CE6451 - FLUID MECHANICS AND MACHINERY UNIT - II NOTES

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R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015
CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 27
UNIT - II - FLOW THROUGH CIRCULAR CONDUCTS
PART - A
2.1) How are fluid flows classified? [AU, May / June - 2012]
2.2) Distinguish between Laminar and Turbulent flow. [AU, Nov / Dec - 2006]
2.3) Write down Hagen Poiseuille’s equation for viscous flow through a pipe.
2.4) Write down Hagen Poiseuille’s equation for laminar flow.
[AU, April / May - 2005, Nov / Dec - 2012]
2.5) Write the Hagen – Poiseuille’s Equation and enumerate its importance.
[AU, April / May - 2011]
2.6) State Hagen – Poiseuille’s formula for flow through circular tubes.
[AU, May / June - 2012]
2.7) Write down the Darcy - Weisbach’s equation for friction loss through a pipe
[AU, Nov / Dec - 2009, April / May - 2011]
2.8) What is the relationship between Darcy Friction factor, Fanning Friction Factor
and Friction coefficient? [AU, May / June - 2012]
2.9) Mention the types of minor losses. [AU, April / May - 2010]
2.10) List the minor losses in flow through pipe.
[AU, April / May - 2005, May / June - 2007]
2.11) What are minor losses? Under what circumstances will they be negligible?
[AU, May / June - 2012]
2.12) Distinguish between the major loss and minor losses with reference to flow
through pipes. [AU, May / June - 2009]
2.13) List the causes of minor energy losses in flow through pipes.
[AU, Nov / Dec - 2009]
2.14) What are the losses experienced by a fluid when it is passing through a pipe?
2.15) What is a minor loss in pipe flows? Under what conditions does a minor loss
become a major loss?
2.16) What do you understand by minor energy losses in pipes?
[AU, Nov / Dec - 2008]
2.17) List out the various minor losses in a pipeline

2.18) What are ‘major’ and ‘minor losses’ of flow through pipes?
[AU, May / June 2007, Nov / Dec - 2007, 2012, April / May - 2010]
2.19) List the minor and major losses during the flow of liquid through a pipe.
2.20) Enlist the various minor losses involved in a pipe flow system.
[AU, Nov / Dec - 2008]
2.21) Write the expression for calculating the loss due to sudden expansion of the pipe.
2.22) What factors account in energy loss in laminar flow. [AU, May / June - 2012]
2.23) Differentiate between pipes in series and pipes in parallel.
[AU, Nov / Dec - 2006]
2.24) What is Darcy's equation? Identify various terms in the equation.
2.25) What is the relation between Dracy friction factor, Fanning friction factor and
friction coefficient? [AU, Nov / Dec - 2010]
2.26) When is the pipe termed to be hydraulically rough? [AU, Nov / Dec - 2009]
2.27) What is the physical significance of Reynold's number?
[AU, May / June, Nov / Dec - 2007]
2.28) Define Reynolds Number. [AU, Nov / Dec - 2012]
2.29) Write the Navier's Stoke equations for unsteady 3 - dimensional, viscous,
incompressible and irrotational flow. [AU, April / May - 2008]
2.30) Define Moody’s diagram
2.31) What are the uses of Moody’s diagram? [AU, Nov / Dec - 2008, 2012]
2.32) Mention the use of Moody diagram. [AU, April / May - 2015]
2.33) State the importance of Moody's chart. [AU, Nov / Dec - 2014]
2.34) Write down the formulae for loss of head due to
(i) sudden enlargement in pipe diameter
(ii) sudden contraction in pipe diameter and
(iii) Pipe fittings.
2.35) Define (i) relative roughness and (ii) absolute roughness of a pipe inner surface.
2.36) How does surface roughness affect the pressure drop in a pipe if the flow is
turbulent? [AU, Nov / Dec - 2013]

2.37) A piping system involves two pipes of different diameters (but of identical length,
material, and roughness) connected in parallel. How would you compare the flow
rates and pressure drops in these two pipes? [AU, Nov / Dec - 2013]
2.38) What do you mean by flow through parallel pipes? [AU, May / June - 2013]
2.39) What is equivalent pipe?
2.40) What is the use of Dupuit’s equations?
2.41) What is the condition for maximum power transmission through a pipe line?
2.42) Give the expression for power transmission through pipes?
[AU, Nov / Dec - 2008]
2.43) Write down the formula for friction factor of pipe having viscous flow.
2.44) Define boundary layer and boundary layer thickness.
[AU, Nov / Dec – 2007, 2012]
2.45) Define boundary layer thickness. [AU, May / June - 2006, Nov / Dec - 2009]
2.46) What is boundary layer? Give its sketch of a boundary layer region over a flat
plate. [AU, April / May - 2003]
2.47) What is boundary layer? Why is it significant? [AU, Nov / Dec - 2009]
2.48) Define boundary layer and give its significance. [AU, April / May - 2010]
2.49) What is boundary layer and write its types of thickness?
[AU, Nov / Dec – 2005, 2006]
2.50) What do you understand by the term boundary layer? [AU, Nov / Dec - 2008]
2.51) Define the following (i) laminar boundary layer (ii) turbulent boundary layer
(iii) laminar sub layer.
2.52) What is a laminar sub layer? [AU, Nov / Dec - 2010]
2.53) Define momentum thickness and energy thickness.
[AU, May / June – 2007, 2012]
2.54) Define the term boundary layer. [AU, May / June - 2009]
2.55) Define the terms boundary layer, boundary thickness. [AU, Nov / Dec - 2008]
2.56) What is boundary layer separation? [AU, Nov / Dec - 2012]
2.57) Give the classification of boundary layer flow based on the Reynolds number.
2.58) Define the following:
(i) Displacement thickness (ii) Momentum thickness

