Examples solutions in open channel flow

Explain clearly what you understand by:
The “most economical section” & “critical depth” for flow in a channel.
What is specific energy curve & Unite discharge curve? Draw net sketches.

A prismatic channel of symmetric trapezoidal section, 1600 mm deep and with top and
bottom widths 3 m and 0.6 m respectively carries water at a rate of 2.6 m3 s–1. Manning’s n
may be taken as 0.012 m–1/3 s.
Estimate:
(a) the normal depth at a slope of 1 in 2500 is:
------------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------
(b) the Froude number at the normal depth is
-----------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------
(c) the critical depth is:
-----------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
--------------------------------------------------
(d) the critical slope is:
------------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------

A channel of semi-circular cross-section, radius 0.7 m, carries water at a rate of
0.8 m3 s–1. Manning’s “n” is 0.013 m–1/3 s.
 the normal depth (relative to the bottom of the channel) at a slope of 2% is:
------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------
 the Froude number at the normal depth is:
------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------
 the critical depth is:
------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------

A prismatic channel, with the cross-section shown, has a stream wise slope of 1 in 50.
Estimate:
 The value of Manning’s “n” is:
----------------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------
if a flow rate is 2 m3 /S and the flow depth (measured from the lowest point of the channel) is
0.6 m,
 the depth in the channel at a flow rate of 3 m3 /S is:
----------------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------
 the Froude number at the flow rate (mentioned above, Q = 3 m3 /s ), is:
----------------------------------------------------------------------------------------------------------------------------
----------------------------------------------------------------------------------------------------------------------------
-------------------------------------------------------
 State whether the channel slope is steep or mild for the flow rate (mentioned above, Q = 3
m3 /s), justifying your answer.
----------------------------------------------------------------------------------------------------------------------------
----------------------------------------------------------------------------------------------------------------------------
------------------------------------------------------

A rectangular channel of width 5 m carries a discharge of 8 m3 s–1. The stream wise slope of
the channel is 1.0x10–4 and Manning’s roughness coefficient may be taken as 0.015 m-1/3 s.
At one point there is a localized narrowing to width 2 m. Assuming a long undisturbed fetch
upstream,
 the depth of flow far upstream of the narrow point is:
---------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------
------------------------------------------------------
 the critical depth and the critical specific energy at the narrow point is:
---------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------
------------------------------------------------------
 Determine the water depths at the narrow point and at stations just up and downstream
of the contracted section if the channel bed in the contracted section is: (i) the same as
the main channel;
 (ii) raised by 0.75 m;
 (iii) lowered by 0.75 m. (you may assume that no hydraulic jump occurs immediately
downstream of the narrow section.)

Water is conveyed at 12 m3 s–1 through a rectangular channel of width 5
m, stream wise slope 0.01% and Manning’s “n” = 0.016. At one point the
channel narrows to a width of 2 m. Assuming that normal-flow conditions
prevail upstream, calculate:
 the normal depth in the main channel;
 the critical depth at the narrow point and show that the flow does not
become critical here;
 the actual water depth at the narrow point is:
 the minimum height by which the bed of the constricted section must
be raised locally in order to force critical conditions there is:
 the depths at the narrow point and in the main channel just up- and
downstream of the constricted section if the bed is raised as in part (d)
is:
(Assume that no hydraulic jumps occur here.)

Water is conveyed at 11 m3.s–1 through a long rectangular channel of
width 4 m, stream wise slope 2×10–3 and Manning’s “n” = 0.02 m–1/3 s.
At one point the channel narrows to a width of 2.5 m. Calculate:
 the normal depth and critical depth in the main channel are:
 the critical depth at the narrow point and show that the flow does
become critical here is:
 the water depths at stations just up and downstream of the
contraction are:
 the depth by which the bed of the constricted section must be sunk
locally in order to just prevent the occurrence of critical conditions
there are:

A river consists of a rectangular channel of width 5 m. At one point the
piers of a simple beam bridge cause a local narrowing to width 3 m. The
bottom of the bridge deck is 1.7 m above the bed of the river.
 When the river flow is 11 m3 s–1 the constriction of the channel by the
bridge causes a subcritical to supercritical flow transition. Calculate the
depths of water upstream, downstream and under the centre of the
bridge, stating any assumptions made.
 At the flow rate above, a hydraulic jump occurs a short distance
downstream of the bridge. Find the depth of flow immediately
downstream of the hydraulic jump.
 Show that if the river flow is 22 m3 s–1 then the flow passage beneath
the bridge will be completely choked.

A sluice gate controls the flow in a channel of width 2.5 m. If the
depths of water upstream and downstream of the gate are 1.4 m
and 0.25 m, respectively, with net calculation:
 the discharge will be:
 the Froude numbers upstream and downstream of the sluice
gate are:
.

Water passes under a sluice gate in a horizontal channel of width 2m.
The depths of flow on either side of the sluice gate are 1.8 m and 0.3 m.
A hydraulic jump occurs a short distance downstream. Assuming no
energy loss at the gate, calculate:
 the force on the gate;
 the depth of flow downstream of the hydraulic jump;
 the fraction of the fluid energy that is dissipated in the jump

Which one of the following is correct?
 the frictional resistance depends on the nature of the surface area of contact
 the frictional resistance is independent of the nature of the surface area of
contact
 the frictional resistance depends on the nature of the surface area of contact for
laminar flows but is independent of the nature of the surface area of contact for
turbulent flows
contact for laminar flows but depends on the nature of the surface area of
contact for turbulent flows
Answer: d
Explanation:
According to the laws of fluid friction, the frictional resistance is independent of
the nature of the surface area of contact for laminar flows but depends on the
nature of the surface area of contact for turbulent flows.

