## Applied Fluid Mechanics - May 2016

### Civil Engineering (Semester 6)

TOTAL MARKS:

TOTAL TIME: HOURS

**1 (a)** State and prove the conditions under which the trapezoidal section of an open
channel will be most economical.(7 marks)
**1 (b)** A smooth pipe of diameter 400 mm and length 800 m carries water at a rate of
0.40 m^{3}/s. determine the head lost due to friction, wall shear stress, centre line
velocity and thickness of laminar sub-layer. Take kinematic viscosity of water as
0.018 stokes and coefficient of friction, f = 0.0791/ (R_{e})^{1/4}(7 marks)
**2 (a)** Enlist the various major and minor energy losses in pipes? Derive an expression
for head loss due to sudden enlargement of pipe.(7 marks)

### Solve any one question from Q2(b) & Q2(c)

**2 (b)** Two reservoirs are connected by two pipes in series of lengths 200 m and 300 m
and of diameters 20 cm and 30 cm respectively. The difference of head between
the two reservoir water surfaces is 10m. The friction factors for the two pipes
are 0.02 and 0.015 respectively. Determine the flow rate.(7 marks)
**2 (c)** Derive an expression for velocity distribution of viscous flow through a circular
pipe and prove that the ratio of maximum velocity to average velocity is 2.(7 marks)

### Solve any two question from Q3(a), Q3(b) & Q3(c), Q3(d)

**3 (a)** Explain the following flow characteristics in the open channel:

1) Steady flow and unsteady flow

2) Uniform flow and Non-uniform flow

3) Laminar flow and turbulent flow

4) Subcritical, Critical and super critical flow(7 marks)
**3 (b)** In a rectangular channel of 0.5 m width, a hydraulic jump occurs at a point where depth of water flow is 0.15 m and Froude number is 2.5. Determine:

1) The specific energy

2) The critical and subsequent depths

3) Loss of Head

4) Energy (Power) dissipated(7 marks)
**3 (c)** Explain with diagram the Specific Energy Curve and Discharge Curve and derive
the mathematical expression for minimum specific energy and maximum
discharge in terms of depth of flow.(7 marks)
**3 (d)** A trapezoidal channel is 5 m wide at bottom and has a side slope of 0.5H: 1V.
The bed slope of the channel is 0.0003. Find the discharge of the most
economical section. Assume Manning's coefficient n = 0.02.(7 marks)

### Solve any two question from Q4(a), Q4(b) & Q4(c), Q4(d)

**4 (a)** Draw a general layout of a Hydroelectric power plant using an impulse turbine and define the following:

1) Gross Head

2) Net Head

3) Hydraulic Efficiency

4) Overall Efficiency of Impulse turbine(7 marks)
**4 (b)** For a Pelton Wheel Turbine, find (a) quantity of water required, (b) diameter of
the wheel, (c) number of jets, (d) number and size of buckets on the wheel, given the following data:

Speed of the wheel = 550 rpm

Head=350m

Shaft power of wheel = 8000 kW

Overall Efficiency = 86%

Assume a jet ratio of 10, Coefficient of velocity = 0.98 and Speed ratio = 0.46.(7 marks)
**4 (c) (i)** What is priming? Why is it necessary in centrifugal pump?(3 marks)
**4 (c) (ii)** What is cavitation? What are its effects? Give necessary precaution against cavitations in pumps.(4 marks)
**4 (d)** An oil of viscosity 0.02 Ns/m^{2} flows between two stationary parallel plates
which are 1m wide and maintained 10 mm apart. The velocity midway between
the plates is 2 m/s.

Calculate:

(i) the pressure gradient along flow

(ii) the
average velocity and

(iii) discharge(7 marks)

### Solve any two question from Q5(a), Q5(b) & Q5(c), Q5(d)

**5 (a)** Discuss the Distorted and Undistorted Models. What are the merits and demerits of Distorted Models?(7 marks)
**5 (b)** A plate 450mm * 150mm has been placed longitudinally in a stream of crude oil having specific gravity 0.925 and kinematic viscosity of 0.9 stoke, which
flows with velocity of 6 m/s. Calculate

1. The friction drag on the plate

2. Thickness of the boundary layer at the trailing edge

3. Shear stress at the trailing edge(7 marks)
**5 (c)** Discuss the phenomenon of boundary layer separation. What are the different
methods of preventing the separation of boundary layer?(7 marks)
**5 (d)** An oil of specific gravity 0.92 and viscosity 0.03 poise is to be transported at the rate of 2500 litres/sec through a 1.2 m diameter pipe. Tests were conducted on a 12 cm diameter pipe using water at 20°C. If the viscosity of water at 20°C is
0.01 poise, find:

1) Velocity of flow in the model

2) Rate of flow in the model(7 marks)