About this previous year paper
Course: B.Tech (Civil Engineering)
Subject Code: CE403
Subject Title: Hydraulics and Hydraulic Machines
Exam Type: Theory (Semester IV, 2016–17)
Duration: 3 Hours
Maximum Marks: 100
SECTION – A (10 × 2 = 20 Marks)
Short conceptual questions checking understanding of fundamental hydraulic principles:
| Question | Topic | Key Concept |
|---|---|---|
| (a) | Uniform & Non-uniform Flow | Uniform flow = constant depth & velocity; non-uniform = variable parameters along flow length. |
| (b) | Assumptions for Gradually Varied Flow (GVF) | Steady flow, small slope, hydrostatic pressure distribution, negligible acceleration. |
| (c) | Manning’s Equation | V=1nR2/3S1/2V = \frac{1}{n}R^{2/3}S^{1/2}V=n1R2/3S1/2 for uniform flow in open channels. |
| (d) | Gradually Varied Flow | Flow where depth changes slowly over a long distance; e.g., river backwater curve. |
| (e) | Dynamic Equation for GVF | dydx=S0−Sf1−(Q2T/gA3)\frac{dy}{dx} = \frac{S_0 - S_f}{1 - (Q^2T/gA^3)}dxdy=1−(Q2T/gA3)S0−Sf for wide rectangular channels. |
| (f) | Surface Profiles | M1, M2, M3 or S1, S2, S3 types — depend on bed slope and flow depth. |
| (g) | Reciprocating Pump Working | Positive displacement pump using piston motion to move fluid. |
| (h) | Air Vessel Function | Reduces acceleration head and friction losses; ensures uniform discharge. |
| (i) | Draft Tube | Converts kinetic energy into pressure energy in reaction turbines. |
| (j) | Surge Tank & Forebay | Surge tank absorbs pressure surges; forebay acts as water buffer before turbines. |
SECTION – B (5 × 10 = 50 Marks)
Attempt any five. This section includes derivations, numerical analysis, and design problems.
Key Topics Covered:
(a) Flow Classification (Subcritical or Supercritical)
Given trapezoidal channel: base = 6 m, side slope 2H:1V, discharge = 17 m³/s, depth = 1.5 m.
→ Determine Froude number to identify flow type.
(b) Most Economical Rectangular Section
Derive that for maximum discharge or minimum perimeter:
b=2yandR=y2b = 2y \quad \text{and} \quad R = \frac{y}{2}b=2yandR=2y
(c) Cavitation in Centrifugal Pump
Given:
patm=101 kPa,pv=2.34 kPa,hloss=1.55 m,H=52.5 m,σ=0.118p_{atm} = 101\,kPa, p_v = 2.34\,kPa, h_{loss} = 1.55\,m, H = 52.5\,m, \sigma = 0.118patm=101kPa,pv=2.34kPa,hloss=1.55m,H=52.5m,σ=0.118.
Find maximum suction height to avoid cavitation.
(d) Inertia Head in Reciprocating Pump
Show:
hi=Lg⋅Aaω2r(1−cosθ)h_i = \frac{L}{g} \cdot \frac{A}{a} \omega^2 r(1 - \cos\theta)hi=gL⋅aAω2r(1−cosθ)
where A = cylinder area, a = pipe area, L = length, r = crank radius.
(e) Chezy’s Formula
Derived as V=CRSV = C\sqrt{RS}V=CRS where C depends on Reynolds number and channel roughness.
(f) Most Economical Trapezoidal Section
Show that for max discharge at constant area:
m=12sin(θ/2)andR=y2m = \frac{1}{2 \sin(\theta/2)} \quad \text{and} \quad R = \frac{y}{2}m=2sin(θ/2)1andR=2y
(g) Gradually Varied Flow Example
Rectangular channel: width = 10 m, slope changes from 0.01 to 0.0064, discharge = 125 m³/s, n=0.015n = 0.015n=0.015.
→ Determine surface profile type (M1, S2, etc.) and compute length of curve.
(h) Centrifugal Pump Construction & Working
Explain impeller, casing, suction, and delivery system with diagram; describe head, power, and efficiency relations.
SECTION – C (2 × 15 = 30 Marks)
Analytical and design-based questions on open channel flow and turbines.
Q3. Flow & Specific Energy
(a) Trapezoidal channel: bottom width = 6 m, slope 1:1, depth = 1.5 m, discharge = 15 m³/s.
→ Determine specific energy and flow type for given and critical depths.
(b) Derive hydraulic jump relation in triangular channel.
Q4. Hydraulic Jump & Pelton Wheel Design
(a) Rectangular channel: width = 4 m, discharge = 16 m³/s, initial depth = 0.5 m.
→ Determine:
If jump occurs,
Sequent depth,
Energy loss.
(b) Pelton Wheel Design:
P=1500 kW,H=160 m,N=420 rpm,η=85%P = 1500\,kW, H = 160\,m, N = 420\,rpm, \eta = 85\%P=1500kW,H=160m,N=420rpm,η=85%
Find jet diameter, wheel diameter, and bucket dimensions.
Q5. Reaction Turbine Design
Given:
Power = 300 kW, speed = 200 rpm, head = 18 m
D1=2D2,ηh=80%,ηm=95%,Q=3.6m3/sD_1 = 2D_2, \eta_h = 80\%, \eta_m = 95\%, Q = 3.6 m³/sD1=2D2,ηh=80%,ηm=95%,Q=3.6m3/s
Find:
Outer & inner diameters,
Vane inlet and exit angles,
Guide vane exit angle.
Use velocity triangles and flow relations for inward flow reaction turbine.
Key Concepts Summary
| Unit | Topic | Core Focus |
|---|---|---|
| I | Open Channel Flow | Uniform, non-uniform, gradually varied flow (GVF) equations |
| II | Hydraulic Pumps | Centrifugal and reciprocating pump theory and design |
| III | Turbines | Pelton, Francis, and Kaplan turbine working principles |
| IV | Flow Measurement | Specific energy, critical flow, and hydraulic jumps |
| V | Cavitation & Efficiency | Energy losses, air vessels, and draft tube design |
Summary
This Hydraulics and Hydraulic Machines (CE403) paper tests both conceptual and analytical skills in fluid mechanics applications.