(iii)Energy thickness.
2.59) What do you mean by displacement thickness and momentum thickness?
[AU, Nov / Dec - 2008]
2.60) What do you understand by hydraulic diameter? [AU, Nov / Dec - 2011]
2.61) What is hydraulic gradient line? [AU, May / June - 2009]
2.62) Define hydraulic gradient line and energy gradient line.
2.63) Brief on HGL. [AU, April / May - 2011]
2.64) Differentiate between Hydraulic gradient line and total energy line.
[AU, Nov / Dec - 2003, April / May - 2005, 2010, May / June–2007, 2009]
2.65) What is T.E.L? [AU, Nov / Dec - 2009]
2.66) Distinguish between hydraulic and energy gradients. [AU, Nov / Dec - 2011]
2.67) Differentiate hydraulic gradient line and energy gradient line.
[AU, May / June - 2014]
2.68) Differentiate between hydraulic grade line and energy grade line.
[AU, Nov / Dec - 2014]
2.69) What are stream lines, streak lines and path lines in fluid flow?
[AU, Nov / Dec –2006, 2009]
2.70) What do you mean by Prandtl’s mixing length?
2.71) Draw the typical boundary layer profile over a flat plate.
2.72) Define flow net. [AU, Nov / Dec - 2008]
2.73) What is flow net and state its use? [AU, April / May - 2011]
2.74) Define lift. [AU, Nov / Dec - 2005]
2.75) Define the terms: drag and lift. [AU, Nov / Dec – 2007, May / June - 2009]
2.76) Define drag and lift co-efficient.
2.77) Give the expression for Drag coefficient and Lift coefficient.
2.78) What is meant by laminar flow instability? [AU, Nov / Dec - 2014]
2.79) Considering laminar flow through a circular pipe, draw the shear stress and
velocity distribution across the pipe section. [AU, Nov / Dec - 2010]
2.80) Considering laminar flow through a circular pipe, obtain an expression for the
velocity distribution. [AU, Nov / Dec - 2012]

2.81) A circular and a square pipe are of equal sectional area. For the same flow rate,
determine which section will lead to a higher value of Reynolds number.
[AU, Nov / Dec - 2011]
2.82) A 20cm diameter pipe 30km long transport oil from a tanker to the shore at
0.01m3
/s. Find the Reynolds number to classify the flow. Take the viscosity μ = 0.1
Nm/s2
and density ρ = 900 kg/m3
for oil. [AU, April / May - 2003]
2.83) Find the loss of head when a pipe of diameter 200 mm is suddenly enlarged to a
diameter 0f 400 mm. Rate of flow of water through the pipe is 250 litres/s.
PART - B
2.84) What are the various types of fluid flows? Discuss [AU, Nov / Dec - 2010]
2.85) Define minor losses. How they are different from major losses?
[AU, May / June - 2009]
2.86) Discuss on various minor losses in pipe flow. [AU, Nov / Dec - 2013]
2.87) Discuss on minor losses in pipe flow. [AU, Nov / Dec - 2014]
2.88) Which has a greater minor loss co-efficient during pipe flow: gradual expansion
or gradual contraction? Why? [AU, April / May - 2008]
2.89) Derive Chezy’s formula for loss of head due to friction in pipes.
[AU, Nov / Dec - 2012]
2.90) What is the hydraulic gradient line? How does it differ from the total energy line?
Under what conditions do both lines coincide with the free surface of a liquid?
2.91) Write notes on the following:
 Concept of boundary layer.
 Hydraulic gradient
 Moody diagram.
2.92) Briefly explain Moody’s diagram regarding pipe friction
[AU, May / June - 2014]
2.93) Describe the Moody's chart. [AU, Nov / Dec - 2014]
2.94) For a flow of viscous fluid flowing through a circular pipe under laminar flow
conditions, show that the velocity distribution is a parabola. And also show that the
average velocity is half of the maximum velocity. [AU, May / June - 2013]

2.95) For flow of viscous fluids through an annulus derive the following expressions:
 Discharge through the annulus.
 Shear stress distribution. [AU, May / June – 2007, 2012]
2.96) For a laminar flow through a pipe line, show that the average velocity is half of
the maximum velocity.
2.97) Prove that the Hagen-Poiseuille’s equation for the pressure difference between
two sections 1 and 2 in a pipe is given by with usual notations.
2.98) Derive Hagen – Poiseuille’s equation and state its assumptions made.
[AU, Nov / Dec - 2005]
2.99) Derive Hagen – Poiseuille’s equation [AU, Nov / Dec - 2008]
2.100) Obtain the expression for Hagen – Poiseuille’s flow. Deduce the condition of
maximum velocity. [AU, Nov / Dec - 2007]
2.101) Give a proof a Hagen – Poiseuille’s equation for a fully – developed laminar
flow in a pipe and hence show that Darcy friction coefficient is equal to 16/Re, where
Re is Reynold’s number. [AU, May / June - 2012]
2.102) Derive an expression for head loss through pipes due to friction.
2.103) Explain Reynold’s experiment to demonstrate the difference between laminar
flow and turbulent flow through a pipe line.
2.104) Derive Darcy - Weisbach formula for calculating loss of head due to friction in
a pipe. [AU, Nov / Dec - 2011]
2.105) Derive Darcy - Weisbach formula for head loss due to friction in flow through
pipes. [AU, Nov / Dec - 2005]
2.106) Obtain expression for Darcy – Weisbach friction factor f for flow in pipe.
[AU, May / June - 2012]
2.107) Explain the losses of energy in flow through pipes. [AU, Nov / Dec - 2009]
2.108) Derive an expression for Darcy – Weisbach formula to determine the head loss
due to friction. Give an expression for relation between friction factor ‘f’ and
Reynolds’s number ‘Re’ for laminar and turbulent flow. [AU, April / May - 2003]
2.109) Prove that the head lost due to friction is equal to one third of the total head at
inlet for maximum power transmission through pipes. [AU, Nov / Dec - 2008]

