Enrolment No.

/Seat No_______________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE- SEMESTER–IV (NEW) EXAMINATION – WINTER 2024
Subject Code: 3140611 Date: 27-11-2024
Subject Name: Fluid Mechanics & Hydraulics
Time: 02:30 PM TO 05:00 PM Total Marks:70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.

Q.1 (a) Define: Dynamic Viscosity and Capillarity 03

(b) Differentiate between Piezometer and U-tube manometer. 04
(c) State and prove Pascal’s law. 07

Q.2 (a) Define Buoyancy, Center of Pressure, and Metacentric height. 03

(b) Explain equilibrium in floating bodies. 04
(c) Derive the expression for total pressure for a vertical plate submerged in the 07
liquid.
OR
(c) Prove that the rate of increase of pressure in a vertically downward 07
direction must be equal to the specific weight of the fluid at that point.

Q.3 (a) Describe the velocity distribution in an open channel flow. 03

(b) Explain the importance of the parameters contained in the Reynolds number to 04
categorize the flow as laminar and turbulent flow.
(c) Explain the components of a venturimeter with a neat proportionate sketch. 07
OR
Q.3 (a) Differrentiate between small & large orifice. 03
(b) State Bernoulli’s equation. What are the practical applications of 04
Bernoulli’s equation?
(c) Define flow net and write in detail characteristics, applications and 07
limitations of flow net.

Q.4 (a) Define: (i) Total energy line (ii) Hydraulic gradient line 03
(b) Write down the Chezy’s equation and Manning’s equation along with their 04
assumptions.
(c) Enlist the major and minor loses in pipes. Derive the Darcy-Weisbach equation 07
for calculating head loss due to friction.
OR
Q.4 (a) Define rapid varied flow and gradually varied flow. 03
(b) Explain with diagram the Specific Energy Curve. 04
(c) Derive for the most economic a trapezoidal channel section is: “Half of the top 07
width is equal to one of the sloping sides”

Q.5 (a) Explain method of selecting repeating variables. 03

(b) Derive the Hagen-Poiseuille equation for laminar flow in the circular pipe. 04

1
 (c) A 2m long pipeline tapers uniformly from 10cm diameter to 20cm diameter at 07
its upper end. The pipe cemtreline slopes upward at an angle of 30֩ to the
horizontal and the flow direction is from smaller to bigger cross section. If the
pressure gauges installed at the lower and upper ends of the pipeline read 200
KPa and 230 KPa respectively. Determine the flow rate and the fluid pressure
at the mid length of pipeline. Assume no energy losses.
OR
Q.5 (a) Define super critical flow, Froude’s number and hydraulic jump. 03
(b) What is Dimensional Homogeneity? What are the applications of 04
Dimensional Homogeneity?
(c) Explain the Buckingham’s π-theorem in dimensional analysis 07

*************

2
 Enrolment No./Seat No_______________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER–IV (NEW) EXAMINATION – SUMMER 2024
Subject Code:3140611 Date:03-07-2024
Subject Name:Fluid Mechanics & Hydraulics
Time:10:30 AM TO 01:00 PM Total Marks:70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.

MARKS
Q.1 (a) Define Non-Uniform flow, Supercritical Flow, RVF 03
(b) Compare flow discharge measurement by Notch and weir. 04
(c) State and explain the theorems associated with dimensional analysis. 07

Q.2 (a) Define Venturimeter, Orificemeter, and Weir. 03

(b) What is Orifice? What are the different hydraulic coefficients associated with 04
orifice.
(c) A horizontal Venturimeter with inlet diameter 25 cm and throat diameter 15 07
cm is used to measure the flow of oil of specific gravity 0.8. The discharge of
oil through Venturimeter is 70 litres/s. Find the reading of the oil-mercury
differential manometer. Take Cd as 0.97
OR
(c) The head of water over a triangular notch of angle 600 is 55 cm and co- 07
efficient of discharge is 0.61. The flow measured by it is to be within an
accuracy of 1.7 % up or down. Find the limiting values of the head.

