16-Civ-A5 Hydraulic Engineering
Worked solutions to 14 past sittings (2013–2019), 84 questions. Pick a sitting, or start from a topic below.
- December 2019
- December 2018
- May 2018
- December 2017
- May 2017
- December 2016
- May 2016
- December 2015
- May 2015
- December 2014
- May 2014
- December 2013
- May 2013
- Undated paper
Topics across the sittings
Topics that come up in more than one sitting, taken from the headings of our worked solutions. A topic counts once per sitting.
- Critical depth (7 sittings): May 2018 Q6 · May 2017 Q6 · December 2016 Q6 · May 2016 Q6 · May 2015 Q6 · December 2014 Q6 · Undated paper Q6
- Valve-controlled transmission main (6 sittings): December 2019 Q3 · December 2018 Q3 · May 2018 Q3 · December 2015 Q2 · May 2014 Q3 · Undated paper Q3
- Normal depth (5 sittings): May 2018 Q6 · May 2017 Q6 · December 2016 Q6 · May 2016 Q6 · May 2015 Q6
- Kinematic (4 sittings): May 2018 Q5 · December 2016 Q5 · December 2015 Q5 · May 2015 Q5
- Pressure heads (4 sittings): December 2017 Q1 · December 2015 Q1 · May 2014 Q1 · December 2013 Q1
- Branched supply network (3 sittings): December 2018 Q1 · May 2018 Q1 · December 2013 Q1
- Specific energy (3 sittings): May 2017 Q6 · December 2016 Q6 · May 2015 Q6
- Two elevated tanks (3 sittings): December 2017 Q4 · December 2015 Q4 · December 2013 Q4
- Flows (2 sittings): May 2016 Q4 · December 2015 Q1
- Normal (2 sittings): December 2014 Q6 · Undated paper Q6
- Penstock (2 sittings): May 2017 Q1 · December 2014 Q1
- Quasi-steady simulation (2 sittings): December 2015 Q4 · December 2013 Q4
- Rectangular channel (2 sittings): May 2016 Q6 · December 2014 Q6
- Regime (2 sittings): May 2018 Q6 · May 2016 Q6
- Single (2 sittings): May 2017 Q1 · December 2014 Q1
Questions by sitting
December 2019
- Question 1: Rigid water-column transient between two reservoirs
- Question 2: Wall shear stress from a pipe force balance
- Question 3: Valve-controlled transmission main
- Question 4: Ten-pipe network — flow split and pressures
- Question 5: Gradually varied flow — profile classification
- Question 6: St-Venant equations after a channel blockage
December 2018
- Question 1: Branched supply network — pressure head under maximum-day and fire flow
- Question 2: Multi-path pipe network between two reservoirs — total flow and pressure extremes
- Question 3: Valve-controlled transmission main
- Question 4: Wall shear stress from a pipe force balance
- Question 5: Momentum across a hydraulic jump
- Question 6: Gutter/crown flow on a curbed roadway
May 2018
- Question 1: Branched supply network — pipe length and pressure under fire flow
- Question 2: Parallel-branch network between two reservoirs
- Question 3: Valve-controlled transmission main
- Question 4: Two-tank quasi-steady draining simulation
- Question 5: Kinematic vs. dynamic wave after sudden gate closure
- Question 6: Trapezoidal channel — normal depth, critical depth, regime
December 2017
- Question 1: Branched pipe network — pressure heads
- Question 2: Ten-pipe system between two reservoirs
- Question 3: Transmission main with a control valve
- Question 4: Two elevated tanks — quasi-steady drawdown
- Question 5: Hydraulic jump in a rectangular channel
- Question 6: Gutter flow on a crowned road
May 2017
- Question 1: Penstock — single and parallel flow
- Question 2: Transmission main with in-line valve
- Question 3: Distribution network — HGL and water age
- Question 4: Hydraulic jump in a rectangular channel
- Question 5: River blocked by a slope failure — unsteady flow
- Question 6: Normal depth, critical depth and specific energy
December 2016
- Question 1: Gravity PVC Main — Velocity Check and Re-sizing
- Question 2: Twin Pumps Delivering Over a High Point
- Question 3: Five-Pipe Distribution Network with a Control Valve
- Question 4: Crowned-Road Gutter Capacity Under Climate Change
- Question 5: Kinematic vs. Dynamic Wave After a Sudden Gate Closure
- Question 6: Normal Depth, Critical Depth and Specific Energy
May 2016
- Question 1: Branched reservoir network — nodal pressure heads
- Question 2: Wall shear stress from a pipe force balance
- Question 3: Transmission main with a control valve
- Question 4: Three-pipe network — flows and nodal pressure heads
- Question 5: Velocity profile in a laminar open-channel film
- Question 6: Rectangular channel — normal depth, critical depth, regime
December 2015
- Question 1: Ten-pipe reservoir network — flow, pressure heads, branch comparison
- Question 2: Valve-controlled transmission main
- Question 3: Three-pipe distribution network
- Question 4: Two elevated tanks — quasi-steady simulation
- Question 5: Kinematic vs. dynamic wave after sudden gate closure
- Question 6: Crowned-road drainage capacity
May 2015
- Question 1: Equivalent-pipe network flow
- Question 2: Transmission main with a control valve
- Question 3: Looped distribution network — supply head and valving
- Question 4: Rigid water-column (mass-oscillation) draining
- Question 5: Kinematic vs dynamic wave after sudden gate closure
- Question 6: Normal depth, critical depth and specific energy
December 2014
- Question 1: Penstock — single and parallel discharge
- Question 2: Transmission main with in-line valve
- Question 3: Three-pipe loop network
- Question 4: Wall shear from a pipe force balance
- Question 5: River blockage — unsteady hydraulics
- Question 6: Rectangular channel — normal & critical depth
May 2014
- Question 1: Branched Distribution Network — Pressure Heads
- Question 2: Looped Pipe Network Between Two Reservoirs
- Question 3: Valve-Controlled Transmission Main
- Question 4: Wall Shear Stress from a Pipe Force Balance
- Question 5: Hydraulic Jump in a Rectangular Channel
- Question 6: Crowned Roadway Drainage Capacity
December 2013
- Question 1: Branched supply network — pressure heads
- Question 2: Ten-pipe twin-path network between two reservoirs
- Question 3: Transmission main with an in-line control valve
- Question 4: Two elevated tanks — quasi-steady simulation
- Question 5: Laminar open-channel film — velocity profile
- Question 6: Crowned roadway gutter flow
May 2013
- Question 1: Two-reservoir supply to a demand node
- Question 2: Ten-pipe network between two reservoirs
- Question 3: Two pumps and a 6-km pipeline over a hill
- Question 4: Quasi-steady simulation of two draining tanks
- Question 5: River blockage by a slope failure
- Question 6: Compound flood-protection channel
Undated paper
- Question 1: Rigid water-column transient between two reservoirs
- Question 2: St. Venant equations after a sudden channel blockage
- Question 3: Valve-controlled transmission main
- Question 4: Momentum on a 45° pipe elbow — downstream pressure
- Question 5: Classify the water-surface profile at a constriction
- Question 6: Trapezoidal channel — normal, critical depth and a weir