here is the video for an explanation of this slide ▶ https://youtu.be/QtuhyQ7grWA Fluid dynamics describes the flow of fluids. Here, we learn about Bernoulli's equation, impulse-momentum equation, venturi meter, orifice meter and so on. This slide is focused for examination purposes, what are all the questions and relevant concepts that can be expected in exams like GATE, ESE, PSUs

1. FLUID
DYNAMICS
10 Questions and
Answers EXPLAINED
Water Resources
Engineering series
MCQ, MSQ, NAT types

2. a) Change in the direction of flow
b) Non-uniform distribution of mass
c) Change in total energy
d) Change in mass rate of flow
Notes:
 Momentum can be written as β. ρ. A. vav
2 | 𝛽 =
1
𝐴𝑉2 𝐴
𝑣2 ⅆ𝐴
 β for uniform flow = 1 | turbulent flow = 1.2 | laminar flow = 1.33
 For velocity distribution
𝑣
𝑣𝑚
= 1 −
𝑟
𝑟0
𝑚
→ 𝛽 =
𝑚+2 2 𝑚+1
4 2𝑚+1
 Kinetic energy correction factor, 𝛼 =
1
𝐴𝑉3 𝐴
𝑣3 ⅆ𝐴
 α for ideal flow profile = 1.0 | turbulent flow = 1.03 to 1.06 | laminar
flow = 2 | parallel plate = 1.543
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3. a) 6.4 m/s
b) 9.0 m/s
c) 12.8 m/s
d) 25.5 m/s
Calculation:
 v = 2gh | h = x
ρm
ρ0
− 1 ∴ 𝑣 = 12.8 𝑚/𝑠
 When ρm < ρo, then h = x 1 −
ρm
ρ0
 Pitot tube: velocity of flow at particular point is reduced to zero (stagnation point), the
pressure there is increased due to conversion of kinetic energy to pressure energy;
increase in the pressure energy at this point is used to find velocity of flow.
 vactual = Cv 2gh | Cv = 0.98 for Pitot tube; 0.99 for Prandtl tube[curved streamlines]
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4. a)
k
k−1
p1
w1
+
v1
2
2g
+ z1 =
k
k−1
p2
w2
+
v2
2
2g
+ z2 + hL
b)
k
k−1
p1
w1
+
v1
2
2g
+ z1 =
k
k−1
p2
w2
+
v2
2
2g
+ z2
c)
k
k−1
p1
w1
+
v1
2
2g
+ z1 + Hm =
k
k−1
p2
w2
+
v2
2
2g
+ z2
d)
p1
w1
+
v1
2
2g
+ z1 + Hm =
p2
w2
+
v2
2
2g
+ z2 + hL
Notes:
 p ρk = c  compressible flow in adiabatic process
 Bernoulli’s equation for steady incompressible flow:
p1
ρg
+
v1
2
2g
+ z1 =
p2
ρg
+
v2
2
2g
+ z2 + hL
 For unsteady compressible flow,
ⅆ𝑝
𝜌
+
ⅆ𝑉
ⅆ𝑡
ⅆ𝑠 +
𝑉2
2
+ 𝑔𝑧 = 𝑐
 Assumptions: steady, incompressible, inviscid, stream line, no friction, pr. force & gravity
force, uniform velocity
 Newton’s eqn  Fa + Fp + Fv + Ft + Fc + Fσ | Reynold’s eqn  Fa + Fp + Fv + Ft |
 Navier-Stoke’s eqn  Fa + Fp + Fv | Euler eqn  Fa + Fp
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5. a) 600 N
b) Zero
c) 320 N
d) 450 N
Calculation:
 When there is no flow, the pressure at both sections is same
 Applying momentum equation, p1A1 – p2A2cosθ – Fx = ρQ(V2cosθ – V1)  Fx =
450N
 In x-direction, p1A1cosθ1 – p2A2cosθ2 – Fx = ρQ(V2cosθ1 – V1cosθ2)
 In y-direction, p1A1sinθ1 + p2A2sinθ2 + Fy – w = ρQ(– V2sinθ1 – V1sinθ2)
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6. a) 17.5 cm
b) 18.5 cm
c) 19.5 cm
d) 20.5 cm
Calculation:
 @section1 |
𝑝1
𝛾
+ 𝑥 + ℎ =
𝑝2
𝛾
+ 0.8 + 𝑥 + 𝑆ℎ [S – relative density of Hg]
 Q = AV = 0.12 m3/s | A1V1 = A2V2  V1 =1.6977 m/s & V2 = 6.79 m/s
 Bernoulli’s eqn @ 1 & 2,
𝑝1
𝛾
+
𝑣1
2
2𝑔
+ 𝑧1 =
𝑝2
𝛾
+
𝑣2
2
2𝑔
+ 𝑧2
 h = 17.5 cm
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7. a) 70 cm
b) 80 cm
c) 90 cm
d) 50 cm
Calculation:
 h1 = x1
ρm
ρ0
− 1 | x1 = 0.20 m | h1 = 3.2 m of oil
 Q1 = 0.16 cumecs | Q2 = 0.08 cumecs
 h2 = x2 1 −
ρm
ρ0
[here, manometric fluid is air] = 0.9985 x2 m of oil
 Q =
Cd.A.a. 2gh
A2−a2
→ Q ∝ h ∴ x2 = 80 cm of air
 Others: Orifice meter, nozzle meter
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8. a) Flow decreases in diverging portion and pressure
increases in d/s direction  adverse pressure gradient, if
it is large
b) Flow separation takes place, if it is large
c) Negative pressure is created at the throat which
obstructs the flow
d) None of these
Notes:
 In convergent cone, flow is accelerating which may be allowed to take place rapidly in
smaller length. While in divergent cone, retardation of flow occurs. If that retardation
takes place in smaller length, then flow separation takes place.
 Divergent portion is not used to calculate discharge.
 If c/s area of throat is so much reduced such that pressure falls below vapour pressure,
cavitation occurs.
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9. a) ½ of the original magnitude when it was full
b) ¼ if the original magnitude when it was full
c) Unchanged
d) zero
Notes:
 Surface will touch the bottom at centre
 Fundamental eqn of vortex flow: ⅆ𝑝 =
𝜌𝑣2
𝑟
ⅆ𝑟 − 𝜌𝑔 ⅆ𝑧
 Free vortex flow: Vr = C | Γ = 2πVr | 𝑧 = 𝑧0 −
1
2
𝑐2
𝑔𝑟2
 Forced cortex flow: V=ωr | 𝑧 − 𝑧0 =
𝜔2𝑟2
2𝑔
|
Vol. of paraboloid = vol. of initial air 
πR2
z
2
= πR2
H
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10. a)
x
2 yH
b)
2x
yH
c)
x
yH
d)
x
4 yH
Notes:
 Jet distance measurement method
 Coefficient of velocity is defined as the ratio of Actual velocity of jet
at vena-contracta to the theoretical velocity.
 Coefficient of contraction is defined as the ratio of the area of jet at
Vena contracta to the area of orifice (theoretical area)
 Cd = Cv x Cc | function of d/D
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11. a) 154 lps
b) 145 lps
c) 541 lps
d) 415 lps
Calculation:

p1
ρg
+ z1 −
p2
ρg
+ z2 = ∆h | ∆h = x
Sm
S
− 1 | x = 0.3m
 Q =
Cd.A.a. 2gh
A2−a2
=
Cda2 2g ∆h
1− D2 D1
4
= 154 lps
 ∆z = z2 – z1 = 0.45sin30o = 0.225 m
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