# Fluid Mechanics Questions and Answers – Velocity and Acceleration

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This set of Fluid Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Velocity and Acceleration”.

1. The velocity vector in a fluid is given V=5x4+3y2+2z( in metre/sec). What is the acceleration of it at point (1,3,4) ?
a) 40 m/s2
b) 20 m/s2
c) 60 m/s2
d) 80 m/s2

Explanation: By differentiating V=5x42+2z, the acceleration obtained is V=20x3+6y+2.
on putting the coordinates, the acceleration obtained is 40 m/s2.

2. Determine the third velocity component such that continuity equation is satisfied if two components are u=2y2, w=2xyz.
a) -2xy+x2y+f(y,z)
b) 4xy-x2y+f(y,z)
c) -4xy-x2y+f(y,z)
d) -2xy-x2y+f(y,z)

Explanation: The continuity equation for incompressible is du/dx+dv/dy+dw/dz = 0.
Here du/dx=0 and w=2xy.
On solving by integrating, we get v = -4xy-x2y+f(y,z).

3. Determine the third velocity component such that continuity equation is satisfied if two components are u=x2+y2+z2, v=xy2 – yz2 + xy
a) -3xz-2xyz+z2/3+f(y,z)
b) -3xz+2xyz+z3/3+f(y,z)
c) -3xz-2xyz+z3/3+f(x,z)
d) -3xz-2xyz+z3/3+f(y,z)

Explanation: The continuity equation for incompressible is du/dx+dv/dy+dw/dz = 0.
Here du/dx=2x and v=2xy-z2
On solving by integrating, we get w = -3xz-2xyz+z3/3+f(y,z),
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4. A fluid flow field is given by
V=x2yi+y2z-(2xyz+yz)k
Calculate it’s acceleration at the point (1,3,5)
a) 28i-3j+125k
b) 28i-3j-125k
c) 28i+3j+125k
d) None of the mentioned

Explanation: First we have to check whether it satisfies the continuity equation,
The continuity equation for incompressible is du/dx+dv/dy+dw/dz = 0.
(here d/dx, d/dy, d/z represent partial derivative)
The given equation doesn’t satisfy the continuity equation.

5. A fluid flow field is given by
V=y2xi+z2x-(2xyz+yz)k
Calculate it’s acceleration at the point (2,4,4)
a) 36i-27j+100k
b) 36i-27j-100k
c) 28i+27j+100k
d) 36ne of the mentioned

Explanation: First we have to check whether it satisfies the continuity equation,
The continuity equation for incompressible is du/dx+dv/dy+dw/dz = 0.
(here d/dx, d/dy, d/z represent partial derivative)
The given equation doesn’t satisfy the continuity equation.

6. Convective acceleration cannot be found if the fluid flow equation is not satisfying
the continuity equation but local acceleration can be found.
a) True
b) False

Explanation: Convective acceleration and local acceleration cannot be found if the fluid flow equation is not satisfying the continuity equation.

7. Local acceleration has constant value for a steady flow.
a) True
b) False

Explanation: Local acceleration is zero for a steady flow.

8. Total acceleration has the same value as convective acceleration in case of unsteady flow.
a) True
b) False

Explanation: Total acceleration has the same value as convective acceleration in case of steady flow as local acceleration value becomes zero.

9. Which equation must be perfunctorily satisfied while dealing with fluid flow problems?
a) Newton’s second law
b) Newton’s third law
c) Law of conservation of momentum
d) Continuity equation

Explanation: Continuity equation must be perfunctorily satisfied while dealing with fluid flow problems.

10. Convective acceleration is defined as the rate of change of velocity due to change of velocity with respect to time.
a) True
b) False

Explanation: Convective acceleration is defined as the rate of change of velocity due to change of position of fluid particles.

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