2.110) Show that for laminar flow, the frictional loss of head is given by
hf= 8 fLQ2
/gπ2
D5
[AU, Nov / Dec - 2009]
2.111) Derive Euler’s equation of motion for flow along a stream line. What are the
assumptions involved. [AU, Nov / Dec - 2009]
2.112) A uniform circular tube of bore radius R1 has a fixed co axial cylindrical solid
core of radius R2. An incompressible viscous fluid flows through the annular passage
under a pressure gradient (-∂p/∂x). Determine the radius at which shear stress in the
stream is zero, given that the flow is laminar and under steady state condition.
[AU, May / June - 2009]
2.113) If the diameter of the pipe is doubled, what effect does this have on the flow rate
for a given head loss for laminar flow and turbulent flow. [AU, April / May - 2011]
2.114) Derive an expression for the variation of jet radius r with distance y downwards
for a jet directed downwards. The initial radius is R and the head of fluid is H.
[AU, Nov / Dec - 2011]
2.115) Distinguish between pipes connected in series and parallel.
[AU, Nov / Dec - 2005]
2.116) Discuss on hydraulic and energy gradient. [AU, Nov / Dec - 2014]
2.117) Determine the equivalent pipe corresponding to 3 pipes in series with lengths
and diameters l1, l2, l3, d1, d2, d3 respectively. [AU, Nov / Dec - 2009]
2.118) For sudden expansion in a pipe flow, work out the optimum ratio between the
diameter of before expansion and the diameter of the pipe after expansion so that the
pressure rise is maximum. [AU, May / June - 2012]
2.119) Obtain the condition for maximum power transmission through a pipe line.
2.120) Explain stream lines, path lines and flow net. [AU, Nov / Dec - 2012]
2.121) What are the uses and limitations of flow net? [AU, May / June - 2009]
2.122) Briefly explain about boundary layer separation. [AU, Nov / Dec - 2008]
2.123) Explain on boundary layer separation and its control.
2.124) Considering a flow over a flat plate, explain briefly the development of
hydrodynamic boundary layer. [AU, Nov / Dec - 2010]
2.125) Discuss in detail about boundary layer thickness and separation of boundary
layer. [AU, April / May - 2011]

2.126) What is boundary layer and write its types of thickness?
2.127) Explain in detail
 Drag and lift coefficients
 Boundary layer thickness
 Boundary layer separation
 Navier’s – strokes equation. [AU, May / June - 2012]
2.128) In a water reservoir flow is through a circular hole of diameter D at the side wall
at a vertical distance H from the free surface. The flow rate through an actual hole
with a sharp-edged entrance (kL
= 0.5) will be considerably less than the flow rate
calculated assuming frictionless flow. Obtain a relation for the equivalent diameter
of the sharp-edged hole for use in frictionless flow relations.
[AU, Nov / Dec - 2011]
2.129) Define : Boundary layer thickness(δ); Displacement thickness(δ*
); Momentum
thickness(θ) and energy thickness(δ**
). [AU, April / May - 2010]
2.130) Briefly explain the following terms
 Displacement thickness
 Momentum thickness
 Energy thickness [AU, May / June - 2014]
2.131) Find the displacement thickness momentum thickness and energy thickness for
the velocity distribution in the boundary layer given by (u/v) = (y/δ), where ‘u’is the
velocity at a distance ‘y’ from the plate and u=U at y=δ, where δ = boundary layer
thickness. Also calculate (δ*
/θ). [AU, Nov / Dec - 2007, April / May - 2010]
2.132) Explain the concept of boundary layer in pipes for both laminar and turbulent
flows with neat sketches. [AU, Nov / Dec - 2013]
2.133) What is hydraulic gradient line? How does it differ from the total energy line?
Under what conditions do both lines coincide with surface of the liquid?
2.134) Derive an expression for the velocity distribution for viscous flow through a
circular pipe. [AU, May / June - 2007]

2.135) Write a brief note on velocity potential function and stream function.
[AU, May / June - 2009]
2.136) Derive an expression for the velocity distribution for viscous flow through a
circular pipe. Also sketch the distribution of velocity cross a section of the pipe.
[AU, Nov / Dec - 2011]
PROBLEMS
2.137) A 20 cm diameter pipe 30 km long transports oil from a tanker to the shore at
0.01m3
/s. Find the Reynold’s number to classify the flow. Take viscosity and
density for oil.
2.138) A pipe line 20cm in diameter, 70m long, conveys oil of specific gravity 0.95 and
viscosity 0.23 N.s/m2
. If the velocity of oil is 1.38m/s, find the difference in pressure
between the two ends of the pipe. [AU, May / June - 2012]
2.139) Oil of absolute viscosity 1.5 poise and density 848.3kg/m3
flows through a
300mm pipe. If the head loss in 3000 m, the length of pipe is 200m, assuming
laminar flow, find
(i) the average velocity,
(ii) Reynolds’s number and
(iii) Friction factor. [AU, May / June - 2012]
2.140) An oil of specific gravity 0.7 is flowing through the pipe diameter 30cm at the
rate of 500litres/sec. Find the head lost due to friction and power required to maintain
the flow for a length of 1000m. Take γ = 0.29 stokes.
[AU, Nov / Dec – 2008, May / June - 2009]
2.141) A pipe line 10km, long delivers a power of 50kW at its outlet ends. The pressure
at inlet is 5000kN/m2
and pressure drop per km of pipeline is 50kN/m2
. Find the size
of the pipe and efficiency of transmission. Take 4f = 0.02.
[AU, Nov / Dec - 2005]
2.142) A lubricating oil flows in a 10 cm diameter pipe at 1 m/s. Determine whether the
flow is laminar or turbulent.
2.143) An oil of specific gravity 0.80 and kinematic viscosity 15 x 106
m2
/s flows in a
smooth pipe of 12 cm diameter at a rate of 150 lit/min. Determine whether the flow
is laminar or turbulent. Also, calculate the velocity at the centre line and the velocity

at a radius of 4 cm. What is head loss for a length of 10 m? What will be the entry
length? Also determine the wall shear. [AU, Nov / Dec - 2014]
2.144) For the lubricating oil 2 μ = 0.1Ns /m and ρ = 930 kg/m3
. Calculate also transition
and turbulent velocities. [AU, April / May - 2011]
2.145) Oil of ,mass density 800kg/m3
and dynamic viscosity 0.02 poise flows through
50mm diameter pipe of length 500m at the rate of 0.19 liters/ sec. Determine
 Reynolds number of flow
 Center line of velocity
 Pressure gradient
 Loss of pressure in 500m length
 Wall shear stress
 Power required to maintain the flow. [AU, May / June - 2012]
2.146) In fully developed laminar flow in a circular pipe, the velocity at R/2 (midway
between the wall surface and the center line) is measured to be 6m/s. Determine the
velocity at the center of the pipe. [AU, April / May - 2008]
2.147) A pipe 85m long conveys a discharge of 25litres per second. If the loss of head
is 10.5m. Find the diameter of the pipe take friction factor as 0.0075.
[AU, Nov / Dec - 2009]
2.148) A smooth pipe carries 0.30m3
/s of water discharge with a head loss of 3m per
100m length of pipe. If the water temperature is 20°C, determine diameter of the
pipe. [AU, May / June - 2012]
2.149) Water is flowing through a pipe of 250 mm diameter and 60 m long at a rate of
0.3 m3
/sec. Find the head loss due to friction. Assume kinematic viscosity of water
0.012 stokes.
2.150) Consider turbulent flow (f = 0.184 Re-0.2
) of a fluid through a square channel
with smooth surfaces. Now the mean velocity of the fluid is doubled. Determine the
change in the head loss of the fluid. Assume the flow regime remains unchanged.
What will be the head loss for fully turbulent flow in a rough pipe?
[AU, Nov / Dec - 2013]
2.151) A pipe of 12cm diameter is carrying an oil (μ = 2.2 Pa.s and ρ = 1250 kg/m3
)
with a velocity of 4.5 m/s. Determine the shear stress at the wall surface of the pipe,

head loss if the length of the pipe is 25 m and the power lost.
[AU, Nov / Dec - 2011]
2.152) Find the head loss due to friction in a pipe of diameter 30cm and length 50cm,
through which water is flowing at a velocity of 3m/s using Darcy’s formula.
[AU, Nov / Dec - 2008]
2.153) For a turbulent flow in a pipe of diameter 300 mm, find the discharge when the
center-line velocity is 2.0 m/s and the velocity at a point 100 mm from the center as
measured by pitot-tube is 1.6 m/s. [AU, April / May - 2010]
2.154) A laminar flow is taking place in a pipe of diameter 20cm. The maximum
velocity is 1.5m/s. Find the mean velocity and radius at which this occurs. Also
calculate the velocity at 4cm from the wall pipe. [AU, May / June - 2009]
2.155) Water is flowing through a rough pipe of diameter 60 cm at the rate of
600litres/second. The wall roughness is 3 mm. Find the power loss for 1 km length
of pipe.
2.156) Water flows in a 150 mm diameter pipe and at a sudden enlargement, the loss of
head is found to be one-half of the velocity head in 150 mm diameter pipe. Determine
the diameter of the enlarged portion.
2.157) A 150mm diameter pipe reduces in diameter abruptly to 100mm diameter. If the
pipe carries water at 30 liters per second, calculate the pressure loss across the
contraction. The coefficient of contraction as 0.6. [AU, Nov / Dec - 2012]
2.158) A pipe line carrying oil of specific gravity 0.85, changes in diameter from
350mm at position 1 to 550mm diameter to a position 2, which is at 6m at a higher
level. If the pressure at position 1 and 2 are taken as 20N/cm2
and 15N/cm2
respectively and discharge through the pipe is 0.2m3
/s. Determine the loss of head.
[AU, May / June - 2007]
2.159) A pipe line carrying oil of specific gravity 0.87, changes in diameter from
200mm at position A to 500mm diameter to a position B, which is at 4m at a higher
level. If the pressure at position A and B are taken as 9.81N/cm2
and 5.886N/cm2
respectively and discharge through the pipe is 200 litres/s. Determine the loss of head
and direction of flow. [AU, Nov / Dec - 2008]
2.160) A 30cm diameter pipe of length 30cm is connected in series to a 20 cm diameter
pipe of length 20cm to convey discharge. Determine the equivalent length of pipe