A liquid flows through pipes 1 and 2 with the same flow velocity. If the ratio of their
pipe diameters D1 : D2 be 3:2, what will be the ratio of the head loss in the two
pipes?
 3:2
 9:4
 2:3
 4:9
Answer: c
Explanation:
According to Darcy-Weisbach formula, ℎ𝑓 = 𝑓
𝐿
𝐷
×
𝑉2
2 𝑔
Where,
ℎ𝑓 : the head loss in the pipe,
𝑓 : the co-efficient of friction,
𝐿 : the length,
𝐷 : the diameter and
𝑉 : is the flow velocity.
Thus, 𝒉𝒇, 𝟏 ∶ 𝒉𝒇, 𝟐 = 𝑫𝟐 ∶ 𝑫𝟏 = 𝟐 ∶ 𝟑.

A liquid flows through two similar pipes 1 and 2. If the ratio of their flow
velocities V1 : V2 be 2:3, what will be the ratio of the head loss in the
two pipes?
a) 3:2
b) 9:4
c) 2:3
d) 4:9
Answer: d
Explanation:
𝐿
𝐷
×
𝑉2
2 𝑔
where
ℎ𝑓 : the head loss in the pipe,
𝐿 : the length,
𝑉 : the flow velocity.
Thus, 𝒉𝒇, 𝟏 ∶ 𝒉𝒇, 𝟐 & 𝑽𝟏 ∶ 𝑽𝟐 = 𝟒 ∶ 𝟗.

A liquid flows with the same velocity through two pipes “1” and “2” having
the same diameter. If the length of the second pipe be twice that of the
first pipe, what should be the ratio of the head loss in the two pipes?
 1:2
 2:1
 1:4
 4:1
Answer: a
Explanation:
𝐿
𝐷
×
𝑉2
2 𝑔
where
ℎ𝑓: the head loss in the pipe,
𝐿 : the length,
𝑉 : the flow velocity.
Thus, 𝒉𝒇,𝟏 = 𝒉𝒇,𝟐 & 𝑳𝟏 = 𝑳𝟐 = 𝟏 ∶ 𝟐.

 Darcy-Weisbach formula is generally used for head loss in flow through both
pipes and open channels
 Chezy’s formula is generally used for head loss in flow through both pipes and
open channels
 Darcy-Weisbach formula is generally used for head loss in flow through both
pipes and Chezy’s formula for open channels
 Chezy’s formula is generally used for head loss in flow through both pipes and
Darcy-Weisbach formula for open channels
Answer: c
Explanation:
Darcy-Weisbach formula is generally used for head loss in flow through both
pipes as it takes into consideration the flow velocity whereas Chezy’s formula is
used for open channels as it considers the pressure difference.

 the frictional resistance is always dependent on the nature of the surface area of
contact
 the frictional resistance is always independent of the nature of the surface area
of contact
 the frictional resistance is dependent on the nature of the surface area of contact
when the liquid flows at a velocity less than the critical velocity
contact when the liquid flows at a velocity less than the critical velocity
Answer: d
Explanation:
Frictional resistance is dependent on the nature of the surface area of contact. But,
when the liquid flows at a velocity less than the critical velocity, a thin stationary film
of the liquid is formed on the supporting surface. Hence, the frictional resistance
becomes independent of the nature of the surface of contact.

The frictional resistance for fluids in motion is
 proportional to the velocity in laminar flow and to the square of the
velocity in turbulent flow
 proportional to the square of the velocity in laminar flow and to the
velocity in turbulent flow
 proportional to the velocity in both laminar flow and turbulent flow
 proportional to the square of the velocity in both laminar flow and
turbulent flow
Answer: c
Explanation:
The major loss for the flow through the pipes is due to the frictional resistance
between adjacent fluid layers sliding over each other. This resistance arises due to
the presence of viscous property of the fluid.

The head loss at the entrance of the pipe is that at it’s exit
 equal to
 half
 twice
 four times
Answer: b
Explanation:
𝐿
𝐷
×
𝑉2
2 𝑔
hi = 0.5V2/ 2g and ho = V2 / 2g,
Where:
hi : the head loss at pipe entrance,
ho : the head loss at pipe exit and
V : the flow velocity.
Thus hi = 0.5 ho.

Which of the following is true?
 the slope of EGL will always be greater than that of the axis of the pipe
 the slope of EGL will always be smaller than that of the axis of the pipe
 the slope of EGL will always be equal to that of the axis of the pipe
 the slope of EGL will always be independent of that of the axis of the
pipe
Answer: d
Explanation:
EGL is obtained by plotting total head at various points along the axis of the pipe. Z
+
𝑃
𝜌 𝑔
+
𝑉2
2 𝑔
= 𝐻
Where:
H : the total head,
P ⁄  g : the pressure head,
z : the potential head, , and
V2 / 2g : the velocity head.
Hence, there is no relation whatsoever between the slope of EGL and that of the
axis of the pipe.

 HGL always drops in the direction of flow
 HGL always rises in the direction of flow
 HGL always remains constant in the direction of flow
 HGL may or may not in the direction of flow
Answer: d
Explanation:
HGL is obtained by plotting Piezometric head at various points along the
axis of the pipe. Since pressure may either rise or fall in the direction of
flow, HGL may or may not change in that direction.

The vertical intercept between EGL and HGL is equal to
 a) pressure head
 b) potential head
 c) kinetic head
 d) Piezometric head
Answer: c
Explanation:
EGL is obtained by plotting total head and HGL is obtained by plotting Piezometric
head at various points along the axis of the pipe.
Hp = P ⁄  g + z = H
Where:
H : the total head,
P ⁄  g : the pressure head,
z :the potential head,
Hp : the Piezometric head, and
V2 / 2g is the velocity head.
H – Hp = V2/ 2g, the vertical intercept between EGL and HGL is equal to the kinetic
head.

The slope of HGL will be:
 greater than that of EGL for a pipe of uniform cross-section
 smaller than that of EGL for a pipe of uniform cross-section
 equal to that of EGL for a pipe of uniform cross-section
 independent of that of EGL for a pipe of uniform cross-section
Answer: c
Explanation:
The vertical intercept between EGL and HGL is equal to the kinetic head.
For a pipe of uniform cross-section, there will be no change in the velocity
of flow across the pipe. Since the kinetic head remain constant, the slope of
HGL will be equal to that of EGL.

For a nozzle, the vertical intercept between EGL and HGL
 increases
 decreases
 remains constant
 may increase or decrease
Answer: a
Explanation:
The vertical intercept between EGL and HGL is equal to the kinetic head. For a
nozzle, the cross-sectional area decreases in the direction of flow leading to an
increase in the velocity of flow across the pipe. Since the kinetic head increases, the
vertical intercept between EGL and HGL will increase.

For a diffuser, the vertical intercept between EGL and HGL
 increases
 decreases
 remains constant
 may increase or decrease
Answer: b
Explanation:
The vertical intercept between EGL and HGL is equal to the kinetic head. For a
diffuser, the cross-sectional area increases in the direction of flow leading to a
decrease in the velocity of flow across the pipe. Since the kinetic head decreases,
the vertical intercept between EGL and HGL will decrease.

 the slope of EGL will always be greater than that of the axis of the
pipe
 the slope of EGL will always be smaller than that of the axis of the
pipe
 the slope of EGL will always be equal to that of the axis of the pipe
 the slope of EGL will always be independent of that of the axis of the
pipe
Answer: d
Explanation:
EGL is obtained by plotting total head at various points along the axis of the pipe.
Z +
𝑃
𝜌 𝑔
+
𝑉2
2 𝑔
= 𝐻
where
H : the total head,
𝑃
𝜌 𝑔
: the pressure head,
Z :the potential head, , and
V2 / 2g is the velocity head.
Hence, there is no relation whatsoever between the slope of EGL and that of the
axis of the pipe.

Pump transfers the mechanical energy of a motor or of an engine into
_________ of a fluid.
a. pressure energy
b. kinetic energy
c. either pressure energy or kinetic energy
d. pressure energy, kinetic energy or both.
ANSWER: pressure energy, kinetic energy or both (C)
Which of the following is NOT a type of positive displacement pumps?
a. Reciprocating pump
b. Rotary displacement pump
c. Centrifugal pump
d. None of the above.
ANSWER: Centrifugal pump

___________ pump is also called as velocity pump.
a. Reciprocating
b. Rotary displacement
c. Centrifugal
d. Screw.
ANSWER: Centrifugal
The process of filling the liquid into the suction pipe and pump casing upto
the level of delivery valve is called as ----------------.
a. filling
b. pumping
c. priming
d. leveling
ANSWER: priming ©

An apparatus for raising, driving or compressing fluids is called
_________
a) Piston
b) Pump
c) Compressor
d) Force drive
Answer: (b)
Explanation: A pump is a device used to transfer or force the liquid
against gravity. There are different types of pumps based on the
requirements and the pumps are designed for different loads.

________ pumps produce a head and a flow by increasing the velocity of
the liquid with the help of the rotating vane impeller.
a) Displacement pumps
b) Positive pumps
c) Centrifugal pumps
d) Rotating pumps
Answer: (c)
Explanation: Centrifugal pumps produce a head and a flow by
increasing the velocity of the liquid with the help of the rotating vane
impeller. Centrifugal pumps include radial, axial and mixed flow units.

The two types of pumps behave very differently regarding pressure head
and flow rate.
a) True
b) False
Answer: (a)
Explanation: There are two types of basic pumps. One is the centrifugal
pump and the other one is positive displacement pump. Centrifugal pump is
also called as a roto-dynamic pump. These two pumps behave very
differently with respect to flow rates and pressure head.

What are the pumps with one or more impellers called?
a) ANSI process pumps
b) API process pumps
c) Centrifugal pumps
d) Positive displacement pumps
Answer:(c)
Explanation: The general name for pumps with one or more impellers is
called centrifugal pumps. Many types and configurations of centrifugal
pumps are used for different applications.

How many impellers does a multistage centrifugal pump have?
a) Zero
b) One
c) Exactly two
d) Two and more
Answer: (a)
Explanation: At each stage in the centrifugal pump, the fluid is directed
to towards the center. The energy usage in pumping installation is
determined by Friction characteristics. Thus, it is the most suitable
option.

Formation of bubbles in an impeller is called ______
a) Cavities
b) Defects
c) Friction
d) Heat burn
Answer: (a)
Explanation: Formation of bubbles in an impeller is called as its as its
cavities. These cavities develop intense shockwaves in the impeller.

With the increase in the flow rate, efficiency ______
a) Decreases
b) Increases
c) Remains same
d) Independent
Answer: (b)
Explanation: With the increase in the flow rate, efficiency increases. The
unit of flow rate in a centrifugal pump is m3/s. It is denoted as ‘Q’. It
plays an important role to determine the efficiency of the pump.

Discharge of a centrifugal pump is proportional to .......
a)-. Impeller diameter(D)
b)- D 2
C)- D 3
d)- 1/D 3
e)- 1/D 2
Answer: (b). D 2
Total Energy gradient line (E.G.L.) represents the sum of .......
A)- Pressure head and kinetic head
B)- Kinetic head and datum head
C)- Pressure head and datum head
d)- Pressure head, kinetic head and datum head
d)- Pressure head, kinetic head and datum head

Cavitation can take place in case of ......
a)- Pelton wheel
b)- Francis turbine
C)- Reciprocating pump
d)- Centrifugal pump
e)-.Both Francis turbine and reciprocating pump
Answer: e) Both Francis turbine and reciprocating pump
In Kaplan turbine runner, the number of blades is generally of the
order......
a) - 2-4
b) - 4-8
C )- .8-16
d )-16-24
Answer. (d) 16-24

A draft tube is used with .......
a) - Impulse turbine
b) - Pelton wheel turbine
C) - Reaction turbine
d) - Very high specific speed turbine
e) - Both Francis turbine and reciprocating pump
Answer : C)- Reaction turbine
Specific speed of a turbine depends upon .........
a) - Speed, power and discharge
b) - Discharge and power
C) - Speed and heat
d) - Speed, discharge and heat
e) - Speed, power and heat
Answer: e) - Speed, power and heat

Francis turbine is best suited for .........
a) - Medium head application from 24 to 180 m
b) - Low head installation up to 30 m
C) - High head installation above 180 m
d) - All types of heads
Answer : a) - Medium head application from 24 to 180 m
Reaction turbines are used for ......
a) - Low head
b) - High head
C) - High head and low discharge
d) - High head and high discharge
e) - Low head and high discharge
Answer: e) - Low head and high discharge

Impellers for high heads usually have .........
a) - High specific speed
b) - Low specific speed
C) - Medium specific speed
d) - Variable specific speed
Answer: b) - Low specific speed
Which of the following pumps is used for pumping viscous fluids......
a) - Centrifugal pump
b) - Screw pump
C) - Reciprocating pump
d) - Jet pump
Answer: b) - Screw pump.

For small discharge and high heads which pump is preferred ......
a) - Centrifugal type
b) - Reciprocating type
C) - Axial flow type
d) - Radial flow type.
Answer: b) - Reciprocating type
Cavitation in hydraulic turbine results in .......
a) - Noise and vibration
b) - Reduction of discharge
c) - Drop in output and efficiency
d) - Rough surface.
Answer: d) - Rough surface

For Flood control and irrigation applications the pump generally used
is.......
a) - Centrifugal type
b) - Reciprocating type
c) - Axial flow type
d) -Radial flow type.
Answer: c) - Axial flow type
Higher specific speed (161 to 500 ) of centrifugal pump indicates that
the pump is .........
a) - Axial type
b) - Mixed flow type
c) - Axial flow
d) - Any of the above.
Answer: a) - Axial type

Higher specific speed (300 to 1000 ) of turbine indicates that the turbine
is......
a) - Pelton wheel
b) - Kaplan
c) - Francis
d) - Any of the above.
Answer: b) - Kaplan
Pilot tube is used for measurement of .......
a) - Pressure
b) - Flow
c) - Velocity at a point
d) – Discharge.
Answer: c) - Velocity at a point

The flow in pipe is laminar if .........
a) - Reynolds number is equal to 2500
b) - Reynolds number is equal to 4200
c) - Reynolds number is more than 2500
d) - None of the above.
Answer: d) None of the above.
A stream line is a line ......
a) - Which is along the path of a particle
b) - Which is always parallel to the main direction of flow
c) - Across which there is no flow
d) - On which tangent drawn at any point gives the direction of velocity.
Answer: c) - Across which there is no flow.

Continuity equation deals with the law of conservation of .......
a) - Mass
b) - Momentum
c) - Energy
d) - None of the above.
Answer: a) - Mass

WORKING PRINCIPLE OF IMPULSE TURBINE
 In Impulse Turbine, there are some fixed nozzles and moving blades
are present on a disc mounted on a shaft.
 Moving blades are in symmetrical order. The flow enters the turbine
casing with some pressure. After that, it passes through one or more
no. of fixed nozzles into the turbine. The relative velocity of flow at the
outlet of the moving blades is same as the inlet to the blades.
 During Expansion, flow's pressure falls. Due to high-pressure drop in
the nozzles the velocity of flow increases.

 This high-velocity jet of flow flows through fixed nozzles and it strikes the
blade with constant pressure.
 An impulse turbine, produced only impulsive force to the blades.
 Now blades are starting to move in the same direction of the flow.
 Due to change in momentum, turbine's shaft is starting to rotate.

WORKING PRINCIPLE OF IMPULSE REACTION STEAM TURBINE:
Working principle of Impulse Reaction turbine depends on reaction force produced
by steam. Here steam flows through the nozzles at the end of the tubes and it is
supported on the bearings. The outlet relative velocity of steam is much less than at
the inlet to the blades.

