Bernoulli's Theorem and Applications - UNSOLVED PRACTICE SET

Q7. State Bernoulli's theorem. Write its mathematical expression and explain each term.

Q8. Derive Torricelli's law (speed of efflux) from Bernoulli's theorem.

Q9. Explain why a spinning cricket ball swings in the air using the Magnus effect.

Q10. In your school, a student blows air between two sheets of paper held vertically and close together. The papers move toward each other. Explain using Bernoulli's principle.

Q11. