Past Year Questions: Fluid Kinematics | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) PDF Download

Question 1.  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    [2019 : 1 Mark, Set-II]
(a) 4i + 12k
(b) 2i + 10k
(c) j + k
(d) 4j + 10k
Answer: (d)
Solution:



Question 2. A flow field is given by u = y², v = - xy, w = 0.Value of the z-component of the angular velocity (in radians per unit time, up to two decimal places) at the point (0, -1 ,1 ) is _____ .     [2018 : 1 Mark, Set-I]
Solution:


Question 3.  The velocity components of a two dimensional plane motion of a fluid are  
The correct statement is:    [2015 : 2 Marks, Set-II]
(a) Fluid is incompressible and flow is irrotational
(b) Fluid is incompressible and flow is rotational
(c) Fluid is compressible and flow is irrotational
(d) Fluid is compressible and flow is rotational
Answer: (a)
Solution: Apply continuity equation for 2D in compressible flow,

Hence, incompressible flow.

Hence, flow is irrotational.

Question 4.  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 _______     [2015 : 1 Mark, Set-II]
Solution: Convective acceleration

 
Question 5. In a two-dimensional steady flow field, in a certain region of the x-y plane, the velocity component in the x-direction is given by v_x = x² and the density varies as  Which of the following is a valid expression for the velocity component in the y-direction, v_y?
(a)
(b)
(c)  v_y = - xy
(d)  v_y = x_y 
Answer: (c)
Solution: Continuity equation in steady flow,

On integrating both sides,
v_y=-x_y 

Question 6.  A particle moves along a curve whose parametric equations are: x = t³ + 2t, y=-3e^-2t and z = 2 sin (5t), where x, y and z show variations of the distance covered by the particle (in cm) with time t(in s). The magnitude of the acceleration of the particle (in cm/s²) at t = 0 is ________ .     [2014 : 2 Marks, Set-I]
Solution:

⇒
⇒
⇒
⇒
⇒Magnitude of acceleration at t =0


Question 7. A plane flow has velocity components   and w = 0 along x, y and z directions respectively, where T₁ (≠ 0) and T₂ (≠ 0) are constants having the dimension of time. The given flow is incompressible if     [2014 : 1 Mark, Set-II]
(a) T₁ = - T₂ 
(b)
(c)
(d) T₁ = T₂ 
Answer: (d)
Solution: For a flow to exist, continuity should be satisfied.


Question 8. An incompressible homogeneous fluid is flowing steadily in a variable diameter pipe having the large and small diameters as 15 cm and 5 cm, respectively. If the velocity at a section at the 15 cm diameter portion of the pipe is 2.5 m/s, the velocity of the fluid (in m/s) at a section falling in 5 cm portion of the pipe is _______ .     [2014 : 1 Mark, Set-I]
Solution:



Question 9.  For a 2-D flow field, the stream function ψ is given as  The magnitude of discharge occurring between the stream line passing through points (0,3) and (3, 4) is    [2013 : 1 Mark]
(a) 6 units
(b) 3 units
(c) 1.5 units
(d) 2 units
Solution: