**Third Semester**

DEPARTMENT OF CIVIL ENGINEERING

DEPARTMENT OF CIVIL ENGINEERING

**MECHANICS OF FUIDS – UNIVERSITY QUESTION PAPER**

**Time : Three hours Maximum : 100 marks**

**Answer ALL questions.**

**PART A — (10 x 2 = 20 marks)**

**1. Distinguish between ideal and real fluids.**

2. Express 3 m of water head in cm of mercury and pressure in KPa.

3. List out the properties of a velocity potential function.

4. Can the path line and a streamline cross each other at right angles? Why?

5. Why is it necessary to assume that the flow is steady before integrating Euler’s equation to derive Bernoulli’s equation?

6. What is the meaning of the term momentum flux? What are its units?

7. What is meant by the term ‘‘Piezometric head’’?

8. A pipe has D = 40 cm, L = 100 m, f = 0.005. Compute the length of an equivalent pipe which has D = 20 cm and f = 0.008.

9. State three demerits of a distorted model.

10. Define momentum thickness.

**PART B — (5 x 16 = 80 marks)**

11. A trapezoidal plate of top width 5 m, bottom width 4 m and height 3 m is immersed vertically in water with its parallel sides parallel to the water level and its top edge at a depth of 2 m below the water level. Find the water thrust on one side of the plate and the depth of center of pressure.

12.
(a) A mercury U–tube monometer shown in the fig. is used to measure the
pressure above atmospheric of water in a pipe, the water being in contact with
the mercury in the left–hand limb.

(i) Explain its action.

(ii) If the mercury is 30 cm below A in the left–hand limb and 20 cm

above A in the right–hand limb, what may be gauge pressure at A?

Specific gravity of mercury is = 13.6.

(iii) If the pressure at A is reduced by 40 kN/m2 what will be the new

difference in level of the mercury?

(i) Explain its action.

(ii) If the mercury is 30 cm below A in the left–hand limb and 20 cm

above A in the right–hand limb, what may be gauge pressure at A?

Specific gravity of mercury is = 13.6.

(iii) If the pressure at A is reduced by 40 kN/m2 what will be the new

difference in level of the mercury?

Or

(b) List out the various methods of construction of flow nets and Explain the graphical method in detail.

13.
(a) Derive Euler’s equations for a three–dimensional fluid flow.

Or

(b) A jet propelled boat moves at 32 km/hr in a fresh water lake. There are two jets each of diameter 20 cm. The absolute velocity of the discharged jets is 25 km/hr. Calculate the pump discharge, force of propulsion, power input and efficiency of propulsion if the inlet orifices are located at amid–ships and in bow.

Or

(b) A jet propelled boat moves at 32 km/hr in a fresh water lake. There are two jets each of diameter 20 cm. The absolute velocity of the discharged jets is 25 km/hr. Calculate the pump discharge, force of propulsion, power input and efficiency of propulsion if the inlet orifices are located at amid–ships and in bow.

14.
(a) Two reservoirs whose water surface elevations differ by 12 m are connected
by the following horizontal compound pipe system starting from the high level
reservoir. = 200 m, = 0.2 m, and

= 500 m, = 0.3 m, = 0.006. Considering all head losses and assuming that all changes of section are abrupt, compute the discharge through the system. Determine the equivalent length of a 0.25 m diameter pipe if minor losses are neglected and friction factors are assumed to be the same. Sketch HGL and TEL.

Or

(b) Water flows through a 10 cm diameter, 30 m long pipe at a rate of

1400 lpm. What percent of head would be gained by replacing the central one third length of pipe by another pipe of 20 cm diameter. Assume that the changes in section are abrupt and f = 0.008 for all pipes. Neglect entrance and exit losses but consider all other losses.

= 500 m, = 0.3 m, = 0.006. Considering all head losses and assuming that all changes of section are abrupt, compute the discharge through the system. Determine the equivalent length of a 0.25 m diameter pipe if minor losses are neglected and friction factors are assumed to be the same. Sketch HGL and TEL.

Or

(b) Water flows through a 10 cm diameter, 30 m long pipe at a rate of

1400 lpm. What percent of head would be gained by replacing the central one third length of pipe by another pipe of 20 cm diameter. Assume that the changes in section are abrupt and f = 0.008 for all pipes. Neglect entrance and exit losses but consider all other losses.

15.
(a) Using Buckingham’s ??theorem, show that the drag of a supersonic aircraft
is given by :

.

Where = Reynolds number, = Mach number,

? = fluid density, V = velocity of aircraft, c = sonic velocity =

K = bulk modulus of fluid, L = chord length, = wing area =

chord x span, ? = a functional notation.

Or

(b) It is desired to obtain the dynamic similarity between a 30 cm diameter pipe carrying linseed oil at 0.5 m3/s and a 5 m diameter pipe carrying water. What should be the rate of flow of water in lps? If the pressure loss in the model is 196 N/m2, what is the pressure loss in the prototype pipe? Kinematic viscosities of linseed oil and water are 0.457 and 0.0113 stokes respectively. Specific gravity of linseed oil = 0.82.

—————————

.

Where = Reynolds number, = Mach number,

? = fluid density, V = velocity of aircraft, c = sonic velocity =

K = bulk modulus of fluid, L = chord length, = wing area =

chord x span, ? = a functional notation.

Or

(b) It is desired to obtain the dynamic similarity between a 30 cm diameter pipe carrying linseed oil at 0.5 m3/s and a 5 m diameter pipe carrying water. What should be the rate of flow of water in lps? If the pressure loss in the model is 196 N/m2, what is the pressure loss in the prototype pipe? Kinematic viscosities of linseed oil and water are 0.457 and 0.0113 stokes respectively. Specific gravity of linseed oil = 0.82.