diameter 25cm, assuming that the friction factor remains the same and the minor
losses are negligible. [AU, April / May - 2003]
2.161) A pipe of 0.6m diameter is 1.5 km long. In order of augment the discharge,
another line of the same diameter is introduced parallel to the first in the second half
of the length. Neglecting minor losses. Find the increase in discharge, if friction
factor f= 0.04. The head at inlet is 40m. [AU, Nov / Dec – 2004, 2005, 2012]
2.162) A pipe of 10 cm in diameter and 1000 m long is used to pump oil of viscosity
8.5 poise and specific gravity 0.92 at the rate of1200 lit./min. The first 30 m of the
pipe is laid along the ground sloping upwards at 10° to the horizontal and remaining
pipe is laid on the ground sloping upwards 15° to the horizontal. State whether the
flow is laminar or turbulent? Determine the pressure required to be developed by the
pump and the power required for the driving motor if the pump efficiency is 60%.
Assume suitable data for friction factor, if required. [AU, Nov / Dec - 2010]
2.163) Oil with a density of 900 kg/m3
and kinematic viscosity of 6.2 × 10-4
m2
/s is being
discharged by a 6 mm diameter, 40 m long horizontal pipe from a storage tank open
to the atmosphere. The height of the liquid level above the center of the pipe is 3 m.
Neglecting the minor losses, determine the flow rate of oil through the pipe.
[AU, Nov / Dec - 2011]
2.164) Oil at 27°C (ρ = 900 kg/m3
and µ = 40 centi poise) is flowing steadily in a
1.25cm diameter 40m long During the flow, the pressure at the pipe inlet and exit is
measured to be 8.25 bar and 0.95 bar, respectively. Determine the flow rate of oil
through the pipe assuming the pipe is [AU, Nov / Dec - 2014]
 Horizontal,
 Inclined 20º upward, and
 Inclined 20º downward.
2.165) 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, if f = 0.008. [AU, Nov / Dec - 2005]
2.166) A 200mm diameter (f = 0.032) 175m long discharges a 65mm diameter water jet
into the atmosphere at a point which is 75m below the water surface at intake. The
entrance to the pipe is reentrant with ke = 0.92 and the nozzle loss coefficient is 0.06.
Find the flow rate and the pressure head at the base of the nozzle.

2.167) A pipe line 2000m long is used for power transmission 110kW is to be
transmitted through a pipe in which water is having a pressure of 5000kN/m2
at inlet
is flowing. If the pressure drop over a length of a pipe is 1000kN/m2
and coefficient
of friction is 0.0065, find the diameter of the pipe and efficiency of transmission.
[AU, May / June - 2012]
2.168) A horizontal pipe of 400 mm diameter is suddenly contracted to a diameter of
200 mm. The pressure intensities in the large and small pipe are given as 15 N/cm2
and 10 N/cm2
respectively. Find the loss of head due to contraction, if Cc = 0.62,
determine also the rate of flow of water.
2.169) A horizontal pipe line 40 m long is connected to a water tank at one end and
discharges freely into the atmosphere at the other end. For the first 25 m of its length
from the tank, the pipe is 150 mm diameter and its diameter is suddenly enlarged to
300 mm. The height of water level in the tank is 8 m above the centre of the pipe.
Considering all losses of head which occur, determine the rate of flow. Take f = 0.01
for both sections of the pipe. [AU, May / June - 2013]
2.170) A 15cm diameter vertical pipe is connected to 10cm diameter vertical pipe with
a reducing socket. The pipe carries a flow of 100 l/s. At a point 1 in 15cm pipe gauge
pressure is 250kPa. At point 2 in the 10cm pipe located 1m below point 1 the gauge
pressure is 175kPa.
 Find weather the flow is upwards /downwards
 Head loss between the two points [AU, Nov / Dec - 2008]
2.171) The rate of flow of water through a horizontal pipe is 0.25 m3
/sec. The diameter
of the pipe, which is 20 cm, is suddenly enlarged to 40 cm. The pressure intensity
in the smaller pipe is 11.7 N/cm2
. Determine the loss of head due to sudden
enlargement and pressure intensity in the larger pipe, power loss due to enlargement.
[AU, May / June - 2009]
2.172) In a city water supply systems, water is flowing through a pipe line 30cm in
diameter. The pipe diameter is suddenly reduced to 20cm. estimate the discharge
through the pipe if the difference across the sudden contraction is 5kPa.
2.173) A 45° reducing bend is connected to a pipe line. The inlet and outlet diameters
of the bend being 600mm and 300mm respectively. Find the force exerted by water

