Total Acceleration of Fluid MCQ Quiz in தமிழ் - Objective Question with Answer for Total Acceleration of Fluid - இலவச PDF ஐப் பதிவிறக்கவும்

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Latest Total Acceleration of Fluid MCQ Objective Questions

Top Total Acceleration of Fluid MCQ Objective Questions

Total Acceleration of Fluid Question 1:

An unsteady velocity field is given by 

u = t2 + 3y

v = 4t + 5x

The acceleration at the point (5,3) at time t = 2 units will be

  1. 103 units
  2. 69 units
  3. 172 units
  4. 124 units

Answer (Detailed Solution Below)

Option 4 : 124 units

Total Acceleration of Fluid Question 1 Detailed Solution

Concept:

Acceleration of a Fluid Particle:

(i) Acceleration is defined as the rate of change of velocity with respect to time.

Velocity(V)=u(x,y,z,t)i^+v(x,y,z,t)j^+w(x,y,z,t)k^

Where, u, v and w are the components of velocity in x, y and z direction respectively.

Acceleration in x-direction:

ax=uux+vuy+wuz+ut

Acceleration in y-direction:

ay=uvx+vvy+wvz+vt

Acceleration in z-direction:

az=uwx+vwy+wwz+wt

Calculation:

Given,

Velocity component in x-direction; u = t2 + 3y

ux=0, uy=3, uz=0, ut=2t

Velocity component in y-direction; v = 4t + 5x

vx=5, vy=0, vz=0, vt=4

Acceleration in x-direction:

ax=uux+vuy+wuz+ut

ax = (t2 + 3y) × 0 + (4t + 5x) × 3 + 0 + 2t

ax = 12t + 15x + 2t

acceleration at the point (5,3) at time t = 2 units

ax = 12 × 2 + 15 × 5 + 2 × 2 = 103 units

Acceleration in y-direction:

ay=uvx+vvy+wvz+vt

ay =  (t2 + 3y) × 5 + 0 + 0 + 4

ay = 5t2 + 15y + 4

acceleration at the point (5,3) at time t = 2 units

ay = 5 × 22 + 15 × 3 + 4 = 69 units

So, Resultant acceleration;

a=ax2+ay2

a=1032+692=123.97

a ≈ 124 units

Total Acceleration of Fluid Question 2:

For a steady two-dimensional flow, the scalar components of the velocity field are Vx = -2x, vy = 2y, vz = 0.The corresponding components of acceleration ax and ay, respectively are;

  1. ax = 0, ay = 0
  2. ax = 4x, ay = 0
  3. ax = 0, ay = 4y
  4. ax = 4x, ay = 4y

Answer (Detailed Solution Below)

Option 4 : ax = 4x, ay = 4y

Total Acceleration of Fluid Question 2 Detailed Solution

ax=ududx+vdudy+wdudz+dudt

= (-2x) × (2) = 4x

ay=udvdx+vdvdy+wdvdz+dvdt

= 0 + 2y × 2 + 0 + 0 = 4y

Total Acceleration of Fluid Question 3:

A steady flow of an incompressible fluid is given by V=(x+2y)i^+(4y+z)j^(x+4z)k^. Calculate the magnitude of acceleration at the point (2, 0, 0) upto one decimal place.

Answer (Detailed Solution Below) 6.6 - 6.7

Total Acceleration of Fluid Question 3 Detailed Solution

Hence, u = x + 2y, v = 4y + z, w = -x – 4z

|a|=(dudt)2+(dvdt)2+(dwdt)2

dudt=ut+uux+vuy+wuz

= 0 + (x + 2y)(1) + (4y + z)(2) + 0

dudt|(2,0,0)=2

dvdt=vt+uvx+vvy+wvz

= 0 +(x+2y) (0) + (4y + z) (4) + (-x – 4z) (1)

dvdt|(2,0,0)=2

dwdz=wt+uwx+vwy+wwz

= 0 + (x + 2y) (-1) + (4y+z) (0) + (-x – 4z) (-4)

dwdz|(2,0,0)=6

|a|=4+4+36=6.633

Total Acceleration of Fluid Question 4:

