Fluid Mechanics (2130602)

B.E. Semester III Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1.1

Module 1 – Properties of Fluids

Theory

1. Define the terms:

(1) Surface tension

(2) Specific gravity

(3) Specific weight

(4) Capillarity

(5) Newtonian fluid

(6) Newton’s law of viscosity

(7) Compressibility and Bulk modulus

2. Explain the capillary action of rise and fall of liquid columns.

3. Define surface tension and derive its expression.

Examples

1. Define compressibility of a fluid. When the pressure of liquid is increased to 7.5x103 kN/m2

from 4x103 kN/m2, its volume is found to reduce by 0.075 percent. Calculate the bulk modulus

of elasticity of the liquid.

2. A square plate of size 1m x 1m and weighing 500 N slides down an inclined plane with a

uniform velocity of 2 m/s. The plane makes an angle of 30 to the horizontal and has oil film

of 1.5 mm thickness. Find the dynamic viscosity of oil.

Fluid Mechanics (2130602)

B.E. Semester III Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 2.1

Module 2 – Fluid Statics

Theory

1. State the Pascal’s law and prove it.

2. Explain construction and working of Bourdon tube pressure gauge.

3. Write a short note on (1) piezometer & (2) inverted U-tube differential manometer with neat

sketches.

4. Explain construction and working of vertical single column manometer with equation.

5. Define Total Pressure & Center Pressure.

6. Derive the expression for total pressure for a vertical plate submerged in the liquid.

7. Explain Buoyancy and Centre of Buoyancy.

8. Define the terms metacenter and metacentric height.

9. Explain equilibrium in floating bodies with proper sketches.

10. Discuss the equilibrium conditions for submerged bodies with proper sketches.

Examples

1. Rectangular lamina of size 3 m x 5 m is immersed vertically in water such that 5m side is

parallel and lies below 1 m to the free water surface. Determine the total hydrostatic force and

centre of pressure.

2. A circular plate 3.5 m diameter is immersed in water in such a way that its greatest and least

depth below free surface is 4 m and 1.5 m respectively. Determine the total pressure on one

face of the plate and position of the center of pressure.

3. The pressure intensity at a point in a fluid is given 5 N/cm2. Find the corresponding height of

fluid when fluid is (i) water (ii) oil of sp. Gravity=0.80 and (iii) kerosene of sp. Gravity = 0.74.

4. Determine the total pressure & center of Pressure on an isosceles triangular plate of base 4m

& altitude 4 m when it is immersed vertically oil of specific gravity = 0.9. The base of the plate

coincides with the free water surface of the oil.

5. Find the volume of the water displaced and the position of center of buoyancy for a wooden

block of width 2.5m and of depth 1.5m, when it floats horizontally in water. The density of

wooden block is 650kg/m3 and its length 6.0m.

Fluid Mechanics (2130602)

B.E. Semester III Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 3.1

Module 3 – Fluid Kinematics

1. Define following terms. a) Stream line b) Streak line c) Path line d) Equipotential line e) Flow net f) Stream tube g) Source flow and sink flow h) Circulation i) Vorticity

2. Derive continuity equation for three dimensional incompressible flow.

3. State and define different types of fluid flow.

Examples

1. A stream function for a two dimensional flow is given by ψ = 2xy, calculate the velocity at point

P (2, 3). Find the velocity potential function ϕ.

2. For a fluid flow, velocity components in x and y directions are u = 2xy and v = x2 – y2 + 4

respectively. Show that the components represent a possible case of fluid flow. Derive stream

function and the flow rate between the stream lines corresponding to points (1, 0) and (1, 1).

Fluid Mechanics (2130602)

B.E. Semester III Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 4.1

Module 4 – Fluid Dynamics

Theory

1. Enlist forces acting on fluid in motion.

2. Derive Euler’s equation of motion along streamline.

3. Give derivation of Bernoulli’s equation from Euler’s equation of motion. Enumerate

assumptions made in derivation and explain the limitation of Bernoulli’s equation.

4. What do you meant by TEL and HGL?

Examples

1. Water is flowing from a tapered pipe having diameter 350 mm and 200 mm at section 1 and

2 respectively. The flow rate through the pipe is 0.05 m3/s.

The section 1 is 10 m above the datum and section 2 is 5 m above the datum. If intensity of

pressure at section 1 is 0.5 MPa. Find intensity of pressure of pressure of section 2.

2. A pump is pumping water at the rate of 7536 lit/min. The pump inlet is 40 cm in diameter

and the vacuum pressure over there is 15 cm of mercury. The pump outlet is 20 cm in

diagram and it is 1.2 m above the inlet. The pressure at the outlet is 107.4 kN/m2. Estimate

the power added by pump.