—————————

**PART – A (10 x 2 = 20Marks)**

- Define Mass density and relative density of fluids. State their dimensions and units.
- Define: Kinematics and Dynamic viscosity of a fluid.
- Define centre of pressure and centre of buoyancy.
- State the properties of stream function.
- State Bernoulli’s theorem.
- Differentiate between laminar and turbulent flow in pipes.
- Define displacement thickness.
- The velocity of water in a pipe 200mm diameter is 5m/s. The length of the pipe is 500m. Find the loss of head due to friction, assuming friction factor as 0.02.
- State Buckingham’s π theorem.
- What are distorted modes?

**PART – B**

11(a) (i) State
Newton’s aw of viscosity. What are capillary rise and capillary
depression?

**(4 Marks)**
(ii) A piece of
pipe 0.5m long weighing 9.81N and having internal diameter of 5.25cm is sipped
over a vertical shaft 5.0cm in diameter and allowed to fall. Calculate the
velocity attained by the pipe if a film of oil of viscosity 0.196Ns/m

^{2}is maintained between the pipe and the shaft.**(12 Marks)****(OR)**

(b) (i) A
Newtonian fluid is filled in the clearance between a shaft and a concentric
sleeve, The sleeve attains a speed of 50cm/s, when a force of 40N is applied to
the sleeve parallel to the shaft. Determine the speed of the shaft, if a force
of 200N is applied.

**(8 Marks)**
(ii) Derive an
expression between the surface tension in a liquid bubble and the pressure
difference between the inside and outside of the bubble. If the pressure
difference between the inside and outside of the air bubble of diameter 3mm is
29.2 kPa, what will be the surface tension of air water interface?

**(8 Marks)**
12 (a) (i) A
simple manometer is used of measure e pressure of oil (sp. gr. = 0.8) flowing
in a pipe line. Its right limb is open to the atmosphere and left limb is
connected to the pipe. The centre of the pipe is 9cm below the level of mercury
(sp.gr.13.6) in the right limb is 15cm; determine the pressure of the
pipe.

**(8 Marks)**
(ii) A
triangular plate of 1m base and 1.5m altitude is immersed in water. The plane
of the plate is inclined at 30° with free water surface and base is parallel to
and at a depth of 2m from water surface. Find the total pressure on e plate and
position of centre of pressure.

**(8 Marks)****(OR)**

(b) (i) The two
dimensional stream function for a flow is Ψ = 9 +6x-4y+7xy. Find the velocity
potential function.

**(8 Marks)**
(ii) Explain the
method of measurement of discharge in an open channel using current meter.

**(8 Marks)**
13(a) (i) state
the practical application of Bernoulli’ theorem. Explain its application in a
pitot tube.

**(6 Marks)**
(ii) A 2m long
conical tube is fixed vertically with its smaller end upwards. It carries
liquid in downward direction. The flow velocities at the smaller and larger end
are 5m/s and 2m/s respectively. The pressure head at the smear end is 2.5m of
liquid. If the loss of head in the tube is 0.35 (V

_{1}– V_{2})^{2}/2g where V_{1}and V_{2}being the velocities at the smaller and larger end respectively. Determine the pressure head at the larger end.**(10 Marks)****OR**

(b) (i) Derive
the Hagen –
Poiseuille equation. Deduce the condition for maximum velocity in the circular
pipe.

**(10 Marks)**
(ii) A
horizontal venturimeter with inlet and throat diameter 300mm and 100mm
respectively is used o measure the flow of water. The pressure intensity at
inlet is 130kN/m

^{2}while the vacuum pressure head at throat I 350mm of mercury. Determine the rate of flow. Take Cd = 0.96.**(6 Marks)**
14(a) (i) for
the laminar boundary layer, the velocity distribution is given by

u/U = 2(y/δ) – 2(y/δ)

^{3}+ (y/δ)^{4}. Compute the displacement thickness.**(8 Marks)**
(ii) A plate
450mm x 150mm has been placed longitudinally in a stream of crude oil (specific
gravity 0.925 and kinematics viscosity of 0.9 stoke) which flows with velocity
of 6m/s. calculate the friction drag on the plate, thickness of the boundary
layer at the trailing edge and the shear stress at the trailing edge.

**(8 Marks)****OR**

(b) (i) two pipe
of diameter 400mm and 200mm are 300mm long. Where the pipe are connected in
series, the discharge through the pipe line is 0.10m

^{3}/s.Find the loss in head. What would the loss of pipeline is 0.10m^{3}/s. Find the loss in head. What would the loss of head in the system to pass the same total discharge when the pipes are connected in parallel? Assume Darcy’s friction factor a 0.03.**(10 Marks)**
(ii) The
diameter of a horizontal pipe which I 300mm is suddenly enlarged to 600mm. the
rate of flow of water through this pipe is 0.4m

^{3}/s. If the intensity of pressure in the smaller pipe I 125kN/m^{2}, determine the loss of head, due to sudden enlargement and the power lost due to enlargement.**(6 Marks)**
15(a) the
resisting fore (R) of a supersonic flight an be considered a dependent upon the
length of the air craft ‘l’ velocity ‘v’, air viscosity ‘ μ’, air density ‘ρ’
and bulk modulus of air ‘k’. Express the functional relationship between these
variables and the resisting fore.

**(16 Marks)****OR**

(i) Explain
Reyond’s law of similitude and Froude’s law of similitude.

**(8 Marks)**
(ii) In an aero
plane model of size (1/10) of its prototype, the pressure drop is 7.5kN/m

^{2}. The mode is tested in water. Find the corresponding pressure drop in the prototype. Assume density of air = 1.24kg/m^{3}density of water = 1000kg/m^{3}: viscosity of air = 0.00018 Poise; viscosity of water = 0.01 Poise.**(8 Marks)**