Q.3 (a) Define Unsteady Flow, Flow Net, Metacentric Height. 03

(b) State Bernoulli’s Theorem with equation. Explain its significance. 04
(c) A solid cylinder of diameter 5 m has a height of 5 m. Find the metacentric 07
height of the cylinder if the specific gravity of the material of cylinder is 0.6
and it is floating in the water with its axis vertical. State whether the
equilibrium is stable or unstable.
OR
Q.3 (a) Define Specific Gravity, Centre of Pressure, Viscosity. 03
(b) State and prove Pascal’s law with suitable sketch. 04
(c) A U-tube manometer is used to measure the pressure of the water in a pipe 07
line, which is in excess of the atmospheric pressure. The right limb of the
manometer contains mercury and is open to atmosphere. The contact between
the water and mercury is in the left limb. Determine the pressure of the water
in the main line, if the difference in the level of mercury in the limbs of U-
tube is 15 cm and the free surface of mercury is in level with the centre of the
pipe.

Q.4 (a) Describe the Prandtl’s mixing length theory with suitable sketch, 03
(b) Derive the energy-momentum equation. 04
(c) Discuss various major and minor losses in pipes. 07

1
 OR
Q.4 (a) Write the continuity equation, momentum equation and Energy equation for 03
the pipe flow.
(b) Derive the Hagen Poiseuille equation. 04
(c) Discuss Hardy Cross method to analyze pipe networks in series and parallel. 07

Q.5 (a) Describe the velocity distribution in an open channel flow. 03

(b) What is Specific Energy. Derive the specific energy equation. 04
(c) Find the discharge through a trapezoidal channel of width 8 m and side slope 07
of 1 horizontal to 3.5 vertical. The depth of flow of water is 1.9 m and the
value of Chezy’s constant, C=45. The slope of the bed of the channel is given
1 in 5000.
OR
Q.5 (a) Discuss direct step method for GVF. 03
(b) Write down the Chezy’s equation and Manning’s equation along with their 04
assumptions.
(c) The discharge of water through a rectangular channel of width 10 m, is 18 07
m3/s when depth of flow of water is 1.4 m. Calculate:
i) Specific energy of the flowing water ii) Critical depth and critical velocity
iii) Value of minimum specific energy

*************

2
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER–IV (NEW) EXAMINATION – WINTER 2023
Subject Code:3140611 Date:24-01-2024
Subject Name: Fluid Mechanics & Hydraulics
Time: 10:30 AM TO 01:00 PM Total Marks:70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.

Q.1 (a) Define: Fluid statics, Fluid Kinematics, Kinematic viscosity 03

(b) State the Newton’s law of viscosity. 04
(c) State and derive Pascal’s law. 07

Q.2 (a) Define the terms metacentre, metacentric height and absolute pressure. 03
(b) Explain equilibrium in floating bodies. 04
(c) Derive the expression for total pressure for a vertical plate submerged 07
in the liquid.
OR
(c) For a most economical trapezoidal channel section, show that half of 07
top width is equals to length of one of the slopping sides.

Q.3 (a) Define coefficient of contraction, coefficient of velocity and coefficient 03

of discharge for the orifice.
(b) Give classification of Orifices. Give the difference between an orifice 04
and a mouthpiece.
(c) A pipe of diameter 100 mm conveys water. The pressure difference 07
between two points 50 m apart is 0.6 m of water. Calculate discharge
through the pipe. Take friction factor f = 0.025.
OR
Q.3 (a) Which are the assumptions made in Bernoulli’s theorem ? 03
(b) What are the advantages of triangular notch over a rectangular notch? 04
(c) A horizontal venturimeter with inlet and throat diameters 30 cm and 15 07
cm respectively is used to measure rate of water. The reading of
differential manometer connected to the venturimeter is 20 cm of
mercury. Determine the rate of flow. Take coefficient of discharge equal
to 0.98

