QUESTION BANK FOR FLUID MECHANICS

II
Sixth Semester B.E. (Civil Engg.)
Q1.
Derive an equation showing that in laminar flow through circular pipes, velocity
of flow varies parabolically.
Q2.
An oil having viscosity of 1.42 poise and specific gravity 0.
9 flows through a pipe
25 mm diameter and 300 m long at Reynolds number of 1800. Find the flow
through the pipe and the power required to maintain the flow.
Q3.
Derive an expression for the velocity distribution for viscous flow through a
circular pipe. A
lso sketch the velocity distribution and shear stress distribution
across a section of the pipe.
Q4.
Calculate the diameter of a parachute to be used for dropping an object weighing
1000 N so that the maximum terminal velocity of dropping is 5 m/sec. The
drag
coefficient for the parachute which may be treated as hemispherical is 1

3 and
mass density of air is 1

216 kg/m .
Q5.
What are the causes which result in separation of boundary layer ?
Q6.
A streamlined train is 310m long with a typical cross

se
ction having a perimeter
of 8.5 m above the wheels. Evaluate the approximate surface drag (friction drag)
of the train running at 90 km/hr. The kinematic viscosity of air at the prevailing
temperature is 1.49 x 10

5
m
2
/sec and its specific weight 12.25 N/m
3
.
Q7.
Derive the expression for velocity variation for a laminar incompressible flow in a
circular pipe.
Q8.
Glycerine of viscosity 0.88 N/m
2
and specific gravity 1.26 is pumped through a
horizontal pipe of diameter 30 mm at a flow rate of 50 lit/min.
Determine whether
the flow is laminar or turbulent. Find also the pressure loss due to the frictional
resistance in a length of 10 m and the power required.
Q9.
Derive the expression for shear stress distribution and velocity distribution for
laminar flo
w in a circular pipe.
Q10.
Oil of viscosity 0.2 Pa

S and Sp. gr. of 0.8 flows through a 150 mm diameter
pipe. If the head loss in 2000 m length pipe is 25 m, estimate
(i)
Shear stress along the pipe,
(ii)
Shear stress at a radial distance of 50 mm from t
he axis of the pipe,
(iii)
Velocity at radial distance of 25 mm from the axis of the pipe,
(iv)
Discharge through the pipe,
(v)
Check weather the flow in laminar.
Q11.
Explain various energy losses in pipes
Q12.
A pipe line, 16 km long, supplies 40 mill
ion litres of water per day to city. The
first 5 km length of the pipe is of 1 m diameter and the remaining part is 80 cm.
diameter pipe. If the water to the city is to be supplied as a residual head of 15 m
of water calculate the supply head at the inlet
end. Neglect minor losses and
assume f = 0.03 for the entire pipeline. Sketch the hydraulic gradient for the pipe
line.
Q13.
A factory is supplied power from a hydraulic power station by a pipe of 0

2 m
diameter, 5 km long. The pressure at the power stati
on is 6 MN/ m
2
. If the
frictional factor for the pipe is 0

02, find the maximum power in kW transmitted
to the factory.
What would be percent reduction in power transmission if efficiency of
transmission changes to 80% ?
Q14.
A steel penstock 60 cm in d
iameter has a shell thickness of 1

2 cm. The modulus
of elasticity of the shell material is 2.1 x 10
5
MPa and bulk modulus of water is
2.1 x 10
3
MPa. The pipe is designed to discharge water at a mean velocity of 2

1
m/sec. Determine the water hammer press
ure rise created by the sudden closure of
a valve at the downstream end.
Q15.
Three pipes with following details are connected in parallel between two points :
Pipe
Length(m)
Diameter(cm)
f
1
1000
20
.02
2
1200
30
.015
3
800
15
.02
When a total discharge of 0.30 m
3
/sec flows through the system, calculate the
distribution of discharge and the head loss between the junctions.
Q16.
A water main of concrete pipe 3200 m long and 30 cm diameter discharges into a
reservoir at the rat
e 10 x 10
6
litres/day. If the water line is gradually closed by
operating a valve at the reservoir end in 16 seconds, comment on the possibility of
pipe burst. The safe pressure of concrete pipe is 0.25 N/mm
2
.
Q17.
Explain with a neat .sketch the phenomen
on of boundary layer separation on a
stationary flat plate.
Q18.
A pipe 250 mm in diameter. 1 500 meters lone is laid at a slope of 1 in 200 for the
first half length and at a slope of 1 in 150 for the remaining length. The pressures
at the upper and low
er ends of the pipe are 100 kPa and 50 kPa respectively. Find
the discharge through the pipe. Take value of Darcy's frictional factor f = 0.028.
Q19.
What do you understand by hydrodynamically smooth and rough
boundaries?
Q20.
Two reservoirs are
connected by a pipe line which rises above the level of the
highest reservoir. What will be the highest point of the syphon above the level if
the length of the pipe leading upto this point from entrance in 500 m, the dia. of
the pipe is 0.35 m. The. diff
erence in level of two reservoirs in 12 m and the total
length of the pipe is 900 m. The syphon must run full. Calculate the rate of flow
through this siphonpipe. Assume Hsep

