FM chapter-7.pdf

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CHAPTER- 7 FLUID DYNAMICS
• It is the study of flow of fluid along with the forces responsible for it.
• Hence, Newton’s second law of motion ( Ԧ
𝐅 = 𝐦𝐚) is used to analyze dynamic
behavior of fluid flow.
• In the fluid flow, various forces acting on it are as follows:
❑ Gravity force
❑ Pressure force
❑ Viscous force
❑ Turbulent force
❑ Force due to compressibility
❑ Force due to surface tension
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NOTE: 1. When all forces are taken into account, the equation of motion is termed
as “Newtonian equation of motion”.
2. When compressibility and surface tension is neglected, it is termed as “Reynold’s
equation of motion”.
3. When compressibility, surface tension and force due to turbulence is neglected
(i.e. only gravity, pressure and viscous force is considered), the equation is termed
as “Navier Stokes equation”.
4. When only gravity and pressure forces are considered, it is termed as “Euler’s
equation of motion”.
(It will be used in dynamics for analysis of fluid flow).
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BERNOULLI’S EQUATION
• It is based on “conservation of energy”.
• It is obtained by integration of Euler’s equation of motion, along a streamline
under steady incompressible flow.
As per Newton’s second law of motion, σ 𝐅𝐬 = 𝐦𝐚𝐬
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Euler’s equation of motion: P dA − P + dP dA − W sinθ = mas
−dP dA − γwdV sinθ = ρwdV
dvs
dt
−dP dA − γwdA ds sinθ = ρwdA ds ×
𝜕v
𝜕s
ds
dt
+
𝜕v
𝜕t
dt
dt
For steady flow,
𝜕v
𝜕t
= 0
−dP − γwds sinθ = ρwds vs
𝜕v
𝜕s
𝐯𝐬𝐝𝐯 + 𝐠 𝐝𝐲 +
𝐝𝐏
𝛒𝐰
= 𝟎
After integrating,
𝐯𝟐
𝟐
+ 𝐠𝐲 + න
𝐝𝐏
𝛒𝐰
= 𝟎
For incompressible fluid, ρw = constant
𝐏
𝛒𝐰
+ 𝐠𝐲 +
𝐯𝟐
𝟐
= 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭
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NOTE: 1. The value of constant in above equation is same along a stream line.
However, if flow is irrotational, the value of constant is same along all the
streamlines.
(i) If flow is rotational, C1 = C2 ≠ C3
P1
ρw
+ gy1 +
v1
2
2
=
P2
ρw
+ gy2 +
v2
2
2
≠
P3
ρw
+ gy3 +
v3
2
2
(i) If flow is irrotational, C1 = C2 = C3
P1
ρw
+ gy1 +
v1
2
2
=
P2
ρw
+ gy2 +
v2
2
2
=
P3
ρw
+ gy3 +
v3
2
2
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2. While analyzing Bernoulli’s equation, only gravity and pressure forces are
considered, hence if any other force except these two is present in the system, then
this equation will not be applicable.
For example:
(i) It is not applicable for long narrow flow passage as viscosity would also be
there.
(ii) It is not applicable beyond Mach number ≥ 0.3, as compressibility would also
be there.
(iii) It is not applicable in diverging flow section as flow separation and energy
losses takes place.
(iv) It is not applicable in flow section that involves fan and turbine or any other
mechanical unit as it involves energy loss and gain or work transfer.
(v) It is not applicable in flow section that involves temperature change as
compressibility comes in picture.
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Q. Bernoulli’s equation is applicable for
a) Viscous and compressible fluid flow
b) Inviscid and compressible fluid flow
c) Inviscid and incompressible fluid flow.
d) Viscous and incompressible fluid flow
[GATE: 2018]
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Q. Bernoulli’s equation is an equation of:
a) Conservation of mass
b) Conservation of linear momentum
c) Conservation of energy.
d) Conservation of angular momentum
[GATE: 1992]
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DIFFERENT FORMS OF BERNOULLI’S EQUATION
Different energy terms in the Bernoulli’s equation can be reported in the following
forms:
a) Per unit mass:
𝐏
𝛒
+
𝐯𝟐
𝟐
+ 𝐠𝐲 = 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭 (𝐂)
Pressure energy
mass
Kinetic energy
mass
Potential energy
mass
b) Per unit weight:
𝐏
𝛄
+
𝐯𝟐
𝟐𝐠
+ 𝐲 = 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭 (𝐂)
Pressure energy
mass
Kinetic energy
mass
Potential energy
mass
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c) Pressure:
𝐏 +
𝛒𝐯𝟐
𝟐
+ 𝛄𝐲 = 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭 𝐂
Where, P = static pressure (actual pressure in fluid)
ρv2
2
= dynamic pressure (pressure developed when fluid in motion is brought to rest)
γy = hydrostatic pressure (pressure due to weight of fluid)
NOTE: 1. Here, sum of static pressure (P) and dynamic pressure (
ρv2
2
) is termed as
“stagnation pressure”.