Q.4 (a) Draw velocity distribution in pipe flow and open channel flow. 03
(b) Explain Prandtl’s mixing length theory. 04
(c) State Bernoulli’s theorem for steady flow of an incompressible fluid. 07
Derive Bernoulli’s expression
OR
Q.4 (a) Define: (i) Total energy line (ii) Hydraulic gradient line 03
(b) Explain with diagram the Specific Energy Curve. 04
(c) Enlist the major and minor loses in pipes. Derive the Darcy-Weisbach 07
equation for calculating head loss due to friction.

Q.5 (a) Differentiate between pipe flow and open channel flow. 03
1
 (b) Derive the Hagen-Poiseuille equation for laminar flow in the circular 04
pipe.
(c) Fluid of density ρ and viscosity μ flows at an average velocity V 07
through a circular pipe diameter d. show by dimensional analysis that
the shear stress of the pipe wall.

OR
Q.5 (a) How repeating variables are selected in the dimensional analysis. 03
(b) Discuss briefly various similarities between the model and the prototype. 04
(c) Explain the Buckingham’s π-theorem in dimensional analysis 07

*************

2
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER– IV(NEW) EXAMINATION – SUMMER 2023
Subject Code:3140611 Date:19-07-2023
Subject Name:Fluid Mechanics & Hydraulics
Time:10:30 AM TO 01:00 PM Total Marks:70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.

MARKS
Q.1 (a) What is capillarity? Explain term cohesion and adhesion. 03
(b) A plate 0.08 mm apart from fixed plate requires stress of 2.25 N/m2 to 04
move at a velocity of 1.80 m/s. Determine viscosity of fluid between the
plates.
(c) For a most economical trapezoidal channel section, show that half of top 07
width is equals to length of one of the slopping sides.

Q.2 (a) State Pascal’s law and its application. 03

(b) Calculate pressure intensity at a point 4.00 m below sea water level. Take 04
specific gravity of sea water 10 KN/m3.
(c) Two pipes A and B laid at same level convey oil of specific gravity 1.35. 07
A differential manometer connected between pipes shows difference in
mercury levels as 20 cm. Find difference in pressures at the point. Take
specific gravity of mercury 13.60

OR
(c) A trapezoidal channel section has a bed width 7.50 m laid at a bed slope 07
of 1 in 3600. Side slope of the channel is 1H : 1V. Depth of flow in the
channel is 2.00 m. Find the discharge in the channel. Take Manning’s
constant 0.015.

Q.3 (a) Explain different types of Equilibrium of floating body. 03

(b) Head over the triangular 90o V-notch is 0.40 m. Find the discharge over 04
the notch. Take Cd = 0.60
(c) Show that stream function Ψ always satisfy continuity equation. 07
OR
Q.3 (a) What is meant by hydraulic coefficient? State the relation between 03
different hydraulic coefficients.
(b) A rectangular uniform wooden body 2.50 m long, 1.25 m wide and 1.00 04
m deep floats in water. The depth of immersion being 0.75 m. Calculate
weight of the body. Also find position of metacenter.

1
 (c) A pipe of diameter 127 mm conveys water. The pressure difference 07
between two points 250 m apart is 3.25 m of water. Calculate discharge
through the pipe. Take friction factor f = 0.025

Q.4 (a) Describe major energy losses and minor energy losses in pipe. 03
(b) A 4.00 m wide rectangular channel conveys 30.00 m3/s of water. Find 04
critical depth.
(c) The velocity in x and y direction is given by: 07
u = -2y and v = 2x. Check whether stream function exists or not? If so
deduce it and Plot set of stream lines.
OR
Q.4 (a) Develop relationship between maximum velocity and average velocity in 03
case of viscous flow between two parallel plates.
(b) A 6.25 m wide rectangular channel conveys 18.00 m3/s of water with a 04
velocity of 4.50 m/s. is there a condition for hydraulic jump to occur?
(c) Draw a sketch of venturimeter and show its component. Develop an 07
expression for rate of flow through venturimeter.