2

4 m of water abdute and f = 0.04. Allow
for all tosses.
Q21.
A water main of
concrete pipe 3200 m long and 30 cm diameter discharges into a
reservoir at the rate 10 x 10
6
liters per day. If the water line is gradually closed by
operating a valve at the reservoir end in 16 seconds, comment on the possibility of
pipe burst. The safe
pressure of concrete pipe is 0.25 N/mm
2
.
Q22.
For a pipe network, shown in the figure 3, determine the flow in each pipe. Take
n = 2. Use Hardy cross method and head loss formula h
f
= rQ
n
.
Q23.
Three reservoirs A, B and C with water surface elevations
40.0 m, 15.0 m and
10.0 m respectively are connected by three pipes by a common junction J. The
pipe details are :
—
Pipe
Dia. (mm)
Length (m)
Value of T
AJ
600
900
0.021
BJ
450
500
0.022
CJ
400
1200
0.020
Estimate the discharge in each pipe and t
he value of H.G.L. at junction J.
Q24.
Explain stepwise procedure of solving pipe network problems by Hardy Cross
method and derive the expression for calculating the correction AQ for the given
circuit.
Q25.
Three reservoirs are connected by pipes 1,
2 & 3. The free surface level in
reservoirs A, B, and C are 126.00 m, 109.00 m and 100.00 in respectively.
Calculate the rate of flow in each pipe assuming f=0.02.
Pipe
Diameter
(mts)
Length
(mts)
Connectivity
1
.15
350
AD
2
.10
200
BD
3
.1
0
250
CD
Q26.
A piping system consists of three pipes arranged in series, the lengths of the pipes
are 1200 m, 750 m. and 500 m and diameters 700 mm, 500 mm and 300 mm
respectively.
(i)
Transform the system to an equivalent 500 mm diameter pipe.
(ii)
For 2000 m long pipe, determine the equivalent diameter of the pipe.
Assume value of f = 0

024 for all the pipes.
Q27.
Describe in brief the Hardy

Cross method of solving pipe networks.
Q28.
Distinguish between laminar boundary layer and turbule
nt boundary layer.
Q29.
Three pipes having lengths 1000 m, 1200 m, 800 m, dia. 250 mm, 300 mm and
200 mm, friction factors 0.02, 0.015 and 0.025 respectively are connected in
parallel between two points. A and B. When total discharge of 0.3 m
3
/s flows
t
hrough the system, calculate the discharge in each pipe and head loss between A
and B. 9
Q30.
If y
1
and y
2
are alternate depths in a rectangular channel, show that,
Q31.
A trapazoidal channel 5.0 m wide and having a side slop
e of 1.5 (H) : 1 (v) is laid
on a slope of 0.00035. The roughness coefficient n = 0.015. Find normal depth
and critical depth for a discharge of 20 m
3
/s through this channel. Also comment
on the type of flow.
Q32.
Show that for a most efficient triangular
channel section, the hydraulic radius :
Q33.
An open channel is to be constructed of trapezoidal section and with side slopes 1
vertical to1.5 horizontal. Find the proportions between bottom width and depth of
flow for minimu
m excavation.
If the flow is to be 2.7 m
3
/sec, calculate the bottom width and depth of flow
assuming C = 44.5 and the bed slope as 1 in 4000.
Q34.
A triangular channel with its vertex downwards has sides sloping at 1.5 H to 1 V
and is laid on a longitud
inal bed slope of 1 in 2000.
Assuming Manning's n = .015 estimate the normal depth corresponding to
discharge of 0.4 m
3
/sec.
Q35.
A channel of trapezoidal section has sides sloping at 60° with the horizontal and a
bed slope of 1 in 800 conveys a discharg
e of 12 m
3
/sec. Find the bottom width
and depth of flow for most economical section. Take Chezy's constant C = 70.
Q36.
A syphon pipe 800 m long connects two reservoirs whose water surface levels
differ by 9 in. The diameter of the pipe is 300 mm. Takin
g Darcy's frictional
factor f = 0