𝐏𝐬𝐭𝐚𝐠𝐧𝐚𝐭𝐢𝐨𝐧 = 𝐏 +
𝛒𝐯𝟐
𝟐
Measurement of stagnation pressure helps in finding the velocity in any system
(pipe flow).
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v = 2
[Pstagnation − P]
ρ
2. Here, sum of static pressure and hydrostatic pressure is termed as “piezometric
pressure”.
𝐏𝐩𝐢𝐞𝐳𝐨𝐦𝐞𝐭𝐫𝐢𝐜 = 𝐏 + 𝛄𝐲
Piezometric head h =
Piezometric pressure
γw
=
P + γy
γ
=
P
γ
+ y
3. Absolute level of water in piezometer indicates pressure head (static), but if level
of water in piezometer is measure from datum, it is termed as “piezometric head”.
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4. Piezometric head is constant at all the depth at a particular section, if stream lines
(pipe) are straight, but if stream lines (pipe) are curved, the piezometric head will
vary across the depth at a particular section.
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NOTE: In real situation, where energy transfer (i.e. energy gain and loss) and head
loss takes place, the Bernoulli’s equation can be modified as follows:
𝐏𝟏
𝛄
+
𝐯𝟏
𝟐
𝟐𝐠
+ 𝐲𝟏 + 𝐄𝐠𝐚𝐢𝐧 =
𝐏𝟐
𝛄
+
𝐯𝟐
𝟐
𝟐𝐠
+ 𝐲𝟐 + 𝐄𝐥𝐨𝐬𝐬 + 𝐡𝐟
Where,
Egain = gain of energy
Eloss = loss of energy
hf = head loss due to friction
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Q. In a Bernoulli’s equation used in pipe flow, each term represents
a) Energy per unit weight.
b) Energy per unit mass
c) Energy per unit volume
d) Energy per unit flow length
[GATE: 2001]
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Q. Water flows steadily down in a vertical pipe of constant cross- section.
Neglecting friction, according to Bernoulli’s equation,
a) Pressure is constant along the length of the pipe
b) Velocity decreases with height
c) Pressure decreases with height.
d) Pressure increases with height
[GATE: 1996]
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CORRECTION FACTORS
• While analyzing Bernoulli’s equation, fluid is considered to be ideal, hence,
velocity is taken to be constant across the section, but in real, velocity varies
across the section.
• Hence, if we want to calculate actual kinetic energy in terms of average velocity, a
factor ‘α’ termed as “kinetic energy correction factor” is to be used along it.
α
1
2
mvavg
2 =
1
2
mvactual
2
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α =
Actual Kinetic Energy
Average Kinetic Energy
K.E. of elemental area = dKE =
1
2
dmv2 =
1
2
ρdAv v2 =
1
2
ρdAv3
Total K.E. = ‫׬‬ dKE = ‫׬‬
1
2
ρdAv3
=
1
2
ρ ‫׬‬ v3
dA … … … … . . (i)
Total K.E. using average velocity =
1
2
ρAvavg
2 α … … … … . . (ii)
From (i) and (ii),
1
2
ρAvavg
2 α =
1
2
ρ ‫׬‬ v3dA
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𝛂 =
‫׬‬ 𝐯𝟑
𝐝𝐀
𝐀𝐯𝐚𝐯𝐠
𝟐
To find vavg, use continuity equation
Q = A vavg = ‫׬‬ v dA
vavg =
‫׬‬ v dA
A
Hence, Bernoulli’s equation using K.E. correction factor is:
P
γ
+ α
v2
2g
+ y = constant
A similar parameter, termed as “momentum correction factor (β)” is defined in
momentum equation.