Q.5 (a) Describe different types of fluid flow. 03

(b) What is meant by dimensional homogeneity? Write dimensions of 04
(1) Specific weight (2) Angular velocity (3) Dynamic viscosity.
(c) A square plate of 2.50 m side is immersed vertically in water such that 07
one side is parallel and lies 2.00 m below the free water surface. Calculate
total hydrostatic force and center of pressure on plate.
OR
Q.5 (a) Which flow is said to be open channel flow? Differentiate open channel 03
flow and pipe flow.
(b) Explain different types of similarities between model and its prototype. 04
(c) A pipe of 20 cm diameter is conveys water at a velocity of 5.00 m/s. Find 07
the velocity and discharge of oil flowing in another pipe of 10 cm
diameter. The viscosity of oil and water is 0.03 poise and 0.01 poise resp.
Take specific gravity of oil = 0.75. Assume that dynamic similarity is
satisfied between two pipes.

*************

2
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER–IV(NEW) EXAMINATION – WINTER 2022
Subject Code:3140611 Date:17-12-2022
Subject Name:Fluid Mechanics & Hydraulics
Time:10:30 AM TO 01:00 PM Total Marks:70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.
MARKS
Q.1 (a) Define: Dynamic Viscosity, Surface tension, Capillarity 03
(b) Explain Buoyancy and Centre of Buoyancy 04
(c) State and prove Pascal’s law. 07

Q.2 (a) Define the terms metacentre, metacentric height and absolute pressure 03
(b) Differentiate between: 04
(a) Compressible and incompressible flow
(b) Uniform and Non Uniform flow
(c) Derive the expression for total pressure for a vertical plate submerged in 07
the liquid.
OR
(c) The mercury manometer shown below indicates a differential reading of 07
0.3m when a pressure in Pipe A is 30 mm of mercury (Hg) vacuum.
Determine the pressure in pipe B (in Pa.)

Q.3 (a) Classify different types of orifices according to its shapes, size, 03
discharge.
(b) Explain the importance of the parameters contained in the Reynolds 04
number to categorize the flow as laminar and turbulent flow.
(c) Explain the components of a venturimeter with a neat proportionate 07
sketch.
OR
Q.3 (a) Differrentiate between small & large orifice. 03
(b) State Bernoulli’s equation. What are the practical applications of 04
Bernoulli’s equation?
(c) Derive an expression for the discharge through triangular notch 07

Q.4 (a) Define: (i) Total energy line (ii) Hydraulic gradient line 03
1
 (b) Explain Prandtl’s mixing length theory. 04
(c) Enlist the major and minor loses in pipes. Derive the Darcy-Weisbach 07
equation for calculating head loss due to friction.
OR
Q.4 (a) Define rapid varied flow and gradually varied flow. 03
(b) Explain with diagram the Specific Energy Curve. 04
(c) Derive for the most economic a trapezoidal channel section is: “Half of 07
the top width is equal to one of the sloping sides”

Q.5 (a) Explain method of selecting repeating variables. 03

(b) Derive the Hagen-Poiseuille equation for laminar flow in the circular 04
pipe.
(c) The pressure drop (ΔP) in a pipe depends upon the mean velocity of flow 07
(v), length of pipe (l), diameter of pipe (d), viscosity of fluid (µ), average
height of roughness projections on the inside surface (k) mass density of
fluid (ρ). By using Buckingham's pi-theorem, obtain a dimensionless
expression ΔP.
OR
Q.5 (a) Define super critical flow, Froude’s number and hydraulic jump. 03
(b) What is Dimensional Homogeneity? What are the applications of 04
Dimensional Homogeneity?
(c) Explain the Buckingham’s π-theorem in dimensional analysis 07

*************

2
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER–IV (NEW) EXAMINATION – SUMMER 2022
Subject Code:3140611 Date:04-07-2022
Subject Name:Fluid Mechanics & Hydraulics
Time:10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.
MARKS
Q.1 (a) Define density, specific weight and specific volume. 03
(b) Calculate the specific weight, density and specific gravity of one litre 04
of liquid which weighs 7 N.

