GATE Past Year Questions: Fluid Dynamics | Fluid Mechanics for Mechanical Engineering PDF Download

Q1: A liquid fills a horizontal capillary tube whose one end is dipped in a large pool of the liquid. Experiments show that the distance L travelled by the liquid meniscus inside the capillary in time t  is given by

where γ is the surface tension, R is the inner radius of the capillary, and μ μ is the dynamic viscosity of the liquid. If k is a dimensionless constant, then the exponent a a is _____ (rounded off to 1 decimal place).  [GATE ME 2024]
Ans: (0.5 to 0.5)

Dimensions - length, L = [ L ]
Surface Tension, γ = [ M T^{− 2}] 
 Radius, R = [L]
Dynamic viscosity, μ = [M L^{− 1} T^{− 1} ]
Time, t = [T]
K is dimensionless

So, a + c = 0 ⇒ c =−a
-2a - c + 1/2 = 0
-a + 1/2 = 0
⇒  a = 1/2
⇒ a = 0.5

Q1: A tube of uniform diameter D is immersed in a steady flowing inviscid liquid stream of velocity V, as shown in the figure. Gravitational acceleration is represented by  g. The volume flow rate through the tube is ______.  [GATE ME 2022, SET-2]
(a) π/4 D²V

(b) π/4 D²

(c) π/4 D²
(d) π/4 D²
Ans: (d) 

By applying Bernoulli's equation between (1) and (2)

Q2: Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m³ and 100 m/s, respectively. At a downstream location in the pipe, the velocity is 170 m/s. If the pressure drop between these two locations is 10 kPa, the force exerted by the gas on the pipe between these two locations is ____________ N. [GATE ME 2022 SET-1]
(a) 350π²
(b)750π
(c) 1000π
(d) 3000
Ans: (b) 

Applying momentum equation to the pipe flow,

= - 750π N
Negative sign shows that assumed direction of force is opposite of actual direction.

Q1: A cylindrical jet of water (density = 1000 kg/m³) impinges at the center of a flat, circular plate and spreads radially outwards, as shown in the figure. The plate is resting on a linear spring with a spring constant k = 1 k N/m k. The incoming jet diameter is D=1cm.

If the spring shows a steady deflection of 1 cm upon impingement of jet, then the velocity of the incoming jet is _______m/s (round off to one decimal place).  [GATE ME 2021, SET-1]
Ans: (11.2 to 11.4)
δ = 1cm
D = 1cm
p = 1000 kg/m³
K = 1kN - m
Force due to jet =  Spring force
pAV² = kx

V = 11.28 m/s ≃ 11.3 m/s

4

Question for GATE Past Year Questions: Fluid Dynamics

Try yourself:Consider steady flow of water in a situation where two pipe lines (pipe 1 and pipe 2) combine into a single pipe line (pipe 3) as shown in figure.
The cross-sectional'area of all three pipelines are constant. The following data is given



Assuming the water properties and the velocities to be uniform across the cross-section of the inlets and the outlet, the exit velocity (in m/s) in pipe 3 is

[2009]

• A.

  1
• B.

  1.5
• C.

  2
• D.

  2.5

Explanation

Q₁ + Q₂ = Q₃
A₁V₁ + A₂V₃ = A₃V₃
1 + 4 = 2.5 V₃
or V₃ = 2 m/s

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