on the bend, if the intensity of pressure at inlet to bend is 8.829N/cm2
and the rate of
flow of water is 600 liters/s. [AU, Nov / Dec - 2007]
2.174) Horizontal pipe carrying water is gradually tapering. At one section the diameter
is 150mm and the flow velocity is 1.5m/s. If the drop pressure is 1.104bar is reduced
section, determine the diameter of that section. If the drop is 5kN/m2
, what will be
the diameter – Neglect the losses? [AU, Nov / Dec - 2009]
2.175) The rate of flow of water through a horizontal pipe is 0.3m3
/sec. The diameter
of the pipe, which is 25cm, is suddenly enlarged to 50 cm. The pressure intensity in
the smaller pipe is 14N/cm2
. Determine the loss of head due to sudden enlargement,
pressure intensity in the larger pipe power lost due to enlargement.
[AU, Nov / Dec - 2003]
2.176) Water at 15°C ( ρ =999.1 kg/m3
andμ = 1.138 x 10-3
kg/m. s) is flowing steadily
in a30-m-long and 4 cm diameter horizontal pipe made of stainless steel at a rate of
8 L/s. Determine (i) the pressure drop, (ii) the head loss, and (iii) the pumping power
requirement to overcome this pressure drop. Assume friction factor for the pipe as
0.015. [AU, April / May - 2008]
2.177) The discharge of water through a horizontal pipe is 0.25m3/s. The diameter of
above pipe which is 200mm suddenly enlarges to 400mm at a point. If the pressure
of water in the smaller diameter of pipe is 120kN/m2
, determine loss of head due to
sudden enlargement; pressure of water in the larger pipe and the power lost due to
sudden enlargement. [AU, May / June - 2009]
2.178) A pipe of varying sections has a sectional area of 3000, 6000 and 1250 mm2
at
point A, B and C situated 16 m, 10 m and 2 m above the datum. If the beginning of
the pipe is connected to a tank which is filled with water to a height of 26 m above
the datum, find the discharge, velocity and pressure head at A, B and C. Neglect all
losses. Take atmospheric pressure as 10 m of water.
2.179) An existing 300mm diameter pipeline of 3200m length connects two reservoirs
having 13m difference in their water levels. Calculate the discharge Q1. If a parallel
pipe 300mm in diameter is attached to the last 1600m length of the above existing
pipe line, find the new discharge Q2. What is the change in discharge? Express it as
a % of Q1. Assume friction factor f = 0.14 in Darcy – Weisbach formula.
[AU, May / June - 2009]

2.180) Two reservoirs with a difference in water surface elevation of 15 m are
connected by a pipe line ABCD that consists of three pipes AB, BC and CD joined
in series. Pipe AB is 10 cm in diameter, 20 m long and has f = 0.02. Pipe BC is of
16 cm diameter, 25 m long and has f = 0.018. Pipe CD is of 12 cm diameter, 15 m
long and has f = 0.02. The junctions with the reservoirs and between the pipes are
abrupt. (a) Calculate the discharge (b) What difference in reservoir elevation is
necessary to have a discharge of 20 litres/sec? Include all minor losses.
2.181) Two tanks of fluid ( ρ = 998 kg/m3
and µ = 0.001 kg/ms.) at 20°C are connected
by a capillary tube 4 mm in diameter and 3.5 m long. The surface of tank 1 is 30 cm
higher than the surface of tank 2. Estimate the flow rate in m3
/h. Is the flow laminar?
For what tube diameter will Reynolds number be 500?
[AU, Nov / Dec - 2013]
2.182) Three pipes of 400mm, 350mm and 300mm diameter connected in series
between two reservoirs. With difference in level of 12m. Friction factor is 0.024,
0.021 and 0.019 respectively. The lengths are 200m, 300m and 250m. Determine
flow rate neglecting the minor losses. [AU, Nov / Dec - 2009]
2.183) Three pipes of diameters 300 mm, 200 mm and 400 mm and lengths450 m, 255
m and 315 m respectively are connected in series. The difference in water surface
levels in two tanks is 18 m. Determine the rate of flow of water if coefficients of
friction are 0.0075, 0.0078and 0.0072 respectively considering: the minor losses and
by neglecting minor losses. [AU, Nov / Dec - 2011]
2.184) Three pipes of diameters 300 mm, 200 mm and 400 mm and lengths 300 m, 170
m and 210 m respectively are connected in series. The difference in water surface
levels in two tanks is 12 m. Determine the rate of flow of water if coefficients of
friction are 0.005, 0.0052 and 0.0048 respectively considering: the minor losses and
by neglecting minor losses [AU, May / June– 2012]
2.185) Three pipes connected in series to make a compound pipe. The diameters and
lengths of pipes are respectively, 0.4m, 0.2m, 0.3m and 400m, 200m, 300m. The
ends of the compound pipe are connected to 2 reservoirs whose difference in water
levels is 16m. The friction factor for all the pipes is same and equal to 0.02. The
coefficient of contraction is 0.6. Find the discharge through the compound pipe if,

minor losses are negligible. Also find the discharge if minor losses are included.
[AU, Nov / Dec - 2010]
2.186) A compound piping system consists of 1800 m of 0.5 m, 1200 m of 0.4 m and
600 m of 0.3 m new cast-iron pipes connected in series. Convert the system to (i) an
equivalent length of0.4 m diameter pipe and (ii) an equivalent size of pipe of 3600
m length. [AU, April / May - 2003]
2.187) A 100m long pipe line of 300mm in diameter contains two 90º elbows and two
gate valves (wide open). Calculate the equivalent pipe length and total loss of head
when the flow rate is 0.5m3
/s, f = 0.005, and the pipe has a sharp entry and exit.
2.188) A pipe line of 600 mm diameter is 1.5 km long. To increase the discharge,
another line of the same diameter is introduced parallel to the first in the second half
of the length. If f = 0.01 and head at inlet is 30 m, calculate the increase in discharge.
2.189) A pipe line of 0.6m diameter is 1.5Km long. To increase the discharge, another
line of same diameter is introduced in parallel to the first in second half of the length.
Neglecting the minor losses, find the increase in discharge if 4f = 0.04. The head at
inlet is 30cm. [AU, April / May - 2011]
2.190) A pipe line of 0.6m diameter is 1.5Km long. To increase the discharge, another
line of same diameter is introduced in parallel to the first in second half of the length.
Neglecting the minor losses, find the increase in discharge if Darcy’s friction factor
0.04. The head at inlet is 300mm. [AU, April / May - 2015]
2.191) Two pipes of 15cm and 30cm diameters are laid in parallel to pass a total
discharge of 100 litres per second. Each pipe is 250m long. Determine discharge
through each pipe. Now these pipes are connected in series to connect two tanks
500m apart, to carry same total discharge. Determine water level difference between
the tanks. Neglect the minor losses in both cases, f=0.02 fn both pipes.
[AU, May / June - 2007]
2.192) Two pipes of diameter 40 cm and 20 cm are each 300 m long. When the pipes
are connected in series and discharge through the pipe line is0.10 m3
/sec, find the
loss of head incurred. What would be the loss of head in the system to pass the same
total discharge when the pipes are connected in parallel? Take f = 0.0075 for each
pipe. [AU, May / June – 2007, 2012, Nov / Dec - 2010]

