Streamline and Turbulent Flow - UNSOLVED PRACTICE SET

Q7. Distinguish between streamline flow and turbulent flow. Give one example of each.

Q8. Define Reynolds number. What is its significance in fluid mechanics?

Q9. Why does water from a slowly opened tap flow smoothly, while water from a fully opened tap splashes chaotically?

Q10. In your school, students observe smoke from an incense stick. Initially, the smoke rises smoothly, then becomes turbulent. Explain why this happens.

Q11. A fluid flows through a pipe of diameter 2 cm with velocity 0.5 m/s. The density is 1000 kg/m³ and viscosity is 10⁻³ Pa·s. Calculate the Reynolds number and determine the nature of flow.

Q12. Explain why aeroplane wings are designed with smooth, streamlined shapes.

Q13. Explain streamline flow and turbulent flow with diagrams. Define Reynolds number and derive its expression. Discuss:

(i) The physical significance of Reynolds number

(ii) The critical Reynolds number for pipe flow

(iii) Factors that promote turbulent flow

(iv) Why turbulent flow is undesirable in some situations but desirable in others

Q14. Water flows through a pipe of diameter 4 cm.

(a) Calculate the maximum velocity for streamline flow. (η = 10⁻³ Pa·s, ρ = 1000 kg/m³, Re_critical = 2000)

(b) If the velocity is doubled, what happens to the flow?

(c) Calculate the Reynolds number if the pipe diameter is halved but velocity remains the same.

(d) How does temperature affect the Reynolds number for water?

(e) Discuss why blood flow in arteries is normally streamline but can become turbulent near constrictions.

Q15. Analyse the flow patterns in the following situations:

(i) Water flowing in a river

(ii) Air flowing over a cricket ball

(iii) Blood flowing in arteries

For each case, discuss:

(a) Whether the flow is likely to be streamline or turbulent

(b) Factors determining the nature of flow

(c) Consequences of turbulent flow in that situation

(d) Engineering or biological solutions to control flow

Q16. An oil of density 900 kg/m³ and viscosity 0.1 Pa·s flows through a pipe of diameter 5 cm.

(a) Calculate the maximum velocity for streamline flow.

(b) Calculate the volume flow rate at this maximum velocity.

(c) If the velocity is increased to 5 m/s, calculate the Reynolds number and predict the flow regime.

(d) The oil is heated, reducing its viscosity to 0.05 Pa·s. What is the new maximum velocity for streamline flow?

(e) Discuss why heating crude oil makes it easier to pump through pipelines.

Q17. A model of an aircraft wing is tested in a wind tunnel. The air speed is 30 m/s, the wing chord length is 0.5 m, air density is 1.2 kg/m³, and viscosity is 1.8 × 10⁻⁵ Pa·s.

(a) Calculate the Reynolds number for flow over the wing.

(b) Predict whether the boundary layer flow is laminar or turbulent.

(c) If the model is scaled down to half size but tested at the same speed, what is the new Reynolds number?

(d) To maintain the same Reynolds number with the scaled model, what should the air speed be?

(e) Discuss why Reynolds number similarity is important in wind tunnel testing.

Q18. In a school experiment, students investigate the transition from laminar to turbulent flow using a glass tube and coloured dye.

(a) Describe the experimental setup and procedure.

(b) At low flow rates, the dye forms a straight line. What does this indicate?

(c) As flow rate increases, the dye line breaks up. At what approximate Reynolds number does this occur?

(d) Design a method to measure the critical velocity for the transition.

(e) How would the critical velocity change if glycerine were used instead of water?