β mvavg = න dm v
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β ρAvavg vavg = න ρdAvactual v
𝛃 =
‫׬‬ 𝐯𝟐
𝐝𝐀
𝐀𝐯𝐚𝐯𝐠
𝟐
Here also, vavg =
‫׬‬ v dA
A
NOTE: 1. For laminar flow condition:
(i) In circular pipe, α =2
(ii) In parallel plates, α = 1.543
2. For turbulent flow condition, in circular pipe, α = 1.03 – 1.06
3. For ideal flow condition, for all pipes, α = 1
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Q. If the velocity distribution is rectangular, the kinetic energy correction factor is
a) Greater than zero, but less than unity
b) Less than zero
c) Equal to zero
d) Equal to unity.
[GATE: 1990]
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Q. Statement (I): Bernoulli’s equation is applicable to any point in the flow field
provided the flow is steady and irrotational.
Statement (II): The integration of Euler’s equation of motion to derive Bernoulli’s
equation involves the assumptions that velocity potential exists and that the flow
conditions do not change with time at any point.
a) Both statement (I) and statement (II) are individually true, and statement (II) is
the correct explanation of statement (I).
b) Both statement (I) and statement (II) are individually true, but statement (II) is
NOT the correct explanation of statement (I)
c) Statement (I) is true; but statement (II) is false
d) Statement (I) is false; but statement (II) is true
[IES: 2018]
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APPLICATION OF BERNOULLI’S
EQUATION
A. VENTURIMETER
• It is a device used to find out discharge through a pipeline.
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• Working principle of venturimeter includes reduction in area at throat, that
results in increase in velocity in steady flow, which further causes decrease in
pressure, the value of which gives the discharge in pipe.
Applying Bernoulli’s equation at section 1 and 2,
P1
γ
+ y1 +
v1
2
2g
=
P2
γ
+ y2 +
v2
2
2g
P1
γ
+ y1 −
P2
γ
+ y2 =
v2
2
− v1
2
2g
= h
Where, h = piezometric head difference =
v2
2−v1
2
2g
h =
Q
a2
2
−
Q
a1
2
2g
𝐐 =
𝐚𝟏𝐚𝟐 𝟐𝐠𝐡
𝐚𝟏
𝟐
− 𝐚𝟐
𝟐
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• In above expression, theoretical discharge losses are not being considered, hence,
actual discharge is given by:
Qactual = Cd Qtheoretical
Where, Cd = co- efficient of discharge which accounts for losses in pipe section
𝐐𝐚 =
𝐂𝐝𝐚𝟏𝐚𝟐 𝟐𝐠𝐡
𝐚𝟏
𝟐
− 𝐚𝟐
𝟐
… … … … … … . (𝐀)
Here,
𝐚𝟏𝐚𝟐 𝟐𝐠
𝐚𝟏
𝟐−𝐚𝟐
𝟐
= 𝐊 = Venturi constant
𝐐𝐚 = 𝐂𝐝𝐊 𝐡
To compute Cd, losses can be considered in energy equation:
P1
γ
+ y1 +
v1
2
2g
=
P2
γ
+ y2 +
v2
2
2g
+ hL
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P1
γ
+ y1 −
P2
γ
+ y2 − hL =
v2
2
− v1
2
2g
Since
P1
γ
+ y1 −
P2
γ
+ y2 = h
𝐐𝐚𝐜𝐭𝐮𝐚𝐥 =
𝐚𝟏𝐚𝟐 𝟐𝐠(𝐡 − 𝐡𝐋)
𝐚𝟏
𝟐
− 𝐚𝟐
𝟐
… … … … (𝐁)
Qactual =
Cda1a2 2gh
a1
2
− a2
2
=
a1a2 2g(h − hL)
a1
2
− a2
2
𝐂𝐝 =
𝐡 − 𝐡𝐋
𝐡
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• In Venturimeter, gradual contraction and expansion is ensured to avoid flow
separation, hence:
a) a2 can be taken as complete area of throat
NOTE: Here, reduction in area of flow is expressed in terms of co- efficient of
contraction (Cc).
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b) Losses due to eddy formation does not takes place (hence, value of Cd is
comparatively more (around 0.98)).
• Since tendency of flow separation is more during expansion than contraction,
angle of divergence (5.6o) is kept less than angle of convergence (22o), and this
portion is not used for discharge measurement.
• Cross- sectional area of throat cannot be reduced beyond a certain limit, as
pressure may fall below vapor pressure leading to cavitation, hence,
𝐝𝟐 =
𝟏
𝟑
−
𝟑
𝟒
𝐝𝟏
Where, d2 = diameter of throat, d1 = diameter of pipe
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Q. Venturimeter is advantageous because:
a) It has much smaller head loss
b) Its co- efficient of discharge is more than for an orifice meter
c) Its accuracy is quite good
d) All of the above.
