Mechanics of Fluids - SAQ from AMIE Exam (Winter 2023)

Choose the correct answer from the given choices:

1. The dimensional formula of kinematic viscosity of a fluid is

(i) LT²

(ii) L²T^{-1 *}

 (iii) ML^-1T^-1

(iv) ML^-2T^-2

Hint: Kinematic Viscosity (ν) = Dynamic Viscosity (μ) / Density (ρ).

= [M¹L⁻¹T⁻¹] / [M¹L⁻³] 

2. An open tank contains 60 cm of water covered with 30 cm of oil of specific gravity 0.8. The pressure intensity at the bottom of the tank is nearly

(i) 2350 N/m²

(ii) 3530 N/m²

(iii) 5880 N/m²

(iv) 8240 N/m² *

Hint: 

P_A = [ρgh]_oil + [ρgh]_water

= [0.8 x 9.81 x 0.3] + [1 x 9.81 x 0.6]

=8.2404 kN/m²

= 8240.4 N/m²  

3. The expression p + wZ + ρv²/2 = constant, commonly used to express Bernoulli s equation has units of total energy per unit

(i) volume*

(ii) mass

(iii) weight

(iv) cross-sectional area of flow

4. The hydraulic diameter used in place of diameter for a non-circular duct is equal to

(i) A/P

(ii) 4xA/P*

(iii) 2A/P

(iv) 4P/A

5. At the point of boundary layer separation

(i) Shear stress is maximum

(ii) Shear stress is zero

(iii) velocity is negative

(iv) density variation is maximum 

Hint: At the point of boundary layer separation, shear stress is zero, because the velocity gradient at the wall becomes zero, causing the viscous force (shear stress) to vanish as the flow detaches from the surface due to an adverse pressure gradient.  

6. Weber number is the ratio of square root of inertia force to

(i) surface tension force*

(ii) gravity force

(iii) pressure force

(iv) viscous force 

Hint: 

• Weber Number (We): Ratio of Inertia Force/Surface Tension Force.
• Reynolds Number: Ratio of Inertia Force/Viscous Force
• Froude Number: Ratio of the square root of Inertia Force to Gravity Force 

7. A sphere having uniform density

(i) is always stable

(ii) is always unstable

(iv) is always neutrally stable*

(iv) could be stable or unstable

Hint: A sphere of uniform density resting on a flat horizontal surface is in neutral equilibrium. This is because its center of gravity (at the geometric center due to symmetry) remains at the same height regardless of how the sphere is rotated or slightly displaced on the surface. When displaced (e.g., rolled slightly), it neither returns to its original position nor moves further away—it stays in the new position with no change in potential energy 

8. The necessary condition for the continuity equation ∇.V = 0 where V is velocity vector to be valid is

(i) incompressible flow*

(ii) irrotational flow

(iii) inviscid flow

(iv) steady flow 

Hint:  (∂ρ/∂t) + ∇(ρV)=0

For ∇.V = 0 to hold exactly, the flow must be incompressible, meaning the material derivative of density is zero: ∂ρ/∂t = 0. 

9. Separation of fluid flow is caused by reduction in pressure in the direction of flow reduction of the boundary layer thickness presence of adverse pressure gradient

(i) reduction in pressure in the direction of flow

(ii) reduction of the boundary layer thickness

(iii) presence of adverse pressure gradient*

(iv) presence of favourable pressure gradient

Hint: Fluid flow separation, like on an airplane wing causing a stall, happens because of a strong adverse pressure gradient  (dp/dx > 0), where pressure increases in the flow direction, fighting the fluid's momentum, causing the slow boundary layer fluid to stop, reverse, and detach from the surface, forming eddies and increasing drag. A decrease in pressure (favorable gradient,  dp/dx < 0) does the opposite, accelerating flow and preventing separation. 

10. According to Blasius law, average skin friction coeifficient in the boundary layer is given by

(i) 0.332/√Re

(ii) 0.664/√Re*

(iii) 0.996/√Re

(iv) 1.328/√Re

By AMIE Study Circle, Roorkee