Impulse Turbine Reaction Turbine
1) In impulse Turbine, only impulsive
force strikes to the blades fixed to the
rotor
1) In reaction turbine, vector sum of
impulsive and reactive force strikes
the blades fixed to the rotor.
2) Steam expands completely when it
passes through the nozzles and its
pressure remains constant.
2) pressure can't expand fully. It partially
expands when it pass through the
nozzles
and rest on the rotor blades.
3) Blades are symmetrical shape. 3) Blades are asymmetrical shape.
4) Since the velocity of stream is high,
speed is high in impulse turbine.
4) But reaction turbine speed is much
lower than impulse turbine because
steam velocity is lower in reaction
turbine as compared to impulse
turbine.
Difference Between Impulse Turbine and Reaction Turbine

Impulse Turbine Reaction Turbine
5) For producing same power, the
number of stages required are much
less.
5) It require more stages to develop
same power.
6) The blade efficiency curve is high.
6) The blade efficiency curve is lower
than impulse turbine.

TOP Hydraulic Machines - Mechanical Engineering Multiple
choice the correct answer of the following Questions and Answers List
Reciprocating pumps are no more to be seen in industrial applications (in
comparison to centrifugal pumps) because of:
 (a) high initial and maintenance cost
 (b) lower discharge
 (c) lower speed of operation
 (d) necessity of air vessel
 (e) all of the above.
Ans.: a
In a centrifugal pump casing, the flow of water leaving the impeller, is:
 (a) rectilinear flow
 (b) radial flow
 (c) free vortex motion
 (d) forced vortex
 (e) none of the above.
Ans.: c

Head developed by a centrifugal pump depends on:
 (a) impeller diameter
 (b) speed
 (c) fluid density
 (d) type of casing
 (e) (a) and (b) of the above.
Ans.: e
For starting an axial flow pump, its delivery valve should be:
 (a) closed
 (b) open
 (c) depends on starting condition and flow desired
 (d) could be either open or closed
 (e) partly open and partly closed.
Ans.: b
The efficiency of a centrifugal pump is maximum when its blades are:
 (a) straight
 (b) bent forward
 (c) bent backward
 (d) bent forward first and then backward
 (e) bent backward first and then forward.
Ans.: c

In a centrifugal pump casing, the flow of water leaving the:
 (a) radial
 (b) radial
 (c) centrifugal
 (d) rectilinear
 (e) vortex.
Ans.: e
Centrifugal pump is started with its delivery valve:
 (a) kept fully closed
 (b) kept fully open
 (c) irrespective of any position
 (d) kept 50% open
Ans.: a
Axial flow pump is started with its delivery valve:
 (a) kept fully closed
 (b) kept fully open
 (c) irrespective of any position
 (d) kept 50% open
Ans.: b

When a piping system is made up primarily of vertical lift and very little pipe
friction, the pump characteristics should be:
 (a) horizontal
 (b) nearly horizontal
 (c) steep
 (d) first rise and then fall
Ans.: c
One horsepower is equal to:
 (a) 102 watts
 (b) 75 watts
 (c) 550 watts
 (d) 735 watts
 (e) 33000 watts.
Ans.: d
Multistage centrifugal pumps are used to obtain:
 (a) high discharge
 (b) high head
 (c) pumping of viscous fluids
 (d) high head and high discharge
 (e) high efficiency.
Ans.: b

When a piping system is made up primarily of friction head and very little of vertical lift,
then pump characteristics should be:
(a) horizontal
(b) nearly horizontal
(c) steep
(d) first rise and then fall
(e) none of the above.
Ans.: b
In a single casing, multistage pump running at constant speed, the capacity rating is to
be slightly lowered. It can be
done by:
 (a) designing new impeller
 (b) trimming the impeller size to the required size by machining
 (c) not possible
 (d) some other alterations in the impeller
Ans.: b

If a pump is handling water and is discharging a certain flow Q at a constant total
dynamic head requiring a definite B.H.P., the same pump when handling a liquid of
specific gravity 0.75 and viscosity nearly same as of water would discharge:
 (a) same quantity of liquid
 (b) 0.75 Q
 (c) Q/0.75
 (d) 1.5 Q
Ans.: a

The horse power required in above case will be:
 (a) same
 (b) 0.75 B.H.P.
 (c) B.H.P./0.75
 (d) 1.5 B.H.P.
Ans.: b
Low specific speed of a pump implies it is:
 (a) centrifugal pump
 (b) mixed flow pump
 (c) axial flow pump
 (d) any one of the above
Ans.: a
The optimum value of vane exit angle for a centrifugal pump impeller is:
 (a) 10-15°
 (b) 20-25°
 (c) 30-40°
 (d) 50-60°
 (e) 80-90°.
Ans.: b

In a centrifugal pump, the liquid enters the pump:
 (a) at the top
 (b) at the bottom
 (c) at the center
 (d) from sides
Ans.: c
For small discharge at high pressure, following pump is preferred:
 (a) centrifugal
 (b) axial flow
 (c) mixed flow
 (d) propeller
 (e) reciprocating.
Ans.: e
In centrifugal pumps, maximum efficiency is obtained when the blades are:
(a) straight
(b) bent forward
(c) bent backward
(d) radial
(e) given aero foil section.
Ans.: c

