THEORY EXAMINATION (SEM–IV) 2016-17 HYDRAULICS AND HYDRAULIC MACHINES

B.Tech General 0 downloads

₹29.00

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−cos⁡θ)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