Key relationship
A₁v₁=A₂v₂; p₂−p₁=½ρ(v₁²−v₂²)−ρg(h₂−h₁).
Physics · Class 11
Narrow a flowing pipe
Mechanical Properties of Fluids
Continuity speeds up liquid where a pipe narrows. Bernoulli links this kinetic-energy increase and any height increase to a pressure decrease. The outlet area control changes both speed and pressure.
Open the interactive experiment →Narrow a flowing pipe
குறுகிய குழாயில் ஓட்ட வேகம் அதிகரிக்கும். பெர்னூலி விதியில் வேகம் அல்லது உயரம் அதிகரித்தால் அழுத்தம் குறையும்.
Key notes, relationships and model limits
Remember
Continuity speeds up liquid where a pipe narrows. Bernoulli links this kinetic-energy increase and any height increase to a pressure decrease. The outlet area control changes both speed and pressure.
Common trap
Bernoulli pressure is not conserved separately when speed or height changes.
Model limits
Steady incompressible inviscid flow along one streamline. Pressure difference is displayed; extreme negative predicted gauge differences require checking cavitation and supply conditions.
What you will learn
Combine continuity with streamline energy balance.
Try the experiment
Try both scenarios, change one control, and predict the result before checking the graph and readouts.
Think of it this way
Change one input while keeping the others fixed, as you would in a controlled experiment.
Worked example
Water at 1 m/s through 20 cm² enters a 10 cm² outlet at 2 m/s. The pressure change is ½×1000×(1−4)=−1500 Pa.
Why this matters
The model connects narrow a flowing pipe with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
At equal height, halving outlet area from inlet area changes speed to what?
- Half the inlet speed
- Twice the inlet speed
- The same inlet speed
Read the explanation
The same volume flow requires A₁v₁=A₂v₂.
Course connection: Class XI Chapter 9. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.