Motion of a liquid in a volute casing of a centrifugal pump is an example of:
 (a) rotational flow
 (b) radial
 (c) forced spiral vortex flow
 (d) forced cylindrical vortex flow
 (e) spiral vortex flow.
Ans.: e
For very high discharge at low pressure such as for flood control and irrigation
applications, following type of pump is Preferred:
 (a) centrifugal
 (b) axial flow
 (c) reciprocating
 (d) mixed flow
Ans.: b
Medium specific speed of a pump:
Ans.: b

High specific speed of a pump implies it is:
Ans.: c
Indicator diagram of a reciprocating pump is a graph between:
 (a) flow vs. swept volume
 (b) pressure in cylinder vs. swept volume
 (c) flow vs. speed
 (d) pressure vs. speed
 (e) swept volume vs. speed.
Ans.: b
Low specific speed of turbine implies it is:
 (a) propeller turbine
 (b) Francis turbine
 (c) impulse turbine
 (e)none of the above.
Ans.: c

Any change in load is adjusted by adjusting following parameter on turbine:
(a) net head
(b) absolute velocity
(c) blade velocity
(d) flow
(e) relative velocity of flow at inlet.
Ans.: d
Runaway speed of a hydraulic turbine is:
 (a) full load speed
 (b) the speed at which turbine runner will be damaged
 (c) the speed if the turbine runner is allowed to revolve freely without
load and with the wicket gates wide open
 (d) the speed corresponding to maximum overload permissible
Ans.: c
The maximum number of jets generally employed in impulse turbine without jet
interference is:
 (a) 4
 (b) 6
 (c) 8
 (d) 12
 (e) 16.
Ans.: b

Medium specific speed of turbine implies it is:
Ans.: b
High specific speed of turbine implies it is:
Ans.: a
The specific speed of turbine is defined as the speed of a unit:
 (a) of such a size that it delivers unit dis-charge at unit head
 (b) of such a size that it delivers unit dis-charge at unit power
 (c) of such a size that it requires unit power per unit head
 (d) of such a size that it produces unit horse power with unit head
Ans.: d

Puck up the wrong statement about centrifugal pump:
 (a) discharge a diameter
 (b) head a speed 2
 (c) head a diameter
 (d) Power a speed 3
 (e) none of the above is wrong.
Ans.: a
A turbine pump is basically a centrifugal pump equipped additionally with:
 (a) adjustable blades
 (b) backward curved blades
 (c) vanned diffusion casing
 (d) inlet guide blades
 (e) totally submerged operation facility.
Ans.: c
Casting of a centrifugal pump is designed so as to minimize:
 (a) friction loss
 (b) cavitation
 (c) static head
 (d) loss of kinetic energy
 (e) starting time.
Ans.: d

In reaction turbine, draft tube is used:
 (transport water downstream without eddies
 (b) to convert the kinetic energy to flow energy by a gradual expansion of
the flow cross-section
 (c) for safety of turbine
 (d) to increase flow rate
 (e) none of the above (a) to (d).
Ans.: b
Guide angle as per the airfoil theory of Kaplan turbine blade design is defined as the
angle between:
 (a) lift and resultant force
 (b) drag and resultant force
 (c) lift and tangential force
 (d) lift and drag
 (e) resultant force and tangential force.
Ans.: a
Francis turbine is best suited for
 (a) medium head application from 24 to 180 m
 (b) low head installation up to 30 m
 (c) high head installation above 180 m
 (d) all types of heads
Ans.: a

The flow rate in gear pump:
(a) increases with increase in pressure
(b) decreases with increase in pressure
(c) more or less remains constant with in-crease in pressure
(d) unpredictable
Ans.: c
Impulse turbine is generally fitted:
(a) at the level of tail race
(b) little above the tail race
(c) slightly below the tail race
(d) about 2.5 m above the tail race to avoid cavitation
(e) about 2.5 m below the tail race to avoid cavitation.
Ans.: b
Francis, Kaplan and propeller turbines fall under the category of:
(a) Impulse turbines
(b) Reaction turbines
(c) Axial flow turbines
(d) Mixed flow turbines
(e) Reaction-cum-impulse turbines.
Ans.: b

Reaction turbines are used for:
 (a) low head
 (b) high head
 (c) high head and low discharge
 (d) high head and high discharge
 (e) low head and high discharge.
Ans.: e
The discharge through a reaction turbine with increase in unit speed:
 (a) increases
 (b) decreases
 (c) remains unaffected
 (d) first increases and then decreases
 (e) first decreases and then increases.
Ans.: b
The angle of taper on draft tube is:
 (a) greater than 15°
 (b) greater than 8°
 (c) greater than 5°
 (d) less than 8°
 (e) less than 3°.
Ans.: d

Specific speed for reaction turbines ranges from:
 (a) 0 to 4.5
 (b) 10 to 100
 (c) 80 to 200
 (d) 250 to 300
Ans.: b
In axial flow fans and turbines, fluid enters and leaves as follows:
 (a) radially, axially
 (b) axially, radially
 (c) axially, axially
 (d) radially, radially
 (e) combination of axial and radial.
Ans.: c
Which place in hydraulic turbine is most susceptible for cavitation
 (a) inlet of draft rube
 (b) blade inlet
 (c) guide blade
 (d) penstock
 (e) draft tube exit.
Ans.: a