(c) Write about different types of fluid in detail with example. 07

Q.2 (a) Differentiate between Piezometer and U-tube manometer 03

(b) Prove that the rate of increase of pressure in a vertically downward 04
direction must be equal to the specific weight of the fluid at that point.
(c) A differential manometer is connected at the two points A and B of two 07
pipes as shown in Fig.1. The pipe A contains a liquid of sp.gr. = 1.5
while pipe B contains a liquid of sp.gr.= 0.9. The pressures at A and B
are 1kgf/𝑐𝑚2 and 1.8 kfg/𝑐𝑚2 respectively. Find the difference in
mercury level in the differential manometer.
OR
(c) State and Prove Pascal’s Law. 07

Q.3 (a) Define Buoyancy, Center of Pressure, and Metacentric height. 03

(b) Derive an expression for Centre of Pressure by using “ Principle of 04
Moments”
(c) A pipe line which is 4 m in diameter contains a gate valve. The pressure 07
at the centre of the pipe is 19.6 N/𝑐𝑚2 . If the pipe is filled with oil of
sp.gr. 0.87, find the force exerted by the oil upon the gate and position
of centre of pressure.
OR
Q.3 (a) Define Laminar flow, stream line and path line. 03
(b) A stream function in a two-dimensional flow is Ψ =2xy. Calculate the 04
velocity at the point (3, 2). Find the corresponding velocity potential Φ.
(c) Define flow net and write in detail characteristics, applications and 07
limitations of flow net.

Q.4 (a) Explain Venturimeter and parts of Venturimeter with diagram. 03

(b) An orifice meter with orifice diameter of 150 mm is used to measure the 04
rate of flow of oil in a pipe of 300 mm diameter. The manometer shows
a pressure difference of 40 cm of mercury. Find the rate of flow of oil
through pipe if sp.gr of oil is 0.8. Take coefficient of discharge for meter
= 0.60
(c) Derive equation of velocity measurement using pitot tube. Also explain 07
different arrangement to know the static pressure head h.
OR
Q.4 (a) Enlist minor losses in flow through pipes. 03
1
 (b) Calculate the discharge through a pipe of diameter 250 mm when the 04
difference of pressure head between the two ends of a pipe 500 m apart
is 3.5 m of water. Take value of friction factor = 0.04
(c) Derive Darcy–Weisbach equation for friction loss in the pipe. 07

Q.5 (a) Define (i) Prismatic channel (ii) Gradually varied flow (iii) Wetted 03
perimeter
(b) An irrigation lined canal of trapezoidal section has to carry a discharge 04
of 12 cumec at a longitudinal slope of 0.00048. Find the dimensions of
most economical section if channel has side slope of 3 horizontal to 2
vertical. Take Manning’s constant n = 0.013.
(c) Derive the geometrical conditions for the most economical section of a 07
triangular channel.
OR
Q.5 (a) Define (i) Reynold’s number (ii) Mach number (iii) Weber number 03
(b) Write in detail about (i) Geometric similarity (ii) Kinematic similarity 04
(c) The efficiency η of a fan depends on the density ρ, dynamic viscosity µ, 07
the angular velocity ω, Diameter D of the rotor and the discharge Q.
Express η in terms of dimensionless parameters.

2
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER–IV (NEW) EXAMINATION – WINTER 2021
Subject Code:3140611 Date:04/01/2022
Subject Name:Fluid Mechanics & Hydraulics
Time:10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.

