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Mechanical Engineering Exam  >  Mechanical Engineering Notes  >  Fluid Mechanics for Mechanical Engineering  >  GATE Past Year Questions: Boundary Layer Theory

GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering PDF Download

Q1: The figure shows two fluids held by a hinged gate. The atmospheric pressure is Pa = 100 k Pa. The moment per unit width about the base of the hinge is ________ kNm/m. (Rounded off to one decimal place) 
Take the acceleration due to gravity to be g = 9.8 m/s2  [GATE ME 2023]
GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering
Ans: (55.9 to 58.5]

GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical EngineeringForces from Pressure diagram
F1 = Area of △ A D E × △ADE × width
F1 = 1/2 x AD x DE x width
= 1/2 × 1 × 9810 × 1 
F1 = 4905 N 
F2 = Area of rectangle DEBF × width 
F2 = 2 × 9810 × 1
F2 = 19620 N
F3 = Area of triangle ΔEFC
= 1/2 × EF × FC ×  width
= 1/2 x 2 x 39240 x 1
F3 = 39240 N
Location of forces from top
F1 → 2/3 x = 2/3 m
F2 → (1m + 2m/2) = 2m
F3 → 1m + 2m x 2/3 = 7/3m
Pressure at depth 1 m =ρ1  gh1 
1000 × 9.81 × 1=9810 N/m2
DE = 9810 N/m2
BF = 9810 N/m2
Pressure at depth 3 m
P1gh1 + P2gh2
9810 + 2000 × 9.81 × 2
9810 + 39240 = 49050 N/m2
(BF) + (FC) = BC
Location of forces from bottom hinge
F1 → 3m - 2/3 m = 7/3 m
F2 → 3m - 2m = 1m
F3 → 3m - 7/3 m = 2/3 m
Moment about hinge F1 × 7/3 + F2 × 1 + F3 × 2 /3
4905 × 7/3 + 19620 + 39240 × 2/3
⇒ 57225Nm = 57.22kNm/m


Q1: A uniform wooden rod (specific gravity = 0.6, diameter = 4 cm and length = 8 m) is immersed in the water and is hinged without friction at point A on the waterline as shown in the figure. A solid spherical ball made of lead (specific gravity = 11.4) is attached to the free end of the rod to keep the assembly in static equilibrium inside the water. For simplicity, assume that the radius of the ball is much smaller than the length of the rod.  [GATE ME 2022, SET-2]
Assume density of water = 103kg/m3 and π = 3.14
Radius of the ball is _______ cm (round off to 2 decimal places).
GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical EngineeringAns: (3.48 to 3.7)
GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical EngineeringAs the system is in equilibrium, 
Σ M o = 0 
GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering
⇒ R = 0.03587m = 3.59cm


Q2: Consider a steady flow through a horizontal divergent channel, as shown in the figure, with supersonic flow at the inlet. The direction of flow is from left to right.  [GATE ME 2022, SET-2]
GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering

Pressure at location B is observed to be higher than that at an upstream location A. Which among the following options can be the reason?
(a) Since volume flow rate is constant, velocity at B is lower than velocity at A
(b) Normal shock
(c) Viscous effect
(d) Boundary layer separation
Ans: (a, b)
If the supersonic flow enters to the diverging duct, it will act as nozzle the pressure of the flow is decreases in the nozzle. But it is given the pressure of the flow at B is more than that A
GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering

It will happen only with the development of normal shoot in the diverging flow (the normal shock wave is the characteristic of only supersonic flow) Because of normal shock wave in the diverging nozzle pressure increases and velocity decreases. But mass flow rate remains unchanged.


Q3: A solid spherical bead of lead (uniform density = 11000 kg/ m3  ) of diameter d = 0.1 mm sinks with a constant velocity V  in a large stagnant pool of a liquid (dynamic viscosity = 1.1 × 1 0 − 3 k g . m − 1 . s − 1 ) The coefficient of drag is given by CD = 24/Re where the Reynolds number (Re) is defined on the basis of the diameter of the bead. The drag force acting on the bead is expressed as D = (C D )(0.5ρV 2 )( πd 2/4  ), where p  is the density of the liquid. Neglect the buoyancy force. Using g = 10 m/s 2  , the velocity V  is __________ m/s.  [GATE ME 2022, SET-1]
(a) 1/24
(b) 1/6
(c) 1/18
(d) 1/12
Ans: (c)
As buoyancy force is neglected we can neglect density of fluid () in the following equation.
GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering


Q4: The figure shows a purely convergent nozzle with a steady, inviscid compressible flow of an ideal gas with constant thermophysical properties operating under choked condition. The exit plane shown in the figure is located within the nozzle. If the inlet pressure ( P 0 ) is increased while keeping the back pressure (P back ) unchanged, which of the following statements is/are true?  [GATE ME 2022, SET-1]

GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering

(a) Mass flow rate through the nozzle will remain unchanged.
(b) Mach number at the exit plane of the nozzle will remain unchanged at unity
(c) Mass flow rate through the nozzle will increase.
(d) Mach number at the exit plane of the nozzle will become more than unity.