024, find the discharge.
If the summit of the syphon pipe is 6 m above surface level of the upper reservoir,
calculate the maximum length of the inlet leg for the pipe to run full. Neglect
minor losses. Take atmospheric p
ressure = 10.3 m of water and separation
pressure head between upper reservoir and the summit = 2.3 m of water. 6
Q37.
What is most economical channel section ? Derive the condition for the
rectangular channel of best section.
Q38.
A pipe network consis
ts of two loops formed by five pipes AB, BC, CD, DA and
BD. Pipe BD is common to both the loops. The inflow at A is 1 m
3
/s and the
outflows at B, C, and D are 0.3 m
3
/s, 0.4 m
3
/s and 0.3 m
3
/s respectively. The
values of K for pipe AB is 50 BC is 30, CD is 3
0, DA is 20 and BD is 15.
Determine the flow in each pipe and the elevation of hydraulic grade line at C, if
the elevation of hydraulic grade line at A is 100 m.
Q39.
A rectangular channel 3.6 m wide had badly damaged surfaces with Manning's n
= 0.030. As
a first phase of repair, its bed was lined with concrete with n = 0.015.
If the depth of the flow remains same at 1.2 m before and after the repair, what is
the increase of discharge obtained as a result of repair?
Q40.
Distinguish between specific force
and specific energy in detail.
Q41.
A rectangular open channel has the following details :
—
(1)
Discharge
—
16m
3
/sec.
(2)
Bed width = 10 m
(3)
Depth of water = 1.0 m.
Find :
(i)
Specific Energy
(ii)
Critical depth
(iii)
Critical velocity
(iv)
M
inimum specific energy required for this discharge.
Q42.
What is specific energy ? Draw and explain specific energy vs. depth of flow
graph at a constant discharge in a rectangular channel.
Q43.
Calculate the critical depth corresponding to a discharge
of 10.2 m
3
/sec for the
following cases :
(i)
Rectangular channel of width 4 m
(ii)
Trapezoidal channel of bottom width 3 m and side slope 1 vertical to 1.25
horizontal.
Q44.
A rectangular open channel has the following details :
(1)
Discharge = 1
6 m
3
/sec
(2)
Bed width = 10 m
(3)
Depth of water = 1.0 mts.
Find:
(i)
Specific energy