MARKS
Q.1 (a) Define: Fluid statics, Fluid Kinematics, Kinematic viscosity 03
(b) State the Newton’s law of viscosity. 04
(c) Derive the expression for total pressure for a vertical plate submerged in the 07
liquid.

Q.2 (a) Explain equilibrium in floating bodies. 03

(b) Differentiate between: 04
(a) Steady and Unsteady flow
(b) Uniform and Non Uniform flow
(c) A U-tube differential manometer is connected to two pipes at A and B shown 07
in figure . Pipe A Contains oil of Specific Gravity 0.92 and pipe B is carrying
water. If the pressure at point A is 125 kN/m2 find the pressure at point B.

OR
(c) A triangular plate of 1 metre base and 1.5 metre altitude is immersed in water 07
shown in figure . The plane of plate is inclined at 300 with free water surface
and the base is parallel to and at a depth of 2 meters from water surface. Find
the total pressure on the plate and position of centre of pressure.

Q.3 (a) Define coefficient of contraction, coefficient of velocity and coefficient of 03

discharge for the orifice.

1
 (b) Give classification of Orifices. Give the difference between an orifice and a 04
mouthpiece.
(c) State Bernoulli’s theorem for steady flow of an incompressible fluid. Derive 07
Bernoulli’s expression
OR
Q.3 (a) Which are the assumptions made in Bernoulli’s theorem ? 03
(b) What are the advantages of triangular notch over a rectangular notch? 04
(c) A horizontal venturimeter with inlet and throat diameters 30 cm and 15 cm 07
respectively is used to measure rate of water. The reading of differential
manometer connected to the venturimeter is 20 cm of mercury. Determine the
rate of flow. Take coefficient of discharge equal to 0.98

Q.4 (a) Draw velocity distribution in pipe flow and open channel flow. 03
(b) Explain Prandtl’s mixing length theory. 04
(c) Enlist the major and minor loses in pipes. Derive the Darcy-Weisbach equation 07
for calculating head loss due to friction.
OR
Q.4 (a) Define: (i) Total energy line (ii) Hydraulic gradient line 03
(b) Explain with diagram the Specific Energy Curve. 04
(c) Derive for the most economic a trapezoidal channel section is: “Half of the top 07
width is equal to one of the sloping sides”
Q.5 (a) Differentiate between pipe flow and open channel flow. 03
(b) Derive the Hagen-Poiseuille equation for laminar flow in the circular pipe. 04

(c) Fluid of density ρ and viscosity μ flows at an average velocity V through a 07

circular pipe diameter d. show by dimensional analysis that the shear stress of
the pipe wall.

OR
Q.5 (a) Explain hydraulically smooth and rough boundaries. 03
(b) Discuss briefly various similarities between the model and the prototype. 04

(c) Explain the Buckingham’s π-theorem in dimensional analysis 07

*************

2
 Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER–IV (NEW) EXAMINATION – SUMMER 2021
Subject Code:3140611 Date:08/09/2021
Subject Name:Fluid Mechanics & Hydraulics
Time:02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.
MARKS
Q.1 (a) Define fluid, Specific gravity, Mass density 03
(b) Define viscosity and differentiate between kinematic and dynamic viscosity 04
its ap
pl
(c) Define surface tension. Prove the relationship between surface tension and 07
inside a droplet of liquid in excess of outside pressure is given by p = 4σ/d.