48. Air vessels in reciprocating pump are used to
(a) smoothen flow
(b) reduce acceleration to minimum
(c) increase pump efficiency
(d) save pump from cavitation
(e) increase pump head.
Ans: b
49. Saving of work done and power by fitting an air vessel to single acting
reciprocating pump is of the order of
(a) 39.2%
(b) 49.2%
(c) 68.8%
(d) 84.8%
(e) 91.6%.
Ans: d
50. Saving of work done and power by fitting an air vessel to double acting
reciprocating pump is of the order of
(a) 39.2%
(b) 49.2%
(c) 68.8%
(d) 84.8%
(e) 91.6%.
Ans: a

51. According to fan laws, for fans having constant wheel diameter, the air or gas
capacity varies
(a) directly as fan speed
(b) square of fan speed
(c) cube of fan speed
(d) square root of fan speed
Ans: a
52. According to fan laws, for fans having constant wheel diameter, the pressure
varies
Ans: b
53. According to fan laws, for the fans having constant wheel diameters, the power
demand varies
Ans: c

According to fan laws, at constant speed and capacity, the pressure and power
vary:
 (a) directly as the air or gas density
 (b) inversely as square root of density
 (c) inversely as density
 (d) as square of density
 (e) as square root of density.
Ans.: a
According to fan laws, at constant pressure, the speed capacity and power vary:
Ans.: b
According to fan laws, at constant weight of air or gas, the speed, capacity and
pressure vary:
Ans.: c

Pressure intensifier increases the pressure in proportion to:
 (a) ratio of diameters
 (b) square of ratio of diameters
 (c) inverse ratio of diameters
 (d) square of inverse ratio of diameters
 (e) fourth power of ratio of diameters.
Ans.: b
A hydraulic accumulator normally consists of:
 (a) two cylinders, two rams and a storage device
 (b) a cylinder and a ram
 (c) two co-axial rams and two cylinders
 (d) a cylinder, a piston, storage tank and control valve
 (e) special type of pump with storage device and a pressure regulator.
Ans.: b
A hydraulic intensifier normally consists of:
 (a) two cylinders, two rams and a storage device
 (b) a cylinder and a ram
 (c) two co-axial rams and two cylinders
 (d) a cylinder, a piston, storage tank and control valve
 (e) special type of pump with storage device and a pressure regulator.
Ans.: c

Hydraulic accumulator is used for:
 (a) accumulating oil
 (b) supplying large quantities of oil for very short duration
 (c) generally high pressures to operate hydraulic machines
 (d) supplying energy when main supply fails
 (e) accumulating hydraulic energy.
Ans: d
Maximum impulse will be developed in hydraulic ram when:
 waste valve closes suddenly
 supply pipe is long
 supply pipe is short
 ram chamber is large
 supply pipe has critical diameter,
Ans:

Spray heads in an agricultural spraying system are to be supplied with water
through 500 ft of drawn aluminum tubing from an engine-driven pump. In its most
efficient operating range, the pump output is 1500 Gpm at a discharge pressure
not exceeding 65 psi (gauge). For satisfactory operation, the sprinklers must
operate at 30 psi (gauge) or higher pressure. Minor losses and elevation changes
may be neglected.
 Determine the smallest standard pipe size that can be used.

Pump
𝑃 ≤ 65 𝑝𝑠𝑖 "𝑔𝑎𝑔𝑒" 𝑃 ≥ 30 𝑝𝑠𝑖 "𝑔𝑎𝑔𝑒"
𝐿 = 500 𝑓𝑡
D
(1) (2)

Both tanks of Fig. 1 have a liquid depth “z”.
Tank (a) discharges a jet of diameter “D” through the rounded orifice from
whence it falls freely,
whereas tank (b) has a pipe with rounded entrance connected to it, and
after a length “L”, it discharges a jet also of diameter “D”.
 Which of the systems has the greater discharge through it? In
answering this question first compare the velocities and discharges at
points 1 and 2 in system (a) with the corresponding points in system (b).
 If the depth “z” in the tank of Fig. 1b is 5m, determine the maximum
length “L” of connecting pipe which may be used without the
occurrence of cavitation if the liquid is water at (a) 20°C; (b) 70°C. What
is the discharge in each case if the pipe diameter is 20 cm?

(a) Consider a large reservoir of diameter “D” filled with a liquid to a height “h” (see
Fig. 1). The reservoir is discharging through a pipe attached to its base. The pipe
has a length “L” and diameter “d”. The pressure on the liquid surface of
the reservoir is Pt and the pressure at the exit of the pipe is Pe. The exit flow
velocity is “Ve” ,
 Find an expression for the outlet velocity Ve at any instant of time as a function
of Pe – Pt, the liquid height h at any instant, and the pipe dimensions.
(Assume uniform flow at liquid surface and at the pipe discharge)
 A 4–in.–diameter pipe, 1000. ft long, is attached to a reservoir 30 ft below the
surface. The pipe has a sharp edged inlet. Take an average value of the friction
factor to be f = 0.032. Assuming that the head is maintained relatively constant,
find the steady-state value of the exit velocity.
 If the pipe has been closed off until t = 0, find the time after opening for the flow
velocity to reach 90 per cent of the steady-state velocity. The reservoir head is
again assumed to be constant.

A pump is to be used to provide water with a velocity 6.50 m. s-1 at
atmospheric pressure through a 7.5– cm. diameter pipe to a building 150 m
above sea level, the water coming from a reservoir at sea level (see
Figure).
 Determine the pump horsepower required. The density of water can be
taken as constant at 1000 kgm/ m3. Moreover, assume negligible
change in the internal energy of the water as it flows through the pipe.

Reservoir
Pump
150 m
See Level

1. The water surface profile for the flow d/s of a sluice gate in a channel with mild
slope is
a. M-1
b. M-2
c. M-3
2. At the control section, the depth is known
a. True
b. False
3. Subcritical flow always occurs when the
a. Depth of flow is less than the critical depth
b. Slope is mild
c. Depth is more than the critical depth
4. The standard step method aims to solve
a. The continuity equation
b. The energy equation
c. The momentum equation
d. None of the above

5. When the depth of water increases in the direction of flow then the surface
profile is classified as back water curve and when it decreases then it is called
as draw down curve.
a. True
b. Fals.
6.In a sustaining slope ‫منحدر‬ ‫يف‬
‫تدام‬‫مس‬
) ( the bottom slope is always
a) Zero
b) Negative
c) Positive
d) Goes from positive to negative.
7. When bottom slope is greater than critical slope the channel slope is termed as
a) Horizontal
b) Mild
c) Critical
d) Steep.
Answers:-
1(c) 2(a) 3(c) 4(a) 5(a) 6(c) 7(d)

A Pelton wheel is supplied with 0.035 m3/s of water
under a head of 92 m. The wheel rotates at 725 rpm and the velocity
coefficient of the nozzle is 0.95. The efficiency of the wheel is 82% and the
ratio of bucket speed to jet speed is 0.45. Determine the following:
1. Speed of the wheel,
2. Wheel to jet diameter ratio,
3. Dimensionless power specific speed of the wheel

Water is taken from a lake by a triangular channel, with side slope of
1V:2H. The channel has a bottom slope of 0.01, and a Manning’s
roughness coefficient of 0.014. The lake level is 2.0 m above the channel
entrance, and the channel ends with a free fall. Determine :
I. The discharge in the channel,
II. The water-surface profile and the length of it by using the direct
integration method.

2. The water-surface profile and the length of it by using the direct
integration method. • The water surface profile will be S-2 type, and the
depth of flow will change between the limits: 1.01y0≤y ≤ycr.

A triangular channel has an apex angle of 60° and carries a flow with a velocity of
2.0 m/s and depth of 1.25 m.
(a) Is the flow subcritical or supercritical?
(b) b) What is the critical depth?
(c) What is the specific energy?
(d) What is the alternate depth possible for this specific energy?
(yc = 1.148 m, E = 1.454 m, y = 1.06 m)

An undershot sluice controls the flow in a long rectangular channel of
width 2.5 m, Manning’s roughness coefficient n = 0.012 m3/ s and stream
wise slope 0.002. The depths of uniform flow upstream and downstream
of the gate are 1.8 m and 0.3 m, respectively.
(a) Assuming no losses at the sluice, find the volume flow rate, Q.
(b) Find the normal and critical depths in the channel.
(c) Compute the distance from the sluice gate to the hydraulic jump,
assuming normal depth downstream of the jump. Use two steps in
the gradually-varied-flow equation.

An undershot sluice is used to control the flow of water in a long wide
channel of slope 0.003 and Manning’s roughness coefficient 0.012 m3/ s.
The flow rate in the channel is 2 m3/ s per meter width.
(a) Calculate the normal depth and critical depth in the channel and show
that the channel is hydro dynamically “steep” at this flow rate.
(b) The depth of flow just downstream of the sluice is 0.4 m. Assuming no
head losses at the sluice calculate the depth just upstream of the
sluice.
(c) Sketch the depth profile along the channel, indicating clearly any flow
transitions brought about by the sluice and indicating where water
depth is increasing or decreasing.
(d) Use 2 steps in the gradually-varied flow equation to determine how far
upstream of the sluice a hydraulic jump will occur.

A long, wide channel has a slope of 1:2750 with a Manning’s n of 0.015 m –
1/3 s. It carries a discharge of 2.5 m 3 s –1 per meter width, and there is a
free overfall at the downstream end. An undershot sluice is placed a
certain distance upstream of the free overfall which determines the nature
of the flow between sluice and overfall. The depth just downstream of the
sluice is 0.5 m.
(a) Determine the critical depth and normal depth.
(b) Sketch, with explanation, the two possible gradually-varied flows
between sluice and overfall.
(c) Calculate the particular distance between sluice and overfall which
determines the boundary between these two flows. Use one step in the
gradually-varied-flow equation.

Physically, integration should start at a control point and proceed:
 Forward in ‘x’, if the flow is supercritical (upstream control)
C P Q
 Backward in ‘x’, if the flow is subcritical (downstream control). There
are two main classes of method:
Q

There are two main classes of method:
 :Standard-step methods: solve for depth ‘h’, at specified distance
intervals Δx.
 Direct-step methods:
solve for distance x at specified depth intervals “Δh”. (One advantage is
that they can calculate profiles starting from a critical point where (1 - 𝐹𝑒
2
=
0), and standard step methods would fail).
h1
h2
h3
h4
h5
ho
∆ 𝒉
∆ 𝒉
∆ 𝒙 ∆ 𝒙
∆ 𝒉

Examples solutions in open channel flow

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Examples solutions in open channel flow

Similar to Examples solutions in open channel flow (20)

More from Dr. Ezzat Elsayed Gomaa

More from Dr. Ezzat Elsayed Gomaa (20)

Recently uploaded

Recently uploaded (20)

Examples solutions in open channel flow