2.193) A main pipe divides into two parallel pipes, which again forms one pipe. The
length and diameter for the first parallel pipe are 2000m and 1m respectively, while
the length and diameter of second parallel pipe are 200m and 0.8m respectively. Find
the rate of flow in each parallel pipe, if total flow in the main is 3m3
/s. The coefficient
of friction for each parallel pipe is same and equal to 0.005.
[AU, May / June - 2007]
2.194) The main pipe is divided into two parallel pipes which again forms one pipe, the
first parallel pipe has length of 1000 m and diameter of 0.8 m. The second parallel
pipe has length of 1000 m and diameter of 0.6 m. The coefficient friction for each
parallel pipe is 0.005. If the total rate of flow in the main pipe is 2 m3
/sec, find the
rate of flow in each parallel pipe. [AU, May / June - 2014]
2.195) For a town water supply, a main pipe line of diameter 0.4 m is required. As pipes
more than 0.35m diameter are not readily available, two parallel pipes of same
diameter are used for water supply. If the total discharge in the parallel pipes is same
as in the single main pipe, find the diameter of parallel pipe. Assume co-efficient of
discharge to be the same for all the pipes. [AU, April / May - 2010]
2.196) Two pipes of identical length and material are connected in parallel. The
diameter of pipe A is twice the diameter of pipe B. Assuming the friction factor to
be the same in both cases and disregarding minor losses, determine the ratio of the
flow rates in the two pipes. [AU, April / May - 2008]
2.197) A pipe line 30cm in diameter and 3.2m long is used to pump up 50Kg per second
of oil whose density is 950 Kg/m3
and whose kinematic viscosity is 2.1 strokes, the
center of the pipe line at the upper end is 40m above than the lower end. The
discharge at the upper end is atmospheric. Find the pressure at the lower end and
draw the hydraulic gradient and total energy line. [AU, April / May - 2011]
2.198) Two water reservoirs A and B are connected to each other through a 50 m long,
2.5 cm diameter cast iron pipe with a sharp-edged entrance. The pipe also involves
a swing check valve and a fully open gate valve. The water level in both reservoirs
is the same, but reservoir A is pressurized by compressed air while reservoir B is
open to the atmosphere. If the initial flow rate through the pipe is 1.5 l/s, determine
the absolute air pressure on top of reservoir A. Take the water temperature to be
25°C. [AU, Nov / Dec - 2011]

2.199) When water is being pumped is a pumping plant through a 600mm diameter
main, the friction head was observed as 27m. In order to reduce the power
consumption, it is proposed to lay another main of appropriate diameter along the
side of existing one, so that the two pipes will work in parallel for the entire length
and reduce the friction head to 9.6m only. Find the diameter of the new main if with
the exception of diameter; it is similar to the existing one in all aspects.
[AU, Nov / Dec - 2007]
2.200) Kerosene (SG = 0.810) at a temperature of 22ºC flows in a 75-mm diameter
smooth brass pipeline at a rate of 0.90 lit/s. Find the friction head loss per meter, For
the same head loss, what would be the flow rate if the temperature of the kerosene
were raised to 40°C? [AU, Nov / Dec - 2014]
2.201) Determine the
 Pressure gradient
 The shear stress at the two horizontal parallel plates and
 Discharge per meter width for the laminar flow of oil with maximum
velocity 2m/s between two horizontal parallel fixed plates which are
10cm apart. Given μ = 2.4525 Ns/m2
2.202) In fully developed laminar flow in a circular pipe, the velocity at R/2 (midway
between the wall surface and the centerline) is measured to be 6 m/s. Determine the
velocity at the center of the pipe. [AU, April / May - 2008]
2.203) A smooth two –dimensional flat plate is exposed to a wind velocity of 100 km/h.
If laminar boundary layer exists up to a value of Rexequal to 3 x 105
, find the
maximum distance up to which laminar boundary layer exists and find its maximum
thickness. Assume kinematic viscosity of air as 1.49 x 10-5
m2
/sec.
2.204) Air is flowing over a flat plate with a velocity of 5 m/s. The length of the plate
is 2.5 m and width 1 m. The kinematic viscosity of air is given as 0.15 x 10-4
m2
/s.
Find the
(i) boundary layer thickness at the end of plate
(ii) shear stress at 20 cm from the leading edge
(iii) shear stress at 175 cm from the leading edge
(iv) Drag force on one side of the plate.

