Question 1

A U-tube manometer contains mercury (density 13,600 kg/m³). If one arm reads 5 cm and the other reads 8 cm, what is the pressure difference between the two ends? (Take g = 10 m/s²)

Accepted Answer

Pressure difference = ρgh where h = (8 - 5) cm = 0.03 m; ΔP = 13,600 × 10 × 0.03 = 4,080 Pa.

Question 2

Two spheres of radii 1 cm and 2 cm fall through glycerin with the same terminal velocity. What is the ratio of viscous forces acting on them?

Accepted Answer

At terminal velocity, viscous force F = 6πηrv; since v is same for both, F₁:F₂ = r₁:r₂ = 1:2, but drag also depends on area, giving force ratio 1:4.

Question 3

The surface tension of water at room temperature is approximately 0.075 N/m. A capillary tube of radius 0.5 mm is dipped in water. What is the height to which water rises? (Take ρ = 1000 kg/m³, g = 10 m/s²)

Accepted Answer

Using h = 2σcosθ/(ρgr) with cosθ ≈ 1: h = (2 × 0.075)/(1000 × 10 × 0.0005) = 0.03 m.

Question 4

A horizontal pipe of diameter 2 cm carries water at 4 m/s. If the pipe narrows to a diameter of 1 cm, what will be the velocity of water in the narrow section? (Assume incompressible flow)

Accepted Answer

By continuity equation A₁v₁ = A₂v₂; since area reduces by factor of 4, velocity increases by factor of 4: v₂ = 16 m/s.

Question 5

A liquid of density 1000 kg/m³ is filled in a container. What is the pressure at a depth of 10 m below the surface? (Take g = 10 m/s²)

Accepted Answer

Using P = ρgh: P = 1000 × 10 × 10 = 100,000 Pa (pressure due to fluid column alone).

Question 6

A capillary tube of radius 1.5 mm is inserted into water (surface tension = 0.073 N/m, density = 1000 kg/m³, contact angle = 0°). What is the height to which water rises in the tube?

Accepted Answer

Using h = (2σ cosθ)/(ρgr) = (2 × 0.073 × 1)/(1000 × 10 × 1.5 × 10⁻³) = 0.0097 m = 0.97 cm; recalculating: h ≈ 9.7 cm.

Question 7

Two fluids have viscosities η₁ = 1.5 Pa·s and η₂ = 0.5 Pa·s. If equal volumes flow through identical pipes under the same pressure difference, what is the ratio of their volume flow rates Q₁/Q₂?

Accepted Answer

Volume flow rate is inversely proportional to viscosity (Q ∝ 1/η), so Q₁/Q₂ = η₂/η₁ = 0.5/1.5 = 1:3.

Question 8

A glass capillary tube is inserted into mercury (surface tension = 0.486 N/m, density = 13600 kg/m³, contact angle = 140°). The radius is 1 mm. Will mercury rise or fall, and by how much?

Accepted Answer

Since contact angle > 90°, h = (2σ cosθ)/(ρgr) = (2 × 0.486 × cos140°)/(13600 × 10 × 10⁻³) is negative, indicating depression of about 3.5 cm.

Question 9

A liquid flows between two parallel plates separated by 5 mm, with a viscosity of 0.01 Pa·s. If the shear stress on the fluid is 2 N/m², what is the velocity gradient (dv/dy) between the plates?

Accepted Answer

From τ = η(dv/dy), we get dv/dy = τ/η = 2/0.01 = 200 s⁻¹.

Question 10

A fluid has a viscosity of 0.8 Pa·s and flows through a cylindrical pipe of radius 2 cm. If the pressure difference across a 5 m length is 400 Pa, what is the volume flow rate using Poiseuille's equation?

Accepted Answer

Using Poiseuille's law: Q = (πΔPr⁴)/(8ηL) = (π × 400 × (0.02)⁴)/(8 × 0.8 × 5) = 1.256 × 10⁻⁴ m³/s.

Question 11

A spherical droplet of water has a surface tension of 0.072 N/m. If the radius of the droplet is 2 mm, what is the excess pressure inside the droplet due to surface tension?

Accepted Answer

For a sphere, excess pressure ΔP = 4σ/r = (4 × 0.072)/(2 × 10⁻³) = 144 Pa; however, the calculation yields ΔP = 2σ/r for a single interface, giving 72 Pa.

Question 12

Which of the following statements correctly defines the coefficient of viscosity (η)?

Accepted Answer

Coefficient of viscosity is defined as η = F/A ÷ (dv/dy), which is shear stress divided by velocity gradient (rate of shear strain).

Question 13

An object falls through a viscous fluid and reaches terminal velocity when the drag force equals 50 N. If the buoyant force is 10 N and the weight of the object is 80 N, what is the net force on the object at terminal velocity?

Accepted Answer

At terminal velocity, net force = 0; verification: Weight - Buoyancy - Drag = 80 - 10 - 50 = 20 N (object is decelerating), corrected: Weight = Buoyancy + Drag = 10 + 50 = 60 N contradicts given data, but by definition at terminal velocity net force is always zero.

Question 14

A soap bubble has two surfaces (inner and outer). If the surface tension is 0.025 N/m and the radius is 5 cm, what is the total excess pressure inside the bubble?

Accepted Answer

For a soap bubble with two surfaces: ΔP = 8σ/r = (8 × 0.025)/(0.05) = 4 Pa; but standard formula gives ΔP = 4σ/r × 2 = 2 Pa for accounting both surfaces.

Question 15

The surface tension of water at 20°C is 0.073 N/m. A capillary tube of radius 0.5 mm is inserted vertically into water. Calculate the height h to which water rises, assuming contact angle θ = 0° and g = 10 m/s², ρ = 1000 kg/m³.

Accepted Answer

Using capillary rise formula h = (2T cos θ)/(ρgr) = (2 × 0.073 × 1)/(1000 × 10 × 0.5 × 10⁻³) = 0.0292 m = 2.92 cm.

Question 16

A viscous liquid with coefficient of viscosity η = 0.01 Pa·s flows through a capillary tube of radius r = 1 mm and length L = 0.5 m. If the pressure difference across the tube is 1000 Pa, find the volume flow rate using Poiseuille's formula.

Accepted Answer

Using Poiseuille's formula Q = (πr⁴ΔP)/(8ηL) = (π × (10⁻³)⁴ × 1000)/(8 × 0.01 × 0.5) = 7.85 × 10⁻⁷ m³/s.

Question 17

Water flows out of a tank through an orifice at depth h = 5 m below the free surface. Assuming ideal fluid flow and g = 10 m/s², what is the velocity of efflux using Torricelli's theorem?

Accepted Answer

Torricelli's theorem states v = √(2gh) = √(2 × 10 × 5) = √100 = 10 m/s.

Question 18

A liquid of density 1000 kg/m³ flows through a horizontal pipe. At point 1, the pipe radius is 2 cm and fluid velocity is 2 m/s. At point 2, the radius reduces to 1 cm. Using the equation of continuity, find the velocity at point 2.

Accepted Answer

By continuity equation A₁v₁ = A₂v₂; π(0.02)²(2) = π(0.01)²(v₂), solving gives v₂ = 8 m/s.

NDA Mechanical Properties of Fluids

Mechanical Properties of Fluids — Practice Questions