(ii)
Critical depth
(iii)
Critical velocity and
(iv)
Minimum specific energy required for this discharge
Q45.
Explain the terms
(i)
Specific Energy Diagram
,
(ii)
Critical depth and Normal depth.
(iii)
Chezy's and Manning's formula for uniform flow.
Q46.
Calculate the critical depth corresponding to a discharge of 10.2 m
3
/sec for the
following cases :
—
(i)
Rectangular channel of width 4 m
(ii)
Trapezoi
dal channel of bottom width 3 m and side slope 1 vertical to 1.25
horizontal.
Q47.
What do you understand by a most economical section of a channel ? Derive the
condition of most economical section for a trapezoidal channel.
Q48.
A trapezoidal channel ca
rries a discharge of 2.5 m
3
/s. If the bed slope is 1 in 5000
and sides of the channel slope at 1 H to 0.5 V design the most economical section
for this channel. Assume Manning's n = 0.02.
Q49.
The width of a rectangular channel is reduced from 3.2 m to
2.5 m and the floor is
raised by 0.25 m in elevation at a given section. If the depth of flow upstream of
the construction is 2.0 m and the drop in the water surface elevation is 0.20 m,
calculate the discharge in the channel if the energy loss is 1/10 of
the upstream
velocity head.
Q50.
Explain in detail various gradually varied flow profiles in mild and steep
channels.
Q51.
State and discuss the assumptions made in the derivation of dynamic equation for
gradually varies flow. Starting from first princip
le, derive the equation for the
slope of the water surface in G.V.F. with respect to bed.
Q52.
A rectangular channel 10 m wide carries a discharge of 30 m
3
/sec at a normal
depth of 2.97 m. It is laid at a slope of 0.0001. If at a section in this channel
the
depth is 1.6 m, how far upstream or downstream from this section will the depth
be 2.0 m ? Take Manning's n = 0.015. Classify the surface profile.
Q53.
A rectangular channel conveying a discharge of 30 m
3
/sec is 12 m wide with a
bed slope of 1 in 600
0 and N = .025. The depth of flow at a section is 1.50. Find
how far upstream or downstream of this section, the depth of flow will be 2.0 mts.
Use step method. [Take only 2 steps]
Q54.
State the assumption made in the derivation of dynamic equation for
G.V.F. and
derive the gradually varied flow equation in the following form :
Q55.
A 9 m wide rectangular channel conveys 20 m
3
/s of water at a depth of 1.5 m.
Calculate :
(i)
Specific energy of the flowing water.
(ii)
Critica
l depth, critical velocity and minimum specific energy.
(iii)
State whether the flow is subcritical or supercritical.
Q56.
Explain with a neat sketch M
1
, M
2
and M
3
profile for a gradually varied flow.
Q57.
Differentiate between alternate depths and se
quent depths.
Q58.
A rectangular channel 2.5 m wide carries a uniform .flow rate of 7.3 m
3
/s at a
depth of 1.6 m. If a smooth hump of height 0.13 m is constructed at a certain
location on the channel bed, determine the change in water surface elevation.
Also
compute the maximum permissible hump height if the upstream depth is not be
altered.
Q59.
For hydraulic jump in a rectangular channel derive equation relating sequent
depths with initial Froude number.
Q60.
Water from a low dam is released through
a sluice gate on a horizontal
rectangular channel. The depth of water upstream of the sluice gate is 16.0 m
above the channel bed and the gate opening is 1.5 m. The sluice gate can be
assumed to be a sharp edged (C
c
= 0.6). If a free hydraulic jump is form
ed just
downstream of the gate, find the sequent depths and the percentage of the initial
energy lost in the jump.
Q61.
Derive the expression for the loss of energy in the formation of a hydraulic jump
in a rectangular channel.
Q62.
A rectangular channe
l 5 m wide carries a discharge of 15 m
3
/sec. at a velocity of
10 m/sec. If a hydraulic jump occurs, find :
(i)
Depth of flow after the jump
(ii)
Energy loss in the jump
(iii)
Height of jump.
Q63.
Define hydraul
ic jump and derive the expression for energy loss in hydraulic
jump in terms of sequent depths.
Q64.
In a horizontal rectangular channel 1.5 m wide, if the observed depths before and
after the jump are 0.2 m and 1.0 m respectively, determine the discharg
e flowing
through the channel.
Q65.
In a rectangular channel of 0.5 m width, a hydraulic jump occurs at a point where
depth of water flow is 0.15 m and Froude number is 2.5. Determine :
(i)
The specific energy at inlet section.
(ii)
The sequent depth
(
iii)
Loss of head.
Q66.
What is 'Hydraulic jump' in an open channel ? Write its applications.
Q67.
Derive the expression for energy loss in hydraulic jump in terms of sequent
depths.
Q68.
A rectangula
r channel 5 m wide carries a discharge of 15 m
3
/s at a velocity of 10
m/s. If hydraulic jump occurs, find
(i)
Depth of flow after the jump,
(ii)
Energy loss in the jump and
(iii)
Height of the jump.
Q69.
Derive the
expression for specific speed (N
s
) of a turbine.
Q70.
Explain Heads and Efficiencies of hydraulic turbines.
Q71.
Why priming is required in centrifugal pumps ? Why can the suction lift of a
pump not exceed a certain limit ?
Q72.
At the design speed o
f 1000 rpm at centrifugal pump is to deliver water against a
head of +5.0 m. The vanes are curved backwards to an angle of 30° with the
periphery. The impeller diameter is 30 cm, the outlet width is 5 cm.
What will be the discharge if the hydraulic effici
ency of the pump is 94% ?
Q73.
Explain the parts and working of a Pelton wheel turbine.
Q74.
A turbine is to operate under a head of 25 m at 200 rpm. The discharge is 9
m
3
/sec. If the efficiency is 90%, determine:
(i)
Specific speed of the machine
(ii
)
Power generated
(iii)
Type of turbine
(iv)
Performance under a head of 20 mts.
Q75.
State and explain Froude's model Law.
Q76.
Derive the expression for specific speed of turbine.
Q77.
1000 kW of power is being developed by a hydraulic turbine
under a head of 20
m and gives 85% efficiency. Calculate the specific speed of the turbine.
Q78.
Define critical slope of channel and draw possible water surface profiles when the
flow over mild slope is followed by a steep slope.
Q79.
A rectangular ch
annel 8 m wide carries a discharged 25 m
3
/s. Bed slope is 0.0001.
If at a section in this channel the depth is 1.7 m, how far upstream or downstream
from this section the depth would be 1.9 m ? Taken = 0.015.
Q80.
A single acting reciprocating pump runs
at 60 r.p.m. The diameter of the plunger
is, 1,5 cm and crank radius is 15 cm. The suction pipe is 10 cm in diameter and 5
m long. Calculate maximum permissible value of suction lift H
s
if separation
takes place at 2.6 m of water absolute.
Q81.
A centri
fugal pump lifts water against a static head of 40 m, of which 4 m is
suction lift. The suction and delivery pipes are both 15 cm diameter; the head loss
in a suction pipe is 2.3 m and in the delivery pipe is 7.4 m. The impeller is 42 cm
diameter and 2.5
cm wide al the mouth, it revolves at 1200 r.p.m. and its effective
vane angle it exist is 35°. If
mano
= 82% and
0
= 72% determine the discharge
delivered by the pump and power required to drive the pump.
Q82.
Define the different efficiencies of a tur
bine and give the appropriate expression
for each one of them.
Q83.
Explain Froude's law of similarity and derive the model scales for :
(i)
Velocity
(ii)
Time.
Q84.
A hydraulic turbine develops 880 kW under a head of 20 m and gives an
efficiency of
90%. Calculate the specific speed of the turbine. Calculate the power
generated if the head is reduced to 15 m. Assume N = 400 rpm.
Q85.
A centrifugal pump is discharged .118 m
3
/sec at a speed of 1450 rpm against a
head of 25 m. The impeller diameter is
25 cm, its width at outlet is 5 cms and the
manometric efficiency is 0.75. Determine the Vane angle at the outer periphery of
the impeller.
Q86.
Explain working of a centrifugal pump with neat sketch,
Q87.
Differentiate between :
(i)
Gross head and net h
ead of a turbine,
(ii)
Impulse turbine and Reaction turbine.
Q88.
A power house is to develop a total of 70 MW of electrical energy. It is proposed
to use four Pelton wheel turbines, each to work under the following specifications
:
—
(i)
Hea
d = 400 r.p.m.
(ii)
Speed = 250 r.p.m.
(iii)
Overall efficiency = 0.9
(iv)
Coefficient of velocity = 0