(v) Take the velocity profile
𝑢
𝑈
=
3
2
(
𝑦
𝛿
) −
1
2
(
𝑦
𝛿
)
3
over a plate as and the
density of air1.24 kg/m3
.
2.205) A plate of 600mm length and 400mm wide is immersed in a fluid of specific
gravity 0.9 and kinematic viscosity of = 10-4
m2
/s. The fluid is moving with velocity
of 6m/s. Determine
 Boundary layer thickness
 Shear stress at the end of the plate
 Drag force on one side of the plate. [AU, Nov / Dec - 2012]
2.206) Water at 20° C enters a pipe with a uniform velocity (U) of 3m/s. What is the
distance at which the transition (x) occurs from a laminar to a turbulent boundary
layer? If the thickness of this initial laminar boundary layer is given by 4.91√(vx/U)
what is its thickness at the point of transition?(v – kinematic viscosity).
2.207) A flat plate 1.5 m x 1.5 m moves at 50 km/h in stationary air of density 1.15
kg/m3
. If the co-efficient of drag and lift are 0.15 and 0.75 respectively, determine
the
(i) Lift force
(ii) Drag force
(iii) The resultant force and
(iv) The power required to set the plate in motion. [AU, Nov / Dec - 2007]
2.208) A jet plane which weighs 29430 N and has the wing area of 20m2
flies at the
velocity of 250km/hr. When the engine delivers 7357.5kW. 65% of power is used to
overcome the drag resistance of the wing. Calculate the coefficient of lift and
coefficient of drag for the wing. Take density of air = 1.21 kg/m3
[AU, May / June - 2009]
2.209) For the velocity profile in laminar boundary layer as u/U = 3/2 (y/δ)-1/2(y/δ)3
.
Find the thickness of the boundary layer and shear stress, 1.8m from the leading edge
of a plate. The plate is 2.5 m long and 1.5 m wide is placed in water, which is moving
with a velocity of 15 cm/sec. Find the drag on one side of the plate if the viscosity
of water is 0.01 poise. [AU, Nov / Dec - 2003]

2.210) Consider flow of oil through a pipe of 0.3m diameter. The velocity distribution
is parabolic with maximum velocity of 3 m/s at the pipe centre. Estimate the shear
stress at the pipe wall and within the fluid 50mm from the pipe wall. The viscosity
of the oil is 1.7Pa.s. [AU, Nov / Dec - 2012]
2.211) The velocity distribution in the boundary layer is given by u/U = y/δ, where u is
the velocity at the distance y from the plate u = U at y = δ, δ being boundary layer
thickness. Find the displacement thickness, momentum thickness and energy
thickness. [AU, April / May - 2010]
2.212) If the velocity distribution in a laminar boundary layer over a flat plate is given
by 𝑢/𝑈∞ = sin(𝜋/2 𝑦 /𝛿), calculate the value of 𝛿, 𝛿∗
, 𝜃 and shear stress.
2.213) Water at 20°C flow through a 160mm diameter pipe with roughness of 0.016
mm. If the mean velocity is 6 m/s, what is the nominal thickness of the viscous sub-
layer? What will be the viscous sub -layer if the velocity is increased to 7.2 m/s?
[AU, Nov / Dec - 2014]
2.214) The flow rate in a 260mm diameter pipe is 220 litres/sec. The flow is turbulent,
and the centerline velocity is 4.85m/s. Plot the velocity profile, and determine the
head loss per meter of pipe. [AU, April / May - 2011]
2.215) An oil of viscosity 0.9Pa.s and density 900kg/m3
flows through a pipe of 100mm
diameter. The rate of pressure drop for every meter length of pipe is 25kPa. Find the
oil flow arte, drag force per meter length, pumping power required to maintain the
flow over a distance of 1km, velocity and shear stress at 15, from the pipe wall.
[AU, Nov / Dec - 2010]
2.216) Consider the flow of a fluid with viscosity m through a circular pipe. The
velocity profile in the pipe is given as where is the maximum flow velocity, which
occurs at the centerline; r is the radial distance from the centerline; is the flow
velocity at any position r; and R is the Reynold's number. Develop a relation for the
drag force exerted on the pipe wall by the fluid in the flow direction per unit length
of the pipe. [AU, April / May - 2008]

2.217) Velocity components in flow are given by U = 4x, V = -4y. Determine the stream
and potential functions. Plot these functions for φ 60, 120, 180, and 240 and Ф 0, 60,
120, 180, +60, +120, +180. Check for continuity. [AU, Nov / Dec - 2009]
2.218) A fluid of specific gravity 0.9 flows along a surface with a velocity profile given
by v = 4y - 8y3m/s, where y is in m. What is the velocity gradient at the boundary?
If the kinematic viscosity is 0.36S, what is the shear stress at the boundary?
[A.U. Nov / Dec - 2008]
2.219) In a two dimensional incompressible flow the fluid velocities are given by u = x
– ay and v = - y – 4x. Show that the velocity potential exists and determine its form.
Find also the stream function. [AU, May / June - 2009]
2.220) A smooth flat plate with a sharp leading edge is placed along a free stream of
water flowing at 3m/s. Calculate the distance from the leading edge and the boundary
thickness where the transition from laminar to turbulent- flow may commence.
Assume the density of water as 1000 kg/m3
and viscosity as 1centipoise.
2.221) A smooth two dimensional flat plate is exposed to a wind velocity of 100 km/hr.
If laminar boundary layer exists up to a value of RN
= 3 x105
, find the maximum
distance up to which laminar boundary layer persists and find its maximum
thickness. Assume kinematic viscosity of air as 1.49x10-5
m2
/s.
[AU, Nov / Dec - 2008]
2.222) A power transmission pipe 10 cm diameter and 500 m long is fitted with a nozzle
at the exit, the inlet is from a river with water level 60 m above the discharge nozzle.
Assume f = 0.02, calculate the maximum power which can be transmitted and the
diameter of nozzle required. [AU, Nov / Dec - 2008]
umax
u(r) = umax(1-r / R )n n
R
r
o

CE6451 - FLUID MECHANICS AND MACHINERY UNIT - II NOTES

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CE6451 - FLUID MECHANICS AND MACHINERY UNIT - II NOTES