# Fluid Mechanics Questions and Answers – Continuity Equation in Two and Three Dimensions

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This set of Fluid Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Continuity Equation in Two and Three Dimensions”.

1. The continuity equation is based on the premise of-
a) Law of conservation of energy
b) Law of conservation of mass
c) Law of conservation of momentum
d) None of the mentioned

Explanation: Continuity equation is based on the the principle of conservation of mass.

2. The continuity equation is only applicable to incompressible fluid.
a) True
b) False

Explanation: The continuity equation is only applicable to incompressible as well as compressible fluid.

3. For incompressible fluid flow, if area reduces then what is the effect on the velocity.
a) increases
b) decreases
c) first increases then decreases
d) first decreases then increases

Explanation: According to continuity equation,
Area × velocity = constant
Hence, as area decreases velocity increases.
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4. For compressible fluid flow in a pipe, having decrease in specific gravity what will be the effect of decrease in diameter?
a) It will cause increase in velocity
b) It will cause decrease in velocity
c) It remains constant
d) None of the mentioned

Explanation: According to continuity equation,
ρ*A*v = constant
Hence, as density and area decreases velocity is bound to increase.

5. What is the most common assumption while dealing with fluid flow problems using continuity equation?
a) Flow is assumed to be compressible
b) Flow is assumed to be unsteady
c) Flow is assumed to be steady
d) Flow is assumed to be turbulent

Explanation: In majority of the fluid flow problems, flow is assumed to be steady.

6. The diameters of a pipe at the sections 1 and 2 are 8 cm and 13 cm respectively. Find the discharge through pipe if the velocity of water flowing through the pipe at section 1 is 6 m/s. Determine also the velocity at section 2.
a) 2.27 m/s
b) 4.54 m/s
c) 1.13 m/s
d) 3.25 m/s

Explanation: According to continuity equation,
Area × velocity = constant
Area1*Velocity1 = Area2*Velocity2
Velocity2=(Area1*Velocity1)/Area2
= (82 * 6) / 132=2.27 m/s.

7. The continuity equation can only be used for analysis of conserved quantity.
a) True
b) False

Explanation: Continuity equation is defined on a control volume and hence, is applicable only to Conserved quantities.

8. The diameter of a pipe at the section 1 is 9 cm. If the velocity of water flowing through the pipe at section 1 is 4.8 m/s and section 2 is 9 m/s, Determine the area at section 2.
a) 33.93 m2
b) 67.86 m2
c) 16.96 m2
d) 38.66 m2

Explanation: According to continuity equation,
Area × velocity = constant
Area1*Velocity1 = Area2*Velocity2
(Area1*Velocity1)/Velocity2=Area2
Area 2= 33.93 m2.

9. For a flow to be physically possible it must primarily satisfy which equation?
a) Equation of conservation of energy
b) Equation of conservation of mass or continuity equation
c) Equation of conservation of momentum
d) None of the mentioned

Explanation: Fluid flow must satisfy equation of conservation of mass or continuity equation, for itto be physically possible.

10. Continuity equation can also be derived for polar coordinate system
a) True
b) False

Explanation: Continuity equation in polar coordinate is also used for analysis.

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