[SSC: 2009]
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INCLINED VENTURIMETER WITH
DIFFERENTIAL MANOMETER
Case (i): GM (G2) > GL (G1)
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Using Pascal’s law, PC = PD
PA + G1γwx1 = PB + G1γwx2 + G2γwx
PA
γw
−
PB
γw
= G1x2 + G2x − G1x1
PA
G1γw
+ ya −
PB
G1γw
+ yb = x2 +
G2
G1
x − x1 + ya − yb
Where, h =
G2
G1
x − x
𝐡 =
𝐆𝟐
𝐆𝟏
− 𝟏 𝐱 = 𝐏𝐢𝐞𝐳𝐨𝐦𝐞𝐭𝐫𝐢𝐜 𝐡𝐞𝐚𝐝 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐜𝐞
𝐐 =
𝐂𝐝𝐚𝟏𝐚𝟐 𝟐𝐠
𝐆𝟐
𝐆𝟏
− 𝟏 𝐱
𝐚𝟏
𝟐
− 𝐚𝟐
𝟐
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Case (ii): GM (G2) < GL (G1)
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Using Pascal’s law, PC = PD
PA − G1γwx1 = PB − G1γwx2 − G2γwx
PA
γw
−
PB
γw
= G1x1 − G2x − G1x2
PA
G1γw
+ ya −
PB
G1γw
+ yb = x1 −
G2
G1
x − x2 + ya − yb
Where, h = 𝑥 −
G2
G1
x
𝐡 = 𝐱 𝟏 −
𝐆𝟐
𝐆𝟏
= 𝐏𝐢𝐞𝐳𝐨𝐦𝐞𝐭𝐫𝐢𝐜 𝐡𝐞𝐚𝐝 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐜𝐞
𝐐 =
𝐂𝐝𝐚𝟏𝐚𝟐 𝟐𝐠 𝟏 −
𝐆𝟐
𝐆𝟏
𝐱
𝐚𝟏
𝟐
− 𝐚𝟐
𝟐
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Q. Statement (I): When flow through a pipeline is measured through fixing a
venturimeter, the computed flow will not be sensitive to the alignment of the centre
line of the set- up (horizontal or sloping, up or down), along the flow direction.
Statement (II): The difference in the readings of the manometer limbs is by itself
always adjusted for the ratio of the densities of the two liquids- the manometer
liquid and the liquid whose flow rate is being measured- in the development of the
formula for computing the discharge
a) Both statement (I) and statement (II) are individually true, and statement (II) is
the correct explanation of statement (I).
b) Both statement (I) and statement (II) are individually true, but statement (II) is
NOT the correct explanation of statement (I)
c) Statement (I) is true; but statement (II) is false
d) Statement (I) is false; but statement (II) is true
[IES: 2017]
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Q. The co- efficient of discharge for venturimeter (Cd) ranges from
a) 0.50 – 0.55
b) 0.61 – 0.69
c) 0.95 – 0.99.
d) 0.61 – 0.65
[SSC: 2018]
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Q. A venturimeter has a differential mercury water manometer connected to its inlet
and throat for a given discharge in the pipe
a) Is independent of the orientation of venturimeter.
b) Depends on the orientation of venturimeter
c) Varies with the slope of the venturimeter with respect to horizontal
d) None of these
[SSC: 2007]
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B. ORIFICEMETER
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• It is used to measure discharge through pipe.
• In this case, a circular plate, with concentric sharp- edged hole is installed in a
pipe such that the plate is perpendicular to the axis of pipe.
• It is comparatively cheaper than venturimeter, as its size is comparatively smaller,
hence it finds its application if there is space restriction.
• As flow separation takes place in this case, head losses are more, which also
results in lower value of Cd = 0.6.
NOTE: 1. The region where flow area is minimum is termed as “Vena Contracta”
(VC).
2. As it is difficult to find the area (a2) at vena contracta, it is expressed in terms of a
parameter, called co- efficient of contraction (Cc).
