Equation of continuity and Bernoulli: Class 11 practice
For incompressible flow, A₁v₁ = A₂v₂: a fluid speeds up where a pipe narrows. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Area of a circle
The idea behind equation of continuity and bernoulli
For incompressible flow, A₁v₁ = A₂v₂: a fluid speeds up where a pipe narrows. Bernoulli: P + ½ρv² + ρgh is constant along a streamline, so faster flow means lower pressure.
Step-by-step method
- A₁v₁ = A₂v₂ for speeds.
- Bernoulli for pressure difference: ΔP = ½ρ(v₂² − v₁²) at the same height.
- Use ρ = 1000 kg/m³ for water.
Worked example 1 (Basic)
Water flows at 3 m/s in a pipe of diameter 3 cm that narrows to 2 cm. Find the speed in the narrow part.
- A₁v₁ = A₂v₂ → v₂ = v₁(d₁/d₂)²
- = 6.75 m/s
- Answer: 6.75 m/s
Worked example 2 (Standard)
Water flows at 2 m/s in a pipe of diameter 2 cm that narrows to 1 cm. Find the speed in the narrow part.
- A₁v₁ = A₂v₂ → v₂ = v₁(d₁/d₂)²
- = 8 m/s
- Answer: 8 m/s
Worked example 3 (Challenge)
For the same pipe (1 m/s → 3.24 m/s, horizontal), find the pressure drop.
- ΔP = ½ × 1000 × (3.24² − 1²)
- = 4748.8 Pa
- Answer: 4748.8 Pa
Common mistakes and misconceptions
- Using diameters instead of areas
- Sign of the pressure change
Practice questions
- (Basic) Water flows at 5 m/s in a pipe of diameter 5 cm that narrows to 2 cm. Find the speed in the narrow part.
- (Basic) Water flows at 5 m/s in a pipe of diameter 9 cm that narrows to 1 cm. Find the speed in the narrow part.
- (Standard) Water flows at 2 m/s in a pipe of diameter 6 cm that narrows to 2 cm. Find the speed in the narrow part.
- (Standard) Water flows at 4 m/s in a pipe of diameter 10 cm that narrows to 2 cm. Find the speed in the narrow part.
- (Challenge) For the same pipe (2 m/s → 14.22 m/s, horizontal), find the pressure drop.
- (Challenge) For the same pipe (2 m/s → 8 m/s, horizontal), find the pressure drop.
Answer key with full working
- Q1: A₁v₁ = A₂v₂ → v₂ = v₁(d₁/d₂)² → = 31.25 m/s → Answer: 31.25 m/s
- Q2: A₁v₁ = A₂v₂ → v₂ = v₁(d₁/d₂)² → = 405 m/s → Answer: 405 m/s
- Q3: A₁v₁ = A₂v₂ → v₂ = v₁(d₁/d₂)² → = 18 m/s → Answer: 18 m/s
- Q4: A₁v₁ = A₂v₂ → v₂ = v₁(d₁/d₂)² → = 100 m/s → Answer: 100 m/s
- Q5: ΔP = ½ × 1000 × (14.22² − 2²) → = 99135.8 Pa → Answer: 99135.8 Pa
- Q6: ΔP = ½ × 1000 × (8² − 2²) → = 30000 Pa → Answer: 30000 Pa
Syllabus note
This skill is listed under "Mechanical Properties of Fluids" for Class 11 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is equation of continuity and bernoulli in?
"Mechanical Properties of Fluids", Class 11 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.