Ans: (b, c)
GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering
(critical temp ratio)
where γ =  Adiabatic index = 1.4 
If P0 increases , mass flow rate increases. Mach number at the exit plane of the nozzle will remain unchanged at unity. Since the maximum expected velocity from the converging nozzle is sound velocity.


Q5: In the following two-dimensional momentum equation for natural convection over a surface immersed in a quiescent fluid at temperature T ∞  (g is the gravitational acceleration, β β is the volumetric thermal expansion coefficient, v v is the kinematic viscosity, u u and v are the velocities in x  and y directions, respectively, and T  is the temperature)  [GATE ME 2022 SET-1]

GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering

the term g β ( T − T ∞ ) represents
(a) Ratio of inertial force to viscous force.
(b) Ratio of buoyancy force to viscous force.
(c) Viscous force per unit mass.
(d) Buoyancy force per unit mass.
Ans: (d) 
GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering
This is the equation that governs the fluid motion in the boundary layer due to effect of Buoyancy
GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering

Buoyancy force is due to density difference and gravitational effect 
g β (T − T ∞ )  represents Buoyancy force per unit mass.


Q1: Which of the following is responsible for eddy viscosity (or turbulent viscosity) in a turbulent boundary layer on a flat plate? [GATE ME 2021, SET-2]
(a) Nikuradse stresses
(b) Reynolds stresses
(c) Boussinesq stresses
(d) Prandtl stresses

Ans: (b)
Reynolds stresses are responsible for eddy viscosity
GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering
where η=  Eddy viscosity.

Q2: Consider fully developed, steady state incompressible laminar flow of a viscous fluid between two large parallel horizontal plates. The bottom plate is fixed and the top plate moves with a constant velocity of U = 4 m/s. Separation between the plates is 5 mm. There is no pressure gradient in the direction of flow. The density of fluid is 800 kg/m3, and the kinematic viscosity is 1.25 × 1 − 4 m2/s The average shear stress in the fluid is ________Pa (round off to the nearest integer). [GATE ME 2021, SET-1]
Ans: (79 to 81)
GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering

V = 4m/s
p = 800 kg/m3
v =1.25 × 10 −4 m2/s
 h = 5 mm
GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering

= 80 Pa


Q1: Water (density 1000 k g/m3) flows through an inclined pipe of uniform diameter. The velocity, pressure and elevation at section A are VA = 3.2 m/s, pA = 186 kPa and zA = 24.5 m  respectively, and those at section B are VB = 3.2 m/s, pB = 260 k P  and zB = 9.1 m , respectively. If acceleration due to gravity is 10 m/s2 then the head lost due to friction is _________ m (round off to one decimal place). [GATE ME 2020, SET-2]
Ans: (7.9 to 8.1)

GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering

GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering

=18.6 + 0.512+  24.5 = 43.612
GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering
=26 + 0.512 + 9.1=35.612
EA > EB ′ so flow from 'A' to 'B'
Heat loss = EA − EB = 43.612 − 35.612 = 8 m = of water head


Q2: Consider steady, viscous, fully developed flow of a fluid through a circular pipe of internal diameter D. We know that the velocity profile forms a paraboloid about the pipe center line, given by: V = -C (r2 - D2/4) m/s, where C is a constant. The rate of kinetic energy (in J/s) at the control surface A-B, as shown in the figure, is proportional to Dn. The value of n is________.  [GATE ME 2020, SET-1]

GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering

Ans: (8 to 8)
GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering
n = 8


Q3: Match the following non-dimensional numbers with the corresponding definitions:  [GATE ME 2020, SET-1]

GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering(a) P-1, Q-3, R-2, S-4
(b) P-3, Q-1, R-2, S-4
(c) P-4, Q-3, R-1, S-2
(d) P-3, Q-1, R-4, S-2
Ans: (d)


Q4: Froude number is the ratio of  [GATE ME 2020, SET-1]
(a) buoyancy forces to viscous forces
(b) inertia forces to viscous forces
(c) buoyancy forces to inertia forces
(d) inertia forces to gravity forces
Ans: (c)

Question for GATE Past Year Questions: Boundary Layer Theory
Try yourself:An incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluid alone is increased by a factor of 4, then the boundary layer thickness at the same location, in mm will be

[2012]

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Question for GATE Past Year Questions: Boundary Layer Theory
Try yourself:Consider an incompressible laminar boundary layer flow over a flat plate of length L, aligned with the direction of an incoming uniform free stream. If F is the ratio of the drag force on the front half of the plate to the drag force on the rear half, then

[2007]

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Question for GATE Past Year Questions: Boundary Layer Theory
Try yourself:A smooth flat plate with a sharp leading edge is placed along a gas stream flowing at U = 10 m/s. The thickness of the boundary layer at section r – s is 10 mm, the breadth of the plate is 1 m (into the paper) and the density of the gas, r = 1.0 kg/m3. Assume that the boundary layer is thin, two-dimensional, and follows a linear velocity distribution, u = U  , at the section r-s, where y is the height from plate.
GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering
​The integrated drag force (in N) on the plate, between p – s, is
 

[2006 ]

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Question for GATE Past Year Questions: Boundary Layer Theory
Try yourself:A smooth flat plate with a sharp leading edge is placed along a gas stream flowing at U = 10 m/s. The thickness of the boundary layer at section r – s is 10 mm, the breadth of the plate is 1 m (into the paper) and the density of the gas, r = 1.0 kg/m3. Assume that the boundary layer is thin, two-dimensional, and follows a linear velocity distribution, u = U GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering , at the section r-s, where y is the height from plate.

GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering
The mass flow rate (in kg/s) across the section q – r is 

[2006]

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Question for GATE Past Year Questions: Boundary Layer Theory
Try yourself:If x is the distance measured from the leading edge of a flat plate, then laminar boundary layer thickness varies as

[2002]

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Question for GATE Past Year Questions: Boundary Layer Theory
Try yourself:Flow separations flow past a solid object is caused by

[2002]

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Question for GATE Past Year Questions: Boundary Layer Theory
Try yourself:The predominant forces acting on an element of fluid in the boundary layer over a flat plate in a uniform parallel stream are

[1990]

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Question for GATE Past Year Questions: Boundary Layer Theory
Try yourself: The instantaneous stream wise velocity of a turbulent flow is given as follows:
u(x, y, z, t) = GATE Past Year Questions: Boundary Layer Theory | Fluid Mechanics for Mechanical Engineering(x, y, z) + u'(x, y, z, t) The time average of the fluctuating velocity u (x, y, z, t) is

[2016]

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Question for GATE Past Year Questions: Boundary Layer Theory
Try yourself: Consider the turbulent flow of a fluid through a circular pipe of diameter D. Identify the correct pair of statements
.I. The fluid is well-mixed
II. The fluid is unmixed
III.ReD < 2300
IV. ReD > 2300
 

[2014]

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Question for GATE Past Year Questions: Boundary Layer Theory
Try yourself:Match the following
P: Compressible flow            U: Reynolds number
Q: Free surface flow              V: Nusselt number
R: Boundary layer flow          W: Weber number
S: Pipe flow                           X: Froude number
T: Heat convection                 Y: Mach number
Z: Skin friction coefficient
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Question for GATE Past Year Questions: Boundary Layer Theory
Try yourself:A phenomenon is modeled using-n dimensional variables with k primary dimensions. The number of non-dimensional variables is

[2010]

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Question for GATE Past Year Questions: Boundary Layer Theory
Try yourself:Prandtl's mixing length in turbulent flow signifies

[1994]

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Question for GATE Past Year Questions: Boundary Layer Theory
Try yourself:The parameters which determines the friction factor for turbulent flow in a rough pipe are

[1988]

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[Question:504379]

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FAQs on GATE Past Year Questions: Boundary Layer Theory - Fluid Mechanics for Mechanical Engineering

1. What is the boundary layer theory in fluid mechanics?
Ans. The boundary layer theory in fluid mechanics describes the behavior of fluid flow near a solid boundary. It explains how the velocity of the fluid changes from zero at the surface of the boundary (due to the no-slip condition) to the free stream velocity away from the surface. This theory is crucial for understanding drag, heat transfer, and mass transfer in various engineering applications.
2. What are the key assumptions of the boundary layer theory?
Ans. The key assumptions of the boundary layer theory include: 1. The flow is steady and incompressible. 2. The effects of viscosity are significant only within a thin layer adjacent to the boundary, known as the boundary layer. 3. The pressure gradient outside the boundary layer is negligible. 4. The flow is laminar or turbulent within the boundary layer, depending on the flow conditions.
3. How do you determine the boundary layer thickness?
Ans. The boundary layer thickness can be determined using various methods, but one common approach is to define it as the distance from the boundary at which the fluid velocity reaches approximately 99% of the free stream velocity. Mathematically, it can often be estimated using empirical formulas based on the Reynolds number and the characteristics of the flow, such as Blasius solution for laminar flow over a flat plate.
4. What is the significance of the Reynolds number in boundary layer theory?
Ans. The Reynolds number is a dimensionless quantity that helps predict flow patterns in different fluid flow situations. In boundary layer theory, it indicates whether the flow is laminar or turbulent. A low Reynolds number (Re < 2000) typically signifies laminar flow, while a high Reynolds number (Re > 4000) indicates turbulent flow. The transition between these regimes significantly affects the characteristics of the boundary layer and the drag force on objects.
5. How does boundary layer separation occur and why is it important?
Ans. Boundary layer separation occurs when the boundary layer can no longer adhere to the surface of an object due to adverse pressure gradients, causing the flow to detach from the surface. This phenomenon is important because it can lead to increased drag, loss of lift in airfoils, and flow instabilities. Understanding and controlling boundary layer separation is crucial in the design of various aerodynamic and hydrodynamic structures to enhance their efficiency.
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