98
(v)
Speed ratio = 0.45.
Find the discharge and least jet diameter.
Q89.
Derive the expression for specific speed of a turbine
.
Q90.
A reaction turbine working under a head of 100 m and at a speed of 700 rpm has
an overall efficiency of 80%. If the specific speed is 175, calculate the discharge,
what would be required if the head is reduced to 80 m ?
Q91.
Write short notes on
any three of the following :

(a)
Centrifugal pump troubles and remedies,
(b)
Double acting reciprocating pump,
(c)
Selection of turbines.
(d)
Classification of hydraulic jumps.
(e)
Froude's model law.
Q92.
Explain the working of a sing
le acting reciprocating pump with a neat sketch.
Q93.
Explain the function of air vessels fitted to a reciprocating pump.
Q94.
A single acting reciprocating pump has a plunger of diameter 50 cm and a stroke
of 80 cm. If the speed of the pump is 60 rpm
and coefficient of discharge is 0.97,
determine the actual discharge and the percentage slip of the pump.
Q95.
Explain with a neat sketch the construction and working of a single acting
reciprocating pump.
Q96.
A single acting single cylinder reciproca
ting pump has the following
characteristics :
(i)
Diameter of the cylinder = 20 cm
(ii)
Stroke length = 45 cm
(iii)
Actual discharge = 6.5 Ips
(iv)
Suction head = 5.0 mts
(v)
Delivery head = 20.0 mts
(vi)
Speed
=
40 rpm
Find the coefficient
of discharge, percent slip and power required to drive the
pump.
Q97.
Write a short note on Multistage Centrifugal Pump.
Q98.
Explain the principles of working of single acting and double acting reciprocating
pumps.
Q99.
A centrifugal pump is running a
t 1200 r.p.m. The outlet vane angle of the impeller
is 30° and velocity of flow at outlet is 4 m/s. The pump is working against a total
head of 30 m and the discharge through the pump is 0.3 m
3
/s. If the manometric
efficiency of the pump is 70%, determine
(i)
the diameter of the impeller and
(ii)
the width of the impeller at outlet. 8
Q100.
Write a short note on Multistage centrifugal pump.
Q101.
For a Single acting reciprocating pump, Pistons diameter is 150 mm, stoke length
is 300 mm, rotational spee
d is 50 rpm. The pump rises the water through 18 m.
Determine the theoretical discharge, if the actual discharge is 4 liters per second.
Also determine the volumetric efficiency, slip and actual power required to lift the
water. Take mechanical efficiency
of the pump is 80%.
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