Fluid Mechanics (2130602)

B.E. Semester III Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 5.1

Module 5 – Flow Measuring Devices

Theory

1. Explain construction and working of venturimeter and derive an expression of discharge

through it.

2. Derive the equation for determining the discharge from Borda’s mouthpiece running full.

3. Define various hydraulic coefficients. How to determine coefficient of velocity

experimentally?

4. Classify various types of notches. Derive the equation for discharge through a rectangular

notch.

5. What is Pitot tube? Derive equation of velocity for flow of fluid through it.

6. What is the difference between a mouthpiece and an orifice?

7. Explain with neat sketches the contracted rectangular notch and Cippoleti notch.

8. Derive the equation for time (T) required to empty a rectangular tank filled with liquid. The

tank has an orifice at its bottom. The initial depth of water in the tank is H1.

Examples

1. A sharp-edged orifice of 125 mm diameter is fixed on vertical side of a tank under a constant

head of 9 m. The orifice is discharging water at a rate of 105 liters/sec. A point on the jet has

horizontal and vertical coordinates of 4.25 m and 0.55 m respectively, which are measured

from the vena-contracta. Calculate coefficient of velocity, coefficient of discharge and

coefficient of contraction. Also estimate area of the jet at the vena-contracta.

2. A pitot tube is inserted in a pipe of 30 cm diameter. The static pressure of the tube is 10 cm

of mercury, vacuum. The stagnation pressure at the centre of the pipe recorded by the pitot

tube is 1.1 N/cm2. Calculate the rate of flow of water through the pipe if mean velocity of

flow is 0.85 times centre line velocity. Take coefficient of pitot tube = 0.98.

3. Estimate the discharge over a 90 triangular notch having head over crest as 45 cm. The

coefficient of discharge Cd = 0.62. If the head over crest becomes` 55 cm calculate the

percentage increase in discharge.

4. Calculate the discharge for flow passing through a trapezoidal notch having base width of

0.75 m and side slope of 1:1. Take the head over crest of notch = 50 cm. The coefficient of

discharge Cd= 0.63.

Fluid Mechanics (2130602)

B.E. Semester III Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 6.1

Module 6 – Flow Immersed Past Bodies

Theory

1. Briefly discuss about drag force and lift force. Explain the types of drag with suitable examples.

2. Differentiate between a stream lined body and a bluff body. Prove that the coefficient of drag

for the drag on sphere is given by CD = 24/Re, when Re (Reynolds’ number) ≤ 0.2.

3. Explain free and forced vortex with suitable examples.

4. Explain the Magnus effect in lift generation around a body.

5. Explain characteristics of airfoil.

Examples

1. Experiments on a flat plate of 1 m length and 0.5 m width were conducted in a wind tunnel in

which wind was blowing horizontally at a speed of 60 Km/hour. The plate was kept at such

an angle that the coefficients of drag and lift were 0.2 and 0.88 respectively. Calculate, (i) drag

and lift forces, (ii) resultant force and its direction and, (iii) power exerted by the air stream

on the plate. Take specific weight of air equal to 11.28 KN/m3.

2. A car has frontal projected area of 1.5 m2 and travels at 55 km/h. Calculate the power required

to overcome wind resistance if coefficient of drag is 0.35. If the drag coefficient is reduced by

streamlining to 0.25 what speed of the car is possible? Take ρair = 1.2 kg/m3

Fluid Mechanics (2130602)

B.E. Semester III Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 7.1

Module 7 – Compressible Flow

Theory

1. Define:

a) sonic flow

b) stagnation point

c) stagnation pressure

2. Prove that velocity of sound wave is square root of the ratio of change of pressure to the

change of density of the fluid.

3. Derive equation for sonic velocity of sound wave in a compressible fluid in terms of the bulk

modulus of elasticity of the fluid medium.

4. Define Mach number. Give classification and explanation of the type of flow based on Mach

number.

5. Distinguish between subsonic and supersonic flow.

Examples

1. A projectile is traveling in air having pressure and temperature as 9 N/cm2 and -5C. If the

mach angle is 35, find the velocity of projectile. Take k=1.4 and R=287 J/kg K

2. An aeroplane is flying at 950 Km/hour through still air having an absolute pressure of 80

KN/m2 and temperature -7C. Calculate stagnation pressure, stagnation temperature and

stagnation density, on the stagnation point on the nose of the plane. Take R = 287 J/ Kg K and

γ = 1.4 for air.