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# UPPSC Lec’21 ME: Daily Practices Quiz. 24-Nov-2021

Quiz: Mechanical Engineering
Exam: UPPSC AE/Lecturer
Topic: Fluid Mechanics

Each question carries 3 marks
Negative marking: 1 mark
Time: 8 Minutes

Q1. If stream function of a fluid flow is Ψ = 2xy, then the velocity of x-component at a point (-1, -2) is equal to _____
(a) -2
(b) -4
(c) 2
(d) 4

Q2. If “dl” is a directed fluid element and V is the velocity of that fluid element, then the equation, (dl) ⃗ × V ⃗ = 0 refers to a
(a) Pathline
(b) Timeline
(c) Streakline
(d) Streamline

Q3. Which one of the following must be the equation of velocity potential function?
(a) φ=lnx
(b) φ=2cosx
(c) φ=2xy
(d) φ=2(x^2+y^2)

Q4. Which one of the following is the correct statement “If streamline function exists for a fluid flow”?
1. It must satisfy continuity equation
2. Flow is only 2D
3.Flow can be rotational or irrotational
(a) Only 2 and 3
(b) Only 1 and 3
(c) Only 1 and 2
(d) All of the above

Q5. Consider the following statements:
1. Stream lines and path lines are instantaneous lines
2. Path lines and streak line are generated by passage of time
3. Path line can be found by time exposure of a marked particle
4. Stream lines, path lines and streak lines are identical in steady flow
Which of the above statements are correct?
(a) 1, 2 and 3 only
(b) 2, 3 and 4 only
(c) 1 and 4 only
(d) 1, 2, 3 and 4

Q6. For laminar flow in a circular pipe, the numerical value of momentum correction factor is _____.
(a) less than 1
(b) 1.03
(c) 1.33
(d) 2

Solutions

S1. Ans. (a)
Sol. We know that, u=dΨ/dy and v=(-dΨ)/dx
Where u and v are velocity of x and y-component
u=dΨ/dy=2x=2×-1=-2
v=(-dΨ)/dx=-2y=-2×-2=4

S2. Ans. (d)
Sol. As we know that, the streamline velocity is tangential to streamline curve. So, velocity V and dl are parallel to each other and both are vector quantity.
If two vectors are parallel then their cross product is zero.
So, streamline is the correct answer.

S3. Ans. (c)
Sol. Velocity potential function φ exists only for irrotational flow i.e., it must satisfy Laplace equation.
Laplace equation is given by
(∂^2 φ)/(∂x^2 )+(∂^2 φ)/(∂x^2 )=0
(∂^2 (2xy))/(∂x^2 )+(∂^2 (2xy))/(∂x^2 )=0+0=0
So, only, φ=2xy satisfied the above Laplace equation.

S4. Ans. (d)
Sol. Streamline function exists for
2D, incompressible flow
It must satisfy continuity equation
Flow can be rotational or irrotational
If it satisfies Laplace equation then the flow must be irrotational

S5. Ans. (b)
Sol.
Stream line is an imaginary line that drawn in such a way that the tangent to it represent the direction of velocity vector at every point in the flow for a given instant.
Path line is the line traced by a single fluid particle during its motion.
Streak line concentrated on fluid particles that have gone through a fixed point.
Path lines and streak line are generated by passage of time.
Path lines can be found by time exposure of a marked particle.
Stream lines, path lines and streak line are identical for the case of steady flow.

S6. Ans. (b)
Sol. For laminar flow through circular pipe
Energy correction factor = 2
Momentum correction factor = 4/3 = 1.33

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