Q.2 (a) Describe the terms atmospheric , absolute, gage and vaccum pressure with 03
sketch
(b) Classify various manometers 04
(c) State Pascal’s law and give some examples where this principle is applied 07
OR
(c) Explain hydrostatic paradox with suitable demonstration 07
Q.3 (a) Classify fluid flows. 03
(b) The velocity potential function is given by ϕ = 5(x2– y2). Calculate the velocity 04
components at the point (4, 5)
(c) Explain flow net & Reynolds experiment. 07
OR
Q.3 (a) Explain the term ‘Total Pressure and Centre of Pressure’. 03
(b) Derive Euler’s equation of motion along a stream line. 04
(c) A horizontal pipe carrying water of 20 cm diameter converges to 10cm 07
diameter. If the pressures at two sections are 450 KN/m2 and 150 KN/m2
respectively. Compute the rate of flow of water.
Q.4 (a) Discuss stability of submerged and floating bodies with neat sketches 03
(b) Explain the different hydraulic & mouth piece. 04
(c) Derive the expression for discharge over the (1) Rectangular notch and (2) 07
Triangular notch
OR
Q.4 (a) Explain the phenomenon of water hammer 03
(b) What is pitot-tube? How the velocity at any point is determined with the help 04
of pitot-tube.
(c) What is venturimeter. Derive an expression for the discharge Through a 07
venturimeter.
Q.5 (a) Define continuity equation & derive it. 03
(b) What are repeating variables? How are they selected for dimensional analysis? 04
(c) Derive an expression for the loss of head due to friction in pipes. 07
OR
Q.5 (a) Explain viscous flow. 03
(b) Explain the terms. specific energy, critical depth, critical velocity, alternate 04
depth
(c) State Buckingham’s π theorem. Why it is considered superior over Rayleigh 07
method for dimension analysis.
*************

1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE- SEMESTER–IV (NEW) EXAMINATION – WINTER 2020
Subject Code:3140611 Date:19/02/2021
Subject Name:Fluid Mechanics & Hydraulics
Time:02:30 PM TO 04:30 PM Total Marks:56
Instructions:
1. Attempt any FOUR questions out of EIGHT questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q.1 (a) Differentiate between liquid and gas. 03

(b) For a liquid having mass 2000 kg and volume 2.5 m3, calculate mass density 04
and weight density.
(c) Enlist fluid properties. Explain any three of them. 07

Q.2 (a) Differentiate between simple manometer and differential manometer. 03

(b) Explain Simple U- tube manometer in brief with sketch. 04
(c) State & prove Pascal’s law. 07

Q.3 (a) Define Buoyancy, Metacentric height and Archimedes principle. 03

(b) Find the volume of water displaced and position of centre of buoyancy for a 04
wooden block of width 2.5 m and depth 1.5 m, when it floats horizontally on
water. The density of wooden block is 700 kg/m3 and length is 5 m.
(c) Derive an expression for the total pressure and position of centre of pressure on 07
a plane surface immersed vertically in a liquid.

Q.4 (a) Define Laminar flow, Turbulent flow and Rotational flow. 03
(b) Differentiate between (i) Steady flow and Unsteady flow (ii) Uniform and Non 04
uniform flow.
(c) Explain Bernoulli’s equation. What are the practical applications of Bernoulli’s 07
equation?

Q.5 (a) Define (i) Co efficient of contraction, (ii) Co efficient of velocity, (iii) Co 03
efficient of discharge.
(b) Calculate the actual discharge and actual velocity of a jet at venacontracta 04
considering the Cd = 0.6 and Cv = 0.98 for an orifice of 40 mm diameter, if the
head over the orifice is 9 m.
(c) Classify different types of orifices according to its shapes, size, discharge 07
condition and shape of upstream edge. Explain all in brief.

Q.6 (a) Define (i) Hydraulic grade line, (ii) Total energy line, (iii) Equivalent pipe. 03
(b) Two reservoirs are connected by three pipes laid in parallel. The pipe diameters 04
are 10 cm, 20 cm and 30 cm respectively and they are of same lengths. If the
discharge through 10 cm pipe is 0.1 m3/s, calculate discharge through the other
two pipes. Assume f is same for both pipes.
(c) Derive Darcy–weisbach equation for friction loss in the pipe. 07

Q.7 (a) Define (i) Hydraulic mean depth, (ii) Wetted perimeter, (iii) Critical velocity. 03
(b) Find the width and depth of a rectangular channel to convey a discharge of 1.5 04
m3/s at a velocity of 0.5 m/s. Take Chezy’s constant equal to 60 and bed slope
equal to 0.00012.