When u = 3 + 2xy + 4t2, v = xy2 + 3t. The x-directional acceleration is given by

  1. 2x2y2 + 4xy2 + 6y + 8t2y + 6tx
  2. 4xy
  3. x/y
  4. 2x2y2 + 6tx

Answer (Detailed Solution Below)

Option 1 : 2x2y2 + 4xy2 + 6y + 8t2y + 6tx

Total Acceleration of Fluid Question 4 Detailed Solution

Concept:

For a velocity field, V=ui^+νj^+wk^

Total acceleration is the vector sum of the convective acceleration vector (directional acceleration vector) and local acceleration vector.

a=DVDt=uVx+νVy+wVz+Vt   ---(1)

Along x-direction, 

ax=uux+vuy+wuz+ut

Calculation:

Given:

u = 3 + 2xy + 4t2, v = xy2 + 3t.

dudx=2y, dudy=2x, dudt=8t

aconv=ududx+vdudy

aconv = (3 + 2xy + 4t2) (2y) + (xy2 + 3t) (2x)

aconv = 2x2y2 + 4xy2 + 6y + 8t2y + 6xt

Total Acceleration of Fluid Question 5:

A nozzle is so shaped that the average flow velocity changes linearly from 1.5 m/s at the beginning to 15 m/s at its end in a distance of 0.375 m. The magnitude of the convective acceleration (in m/s2) at the end of the nozzle is ___________.

Answer (Detailed Solution Below) 540

Total Acceleration of Fluid Question 5 Detailed Solution

Concept:

The total accelration is given by,

an=dVndt=[Vnt]+[UVnx+VVny+WVnz]

Where,

[Vnt]= Local accelration or temporal acceleration

[UVnx+VVny+WVnz]= Convective acceleration

Local acceleration:

Acceleration calculated due to variation of velocity with respect to time.

Convective Acceleration:

Accleration calculated due to variation of velocity with respect to space is known as convective accelration.

Convective acceleration in x direction is given as

uux+vuy+wux

Calculation:

Vavg1=1.5m/sVavg2=15m/s

∂x = 0.375 m

Convective acceleration =uux

uux=15(151.5)0.375=540m/s2

Total Acceleration of Fluid Question 6:

In a two-dimensional velocity field with velocities u and v along the x and y directions respectively, the convective acceleration along the x-direction is given by

  1. uudx+vudy
  2. uudx+vvdy
  3. uvdx+vudy
  4. vudx+uudy

Answer (Detailed Solution Below)

Option 1 : uudx+vudy

Total Acceleration of Fluid Question 6 Detailed Solution

ax=dudt=u×dudx+v×dudy

Total Acceleration of Fluid Question 7:

The velocity field in a flow system is given by v=2i+(x+y)j+(xyz)k. The acceleration of the fluid at (1, 1, 2) is

  1. j + k
  2. 2i + 10 k
  3. 4j + 10 k
  4. 4i + 12 k

Answer (Detailed Solution Below)

Option 3 : 4j + 10 k

Total Acceleration of Fluid Question 7 Detailed Solution

Velocity field (v)=2i+(x+y)j+(xyz)k

Acceleration(an)=(δvδt)+(uδvδx+vδvδy+w(δv)δz)

