A fluid undergoes viscous deformation with velocity gradient du/dy = 50 s⁻¹. For Newtonian fluid with μ = 0.1 Pa·s, the shear stress is:
A
5 Pa
B
500 Pa
C
5000 Pa
D
0.002 Pa
τ = μ(du/dy) = 0.1 × 50 = 5 Pa
For steady flow of an incompressible fluid through a variable area duct, which equation relates velocities at different sections?
A
Bernoulli equation
B
Continuity equation (A₁v₁ = A₂v₂)
C
Energy equation
D
Momentum equation
Correct Answer:
B. Continuity equation (A₁v₁ = A₂v₂)
Continuity equation for incompressible flow states Q = constant, so A₁v₁ = A₂v₂
For flow through an orifice, the discharge coefficient Cd is always:
A
Greater than 1
B
Equal to 1
C
Less than 1
D
Zero
Correct Answer:
C. Less than 1
Cd < 1 accounts for vena contracta and frictional losses in actual orifice flow compared to ideal flow.
Which of the following statements about boundary layers is correct?
A
Boundary layer thickness increases linearly with distance
B
Shear stress is zero at the wall surface
C
Boundary layer develops due to viscous effects near the surface
D
Boundary layer is independent of Reynolds number
Correct Answer:
C. Boundary layer develops due to viscous effects near the surface
Boundary layer develops due to viscous effects that cause velocity gradient near solid surfaces, creating shear stress.
For laminar flow in a circular pipe, the Hagen-Poiseuille equation gives volumetric flow rate as Q = πΔPd⁴/(128μL). This assumes:
A
Turbulent flow with smooth pipes
B
Incompressible, fully developed laminar flow
C
Compressible flow with entrance effects
D
Flow with variable viscosity
Correct Answer:
B. Incompressible, fully developed laminar flow
Hagen-Poiseuille equation is valid for incompressible, fully developed laminar flow in circular pipes without entrance effects.
A fluid with dynamic viscosity μ = 0.8 Pa·s and density ρ = 800 kg/m³ flows through a pipe. What is the kinematic viscosity?
A
1.0 × 10⁻³ m²/s
B
6.4 × 10⁻⁴ m²/s
C
1.25 × 10⁻³ m²/s
D
8.0 × 10⁻⁴ m²/s
Correct Answer:
A. 1.0 × 10⁻³ m²/s
Kinematic viscosity ν = μ/ρ = 0.8/800 = 1.0 × 10⁻³ m²/s
In a converging nozzle, as the cross-sectional area decreases, the velocity of incompressible flow:
A
Decreases
B
Increases
C
Remains constant
D
First increases then decreases
Correct Answer:
B. Increases
From continuity equation A₁V₁ = A₂V₂, when area decreases, velocity must increase to maintain constant mass flow rate.
Water at 20°C flows through a pipe network. The dynamic viscosity of water at 20°C is approximately:
A
0.001 N·s/m²
B
0.01 N·s/m²
C
0.1 N·s/m²
D
1.0 N·s/m²
Correct Answer:
A. 0.001 N·s/m²
The dynamic viscosity of water at 20°C is approximately 1.002 × 10⁻³ N·s/m² or 0.001 N·s/m², which is used in Reynolds number calculations.
Bernoulli's equation applies to:
A
Viscous flow with heat transfer
B
Inviscid, incompressible, steady flow along a streamline
C
Compressible flow with friction
D
Turbulent flow in pipes
Correct Answer:
B. Inviscid, incompressible, steady flow along a streamline
Bernoulli's equation is valid for inviscid (frictionless), incompressible, steady flow along a streamline. It represents energy conservation in such flows.
What is the dimension of pressure coefficient (Cₚ)?
A
Dimensionless
B
[M L⁻¹ T⁻²]
C
[M L² T⁻³]
D
[M L T⁻¹]
Correct Answer:
A. Dimensionless
Pressure coefficient Cₚ = (P - P∞)/(0.5ρV∞²) is a dimensionless quantity used in aerodynamics and fluid mechanics.