𝐂𝐜 =
𝐚𝟐
𝐚𝐨
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Applying Bernoulli’s equation at section 1 and 2:
P1
γ
+ y1 +
v1
2
2g
=
P2
γ
+ y2 +
v2
2
2g
= h
Q
a2
2
−
Q
a1
2
= 2gh
Q =
a1a2 2gh
a1
2
− a2
2
Q =
Cca1ao 2gh
a1
2
− [ ao
2
Cc]2
Qactual = Cd Qtheoretical
𝐐𝐚𝐜𝐭𝐮𝐚𝐥 =
𝐂𝐝𝐚𝟏𝐚𝐨 𝟐𝐠𝐡
𝐚𝟏
𝟐
− 𝐚𝐨
𝟐
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NOTE:
Co- efficient of discharge = co- efficient of contraction × co- efficient of velocity
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𝐐𝐚 =
𝐂𝐝𝐚𝟏𝐚𝐨 𝟐𝐠𝐡
𝐚𝟏
𝟐
− 𝐚𝐨
𝟐
• If area of flow is not reduced after passing through orifice, i.e. ao = a2, i.e. Cc = 1
and Cd = Cv.
• At Vena Contracta, streamlines are straight, hence piezometric head is constant
throughout the section.
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Q. The discharge co- efficient (Cd) of an orifice meter is:
a) Greater than Cd of a venturimeter
b) Smaller than the Cd of a venturimeter.
c) Equal to the Cd of a venturimeter
d) Greater than one
[GATE: 1998]
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C. NOZZLEMETER
• The nozzle meter is a truncated form of venturimeter, without diverging portion.
• It is simply a contraction, with well- rounded entrance placed in the pipe line.
• It is simpler than venturimeter.
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D. ELBOWMETER
• It is also used to measure discharge in pipe.
• It is based on the principle that when liquid moves along pipe bend, it follows
“free vortex” condition.
i.e. vR = constant (C)
𝐯 =
𝐂
𝐑
Since R1>R2, v1 < v2
From energy conservation,
P1 > P2
Qact = CdA 2gh (A= area of pipe)
h = x
G2
G1
− 1
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Q. Which of the following parameter is measured with the help of elbow meter?
a) Acceleration
b) Velocity
c) Viscosity
d) Discharge.
[SSC: 2017]
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E. PITOT TUBE
• It is used to measure velocity of fluid, when section of pipe is straight.
• Difference in reading of pitot tube and piezometer (h) is noted, which indicates the
velocity head.
h =
vB
2
2g
vB = 2gh
vactual = Cv vB = Cv 𝟐𝐠𝐡
Cv = 0.98 (for pitot tube)
NOTE: Anemometer is used to measure air/ gas velocity.
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F. PITOT- STATIC TUBE/ PRANDTL TUBE
• This is also used to measure velocity at a point in fluid flow (specially when
stream lines are curved).
• As, if stream lines are curved, the piezometric head is not constant throughout the
section, hence, in such case, it is necessary to find out the piezometric head at
same point at which velocity is to be measured.
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• Hence, Prandtl tube/ pitot static tube is used in this case, as it satisfies the above
purpose.
• The front portion of this tube is rounded to avoid separation of flow and on it,
shaft holes are provided at certain distance, where stream lines become parallel.
v2
2g
= h
𝐯 = 𝟐𝐠𝐡
Vact = Cv v = Cv 𝟐𝐠𝐡
Where, Cv = 0.99
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Q. Pitot tube is used to measure
a) Static pressure of a flowing fluid
b) Dynamic pressure of a flowing fluid
c) Total pressure of a flowing fluid.
d) Surface tension of a flowing fluid
[GATE: 1992]
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Q. The pitot- static tube measures
a) Static pressure
b) Dynamic pressure
c) Difference in static and dynamic pressure
d) Difference in total and static pressure.
[GATE: 1989]
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MOMENTUM EQUATION AND ITS
APPLICATION
• Momentum is a vector quantity and its direction is given by the direction of
velocity.
• To apply the momentum equation for a flowing fluid, we have to consider the
volume of fluid, termed as “control volume”.
• Control volume is selected in such a way that force needed to calculate becomes
the external force to the control volume.
• According to momentum equation,
Net force on C.V. in given direction (σ 𝐅) = Change in momentum flux in same direction (
∆𝐦𝐯
𝐭
)
σ F= [momentum flux going out of C.V. in given direction]-[momentum flux
coming into the C.V. in given direction]
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෍ 𝐅 = 𝛃𝟐𝛒𝐐𝐯𝟐 − 𝛃𝟏𝛒𝐐𝐯𝟏
• The above equation is valid for steady flow only.
• If flow is unsteady, add one more term
d(mv)
dt
on R.H.S.
Where, m = mass of fluid in C.V.
v = velocity of C.V. in given direction
mv = momentum of C.V. in given direction
v2 and v1 are velocity component for outgoing fluid and incoming fluid in given
direction
NOTE: 1. v2 and v1 can be absolute velocity or relative velocity.