Where (δvδt)Localaccelaration

(uδvδx+vδvδy+w(δv)δz)Convectiveaccelaration

Here, u=2,v=x+y,w=xyz,t=0, n is direction

ax=0+2×x(2)+(x+y)×(2)y+(xyz)×(2)z 

ax = 0

ay=0+2×(x+y)x+(x+y)×(x+y)y+(xyz)×(x+y)z 

ay = 2 + x + y

az=0+2×(xyz)x+(x+y)×(xyz)y+xyz×(xyz)z 

= 0 + 2yz + (x + y) × (xz) + xyz × xy

az = 2yz + (x + y) × (xz) + x2y2z

Acceleration = axi + ayj + azk

a=0+(2+x+y)j+(2yz+(x+y)xz+x2y2z)k

a(1,1,2)=0+(2+1+1)j+(2×1×2+(1+1)×1×2+12×12×2)k

a=4j+(4+4+2)k=4j+10k

Total Acceleration of Fluid Question 8:

A steady incompressible flow field is given by u = 2x2 + y2 and v = -4xy. The convective acceleration, along x - direction at point (1, 2) is 

  1. 6 units
  2. 24 units
  3. -8 units 
  4. -24 units
  5. 8 units 

Answer (Detailed Solution Below)

Option 3 : -8 units 

Total Acceleration of Fluid Question 8 Detailed Solution

Concept:

Convective acceleration is given by,

ax=uux+vuy+wuz

ay=uvx+vvy+wvz

az=uwx+vwy+wwz

Calculation:

Given:

u = 2x2 + yand v = -4xy

To get, ax=uux+vuy+wuz

At point (1, 2)

uux=(2x2+y2)×(2x2+y2)x=(2x2+y2)×(4x)

Now putting the coordinates of x and y in the above equation (x = 1, y = 2)

uux=(2x2+y2)×(4x)=(2×12+22)×(4×1)=24units

Same

vuy=4xy×(2x2+y2)y=8xy2

Now putting the coordinates of x and y in the above equation (x = 1, y = 2)

vuy=8xy2=8×1×22=32

wuz=0Since,uisindependentofz

Therefore,

ax=uux+vuy=2432=8units

Total Acceleration of Fluid Question 9:

A Rectangular tank of dimensions 2 m (l) × 4 m (b) × 2 m (h) contains water up to a depth of 1.2 m. A horizontal acceleration is imparted to the tank in the direction of its length so that there is just no spilling of water from the tank. The acceleration imparted will be

Take g = 10 m/s2 

  1. 6 m/s2
  2. 8 m/s2
  3. 10 m/s2
  4. 12 m/s2

Answer (Detailed Solution Below)

Option 2 : 8 m/s2

Total Acceleration of Fluid Question 9 Detailed Solution

Concept:

When a tank partially filled with liquid is given a constant horizontal acceleration, the horizontal free surface of liquid will become inclined as shown in the below figure,

quesImage3939

The dotted line is original surface and the inclined line is new surface.

As there is just no spilling of water, the new surface will touch the left side top of the tank.

The tan of the inclination is given by 

tanθ=ag

Where a - acceleration imparted;

Calculation:

From the given figure,

tanθ=ag=0.81

⇒ a = 0.8g = 8 m/s2

Total Acceleration of Fluid Question 10:

Consider the velocity field for a flow as:

V=(10x+5y)i^+(15xy2z)j^+(13x+20y)k^

Determine the magnitude of convective acceleration in y direction at point (1, 0, -3):

  1. 0 units
  2. 13 units
  3. 10 units
  4. 23 units

Answer (Detailed Solution Below)

Option 1 : 0 units

Total Acceleration of Fluid Question 10 Detailed Solution

Concept:

The convective acceleration in y-direction is given by:

ay=uvx+vvy+wvz

Where,

u, v, w are the velocity in x, y and z direction respectively.

Calculation:

u = 10 x + 5 y

at, (1, 0, -3)

u = 10 units

v = 15 xy2z

at, (1, 0, -3)

v = 15 × 1 × 0 = 0 units

w = 13 x + 20 y

at, (1, 0, -3)

w = 13 × 1 + 0 = 13 units

vx=15y2z=0

vy=30xyz=0

vz=15xy2=0

ay = 10 × 0 + 0 + 13 × 0

ay = 0 units
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