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 (c) Derive the geometrical conditions for the most economical section of a 07
trapezoidal channel.

Q.8 (a) Define (i) Reynolds’s number, (ii) Froude’s number (iii) Euler’s number. 03
(b) What is Dimensional Homogeneity? What are the applications of Dimensional 04
Homogeneity?
(c) The resisting force R of a supersonic plane during flight can be considered as 07
dependent upon the length of aircraft l, velocity V, air viscosity µ, air density ƿ
and bulk modulus of air K. Express the functional relationship between these
variables using Buckingham’s π- theorem.

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Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER– IV EXAMINATION – SUMMER 2020
Subject Code: 3140611 Date:04/11/2020
Subject Name: Fluid Mechanics & Hydraulics
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q.1 (a) Define density, specific volume & surface tension. 03

(b) The velocity distribution for flow over a flat plate is given by 04
u = 0.75 y - y2 in which u is the velocity in metre per second at a
distance y metre above the plate. Determine the shear stress at
y = 0.20 m. Take dynamic viscosity of fluid as 8.0 poise.
u=3/4 the phenomenon of capillarity.Obtain an expression for
(c) Explain 07
capillary rise of a liquid.
Q.2 (a) Define atmospheric, absolute & vaccum pressure. 03
(b) Explain hydrostatic paradox. 04
(c) Write short note on manometers. 07
OR
(c) State & prove Pascal’s law. 07
Q.3 (a) Define total pressure, centre of pressure & buoyancy. 03
(b) A rectangular plane surface is immersed vertically in water such that 04
its upper edge is touching free surface of liquid. Show that the depth
of centre of pressure is 2/3 d for rectangular surface of width b and
depth d.
(c) Define metacentre & metacentric height. How will you determine 07
metacentric height of a floating body experimentally? Explain with
neat sketch.
OR
Q.3 (a) Define stream lines, streak lines & flow net. 03
(b) Differentiate between (i) Uniform & non uniform flow (ii) Sub 04
critical & super critical flow.
(c) State & prove Bernoulli’s equation & write assumption made for 07
such a derivation.
Q.4 (a) Define orifice, mouthpiiece & notches. 03
(b) Find the discharge of water flowing over a rectangular notch of 2.0 04
m length when the constant head over the notch is 500 mm.Take Cd
= 0.62
(c) Differrentiate between small & large orifice.Obtain an expression 07
for discharge through large orifice.
OR
Q.4 (a) Define major energy losses in pipe, hydraulic gradient line & total 03
energy line.
(b) Three pipes of lengths 800 m, 500 m and 400 m and of diameters 04
500 mm, 400 mm & 300 mm respectively are connected in series.
These pipes are to be replaced by a single pipe of length 1700 m.
Find the diameter of the single pipe.
(c) Define viscous flow. Derive expression for Hagen-Poiseuille’s 07
formula.

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Q.5 (a) Define turbulent flow in open channel, specific energy curve & 03
hydraulic jump.
(b) A sluice get discharges water into a horizontal rectangular channel 04
with a velocity of 10 m/sec & depth of flow of 1 m.Determine the
depth of flow after the jump & consequent losses in total head.
(c) Define gradually varied flow. Derive equation of gradually varied 07
flow.
OR
Q.5 (a) Define dimensional homogeneity, similitude & undistorted models 03
(b) Explain method of selecting repeating variables. 04
(c) The pressure difference Δp in a pipe of diameter D and length l due 07
to viscous flow depends on the velocity V, viscosity μ & density ρ.
Using Buckingham’s π theorem obtain an expression for Δp.