2. Velocity w.r.t. ground is “absolute velocity” and velocity w.r.t. some other
reference is termed as “relative velocity”.
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APPLICATION OF MOMENTUM EQUATION
• According to this, net torque on fluid in any direction equals to change of angular
momentum flux in same direction.
• It find its application in sprinkler problems:
a) Discharging arm in same direction
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u1 and u2 are relative velocity of jet at points 1 and 2 (i.e. velocity of jet w.r.t.
sprinkler)
v1 and v2 are absolute velocity of jet at points 1 and 2
ωr1 and ωr2 are absolute velocity of sprinkler at points 1 and 2
Torque on jet in ACW direction = ρQ1v1r1 − ρQ2v2r2 − [0]
T = ρ A1u1 v1r1 − ρ(A2u2)v2r2
v1 = u1 + ωr1; v2 = u2 − ωr2
𝐓 = 𝛒 𝐀𝟏𝐮𝟏 (𝐮𝟏 + 𝛚𝐫𝟏)𝐫𝟏 − 𝛒(𝐀𝟐𝐮𝟐)(𝐮𝟐 − 𝛚𝐫𝟐) 𝐫𝟐
Also, torque applied by jet on sprinkler is same in magnitude but opposite in
direction.
NOTE: If sprinkler is frictionless, torque, T = 0
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b) Discharging arm in opposite direction
Torque on jet in ACW direction = Torque going out - torque coming in
= ρQ1v1r1 − ρQ2v2r2 − [0]
T = ρ A1u1 v1r1 − ρ(A2u2)v2r2
v1 = u1 + ωr1; v2 = −(u2 + ωr2)
𝐓 = 𝛒 𝐀𝟏𝐮𝟏 𝐮𝟏 + 𝛚𝐫𝟏 𝐫𝟏 + 𝛒(𝐀𝟐𝐮𝟐)(𝐮𝟐 + 𝛚𝐫𝟐) 𝐫𝟐
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Q. Which of the following pairs are correctly matched?
a) 1, 2 and 3 only
b) 1, 3 and 4 only.
c) 2, 3 and 4 only
d) 1, 2, 3 and 4
[IES: 2012]
1. Piezometric head Sum of datum head and pressure head
2. Dynamic head Sum of datum head and velocity head
3. Stagnation head Sum of piezometric head and velocity head
4. Total head Sum of piezometric head and dynamic head
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Q. A fire hose has a nozzle attached to it, and the nozzle discharges a jet of water
into the atmosphere at a velocity of 20m/s. This causes the joint of the nozzle with
the hose to be in:
a) Tension.
b) A state of zero stress
c) Compression
d) Bending stress
[IES: 2011]
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Q. Match List- I with List- II and select the correct answer using the code given
below the lists:
Codes: A B C D
a) 4 1 2 3
b) 2 3 4 1.
c) 4 3 2 1
d) 2 1 4 3
[IES: 2005]
List -I List - II
A. Equation of motion along a streamline 1. Principle of moment of momentum
B. Euler’s equation 2. Bernoulli’s equation
C. Pressure exerted by a free jet 3. equation for conservation of momentum
D. Rotating lawn sprinkler 4. Momentum equation
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Q. Assertion (A): Pressure intensity in a liquid flow is a form of energy
Reason (R): The pressure gradient is a measure of the rate of energy dissipation in
steady uniform flow
a) Both Assertion (A) and Reason (R) are individually true, and (R) is the correct
explanation of (A).
b) Both Assertion (A) and Reason (R) are individually true, but (R) is NOT the
correct explanation of (A)
c) (A) is true; but (R) is false
d) (A) is false; but (R) is true
[IES: 1997]
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Q. Match List- I (Device) with List- II (Use) and select the correct answer using the
codes given below:
Codes A B C D
a) 1 2 4 3
b) 2 1 3 4
c) 2 1 4 3.
d) 4 1 3 2
[GATE: 2010]
List - II List- II
A. Pitot tube 1. Measuring pressure in a pipe
B. Manometer 2. Measuring velocity of flow in a pipe
C. Venturimeter 3. Measuring air and gas velocities
D. Anemometer 4. Measuring discharge in a pipe
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Q. Speed of a submarine can be measured by-
a) Pitot tube.
b) Hot wire anemometer
c) Pirani gauge
d) Inclined manometer
[SSC: 2016]
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Q. Energy loss in flow through nozzle as compared to venturimeter is
a) Same
b) More.
c) Less
d) Unpredictable
[SSC: 2016]
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