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QUESTION: 1

The velocity vector in a fluid is given V=5x^{4}+3y^{2}+2z( in metre/sec). What is the acceleration of it at point (1,3,4) ?

Solution:

Explanation: By differentiating V=5x^{42}+2z, the acceleration obtained is V=20x^{3}+6y+2.

on putting the coordinates, the acceleration obtained is 40 m/s^{2}.

QUESTION: 2

Determine the third velocity component such that continuity equation is satisfied if two components are u=2y^{2}, w=2xyz.

Solution:

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-x^{2}y+f(y,z).

QUESTION: 3

Determine the third velocity component such that continuity equation is satisfied if two components are u=x^{2}+y^{2}+z^{2}, v=xy^{2} – yz^{2} + xy

Solution:

Explanation: The continuity equation for incompressible is du/dx+dv/dy+dw/dz = 0.

Here du/dx=2x and v=2xy-z^{2}

On solving by integrating, we get w = -3xz-2xyz+z^{3}/3+f(y,z),

QUESTION: 4

A fluid flow field is given by

V=x^{2}yi+y^{2}z-(2xyz+yz)k

Calculate it’s acceleration at the point (1,3,5)

Solution:

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.

QUESTION: 5

A fluid flow field is given by

V=y^{2}xi+z^{2}x-(2xyz+yz)k

Calculate it’s acceleration at the point (2,4,4)

Solution:

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.

QUESTION: 6

Convective acceleration cannot be found if the fluid flow equation is not satisfying the continuity equation but local acceleration can be found.

Solution:

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

QUESTION: 7

Local acceleration has constant value for a steady flow.

Solution:

Explanation: Local acceleration is zero for a steady flow.

QUESTION: 8

Total acceleration has the same value as convective acceleration in case of unsteady flow.

Solution:

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

QUESTION: 9

Which equation must be perfunctorily satisfied while dealing with fluid flow problems?

Solution:

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

QUESTION: 10

Convective acceleration is defined as the rate of change of velocity due to change of velocity with respect to time.

Solution:

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

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