Question

Find the thrust developed (in N) when water is pumped through a 300 mm diameter pipe in the bow of a boat at v=2 m/s and ommited through a 200 mm. Diameter pipe in the stern

Answer 1

Correct Question :

Find the thrust developed (in N) when water is pumped through a 300 mm diameter pipe in the bow of a boat at v = 2 m/s and emitted through a 200 mm diameter pipe in the stern$.$

Answer :

Diameter of pipe at point A = 300mm

Diameter of pipe at point B = 200mm

Velocity of water at point A = 2m/s

We have to find magnitude of developed thrust.

★ We know that thrust is defined as the rate of change of momentum. In order to find final momentum, first we need to find velocity of water at point B.

Equation of continuity

• A₁v₁ = A₂v₂

a denotes area of cross section

v denotes velocity

➠ A₁v₁ = A₂v₂

➠ (πr₁)²v₁ = (πr₂)²v₂

➠ (300)² × 2 = (200)² × v₂

➠ v₂ = 9/4 × 2

➠ v₂ = 4.5 m/s

∴ Velocity of water at point B = 4.5 m/s

★ Mass of water flowing per second :

• Mass = Density × volume

➠ M = ρ × A × v

• (∵ volume = area × velocity)

➠ M = ρ × (π r²) × v

• radius = 300/2 = 150mm = 0.15m

➠ M = 1000 × 3.14 × 0.15² × 2

➠ M = 141.3 kg

∴ Mass of water flowing per second = 141.3 kg

★ Calculation of thrust :

➠ Thrust = m(v₂ - v₁)

➠ Thrust = 141.3(4.5 - 2)

➠ Thrust = 353.25 N