraulics asked in 6 of 8 papers 2019–26); ICAR AIEEA-PG Unit III; ICAR AICE subject 43 Unit 2; NCEES FE 12–18 questions (largest FE area)
ICAR AIEEA-PG — Agricultural Engineering & Technology (Unit III)
Single-answer MCQs on fluid properties and their units, Bernoulli assumptions, coefficients of orifices and mouthpieces, flow-meter coefficients, laminar flow results (f = 64/Re, u_max = 2V), minor-loss formulas, maximum power transmission, weir and notch formulas, best channel sections and dimensionless numbers, with short calculations.
How our questions for ICAR AIEEA-PG spread across the units of Fluid Mechanics & Open Channel Hydraulics. Difficulty: 32 easy, 50 medium, 3 hard.
| Properties of fluids | 7 | |
| Hydrostatics and manometry | 6 | |
| Forces on submerged surfaces and buoyancy | 6 | |
| Bernoulli's equation: venturimeter, orifice meter and pitot tube | 6 | |
| Orifices, mouthpieces and tank emptying | 6 | |
| Weirs and notches | 6 | |
| Dimensional analysis and similitude | 6 | |
| Laminar and turbulent flow in pipes | 5 | |
| Darcy-Weisbach equation and Moody diagram | 5 | |
| Most economical channel section | 5 | |
| Continuity equation | 4 | |
| Minor losses | 4 | |
| Pipes in series and parallel | 4 | |
| Hydraulic jump | 4 | |
| Momentum equation | 3 | |
| Uniform flow in open channels: Manning and Chezy | 3 | |
| Specific energy and critical depth | 3 | |
| Hazen-Williams equation | 2 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
A U-tube mercury manometer (relative density 13.6) is connected to a pipe carrying water; the other limb is open to air. The pipe centre is 0.2 m above the mercury surface in the pipe-side limb, and the mercury in the open limb stands 0.3 m above that surface. What is the gauge pressure at the pipe centre?
C. 38.1 kPa
Start at the pipe centre and move to the open surface: p_A + ρ_w g(0.2) − ρ_Hg g(0.3) = 0, so p_A = 13 600 × 9.81 × 0.3 − 1000 × 9.81 × 0.2 = 40025 − 1962 = 38063 Pa ≈ 38.1 kPa. Adding the water column gives 42.0 kPa; ignoring it gives 40.0 kPa. 35.1 kPa counts the whole 0.5 m (0.2 + 0.3 m) as a water column on the pipe side.
Further reading: Munson et al., Fundamentals of Fluid Mechanics
A vertical rectangular gate 1.5 m wide and 2 m high has its top edge 1 m below the water surface. At what depth below the water surface does the resultant hydrostatic force act?
A. 2.17 m
h_cp = h̄ + I_G/(A h̄). h̄ = 2 m, A = 3 m², I_G = bd³/12 = 1.5 × 8/12 = 1.00 m⁴. h_cp = 2 + 1/(3 × 2) = 2.17 m. The centre of pressure is always below the centroid (2.00 m); forgetting to divide by h̄ gives 2.33 m. 1.83 m subtracts I_G/(A h̄) and so puts the centre of pressure above the centroid.
Further reading: Modi and Seth, Hydraulics and Fluid Mechanics
Water issues from a small orifice 5 m below the free surface of a large open tank. Neglecting losses, what is the jet velocity?
D. 9.90 m/s
Torricelli's theorem: V = √(2gH) = √(2 × 9.81 × 5) = 9.90 m/s. 7.00 m/s drops the 2, and 98.1 forgets the square root. 49.1 m/s drops both the 2 and the square root (9.81 × 5).
Further reading: Modi and Seth, Hydraulics and Fluid Mechanics
Oil (density 900 kg/m³, dynamic viscosity 0.2 Pa·s) flows at a mean velocity of 1 m/s through 100 m of 100 mm pipe. What is the friction head loss?
D. 7.25 m of oil
Re = ρVD/μ = 900 × 1 × 0.1/0.2 = 450, laminar. Hagen-Poiseuille: h_f = 32μVL/(ρgD²) = 32 × 0.2 × 1 × 100/(900 × 9.81 × 0.01) = 7.25 m. The same comes from f = 64/Re = 0.142 in Darcy-Weisbach. Assuming a turbulent f = 0.02 gives 1.02 m, far too low. 3.62 m uses 16 instead of 32 in Hagen-Poiseuille; 14.5 m uses 64.
Further reading: Modi and Seth, Hydraulics and Fluid Mechanics
An Indian textbook writes the pipe friction loss as h_f = 4fLV²/(2gD) and quotes f = 0.005. What is the equivalent Darcy friction factor used in h_f = fLV²/(2gD)?
B. 0.020
The 4f form uses the Fanning coefficient, which is one quarter of the Darcy factor. 4 × 0.005 = 0.020. Mixing the two forms is a common source of answers four times too large or too small. 0.00125 divides by 4 instead of multiplying; 0.010 doubles the Fanning value.
Further reading: Modi and Seth, Hydraulics and Fluid Mechanics
A 90° V-notch with C_d = 0.6 is used to measure a tubewell's discharge. The head over the vertex is 0.2 m. What is the discharge?
D. 25.4 L/s
Q = (8/15) C_d √(2g) tan(θ/2) H^2.5 = (8/15) × 0.6 × 4.429 × tan 45° × 0.2^2.5 = 1.417 × 0.0179 = 0.0254 m³/s = 25.4 L/s. Using H^1.5 gives 127 L/s, a large overestimate. 56.7 L/s uses H² instead of H^2.5; 31.7 L/s uses the rectangular 2/3 instead of 8/15.
Further reading: USBR Water Measurement Manual; Modi and Seth
The head over a triangular notch is measured with an error of 2 per cent. What is the resulting percentage error in the computed discharge?
D. 5 %
Q ∝ H^2.5, so dQ/Q = 2.5 dH/H = 2.5 × 2 = 5 %. For a rectangular weir (Q ∝ H^1.5) it would be 3 %, which is why head must be measured more precisely on a V-notch. 4 % uses an exponent of 2.
Further reading: Modi and Seth, Hydraulics and Fluid Mechanics
If both the bed width and the side slope of a trapezoidal channel are free to be chosen, what shape is the most economical section?
B. Half a regular hexagon, with sides at 60° to the horizontal
Optimising side slope as well as width gives z = 1/√3 (sides at 60°), with the bed and the sloping sides of equal length: half a regular hexagon. The b = 2y rectangle is the best only among rectangles.
Further reading: Chow, Open-Channel Hydraulics
For a given discharge in an open channel, what is true of the flow at critical depth?
B. The specific energy is a minimum
On the specific-energy curve for a fixed q, the critical depth is the point of minimum E; equivalently, for a fixed E, discharge is maximum there. In a rectangular channel the velocity head at critical depth is y_c/2, not y_c, and Fr = 1.
Further reading: Subramanya, Flow in Open Channels
In a 1:36 Froude model of a canal fall, a flood wave takes 1 minute to pass through the model. How long does it take in the prototype?
D. 6 minutes
Under Froude similarity T_r = L_r^0.5 = √36 = 6, so 1 min in the model is 6 min in the prototype. 36 would be the length ratio and 216 = 36^1.5 has no meaning here.
Further reading: Modi and Seth, Hydraulics and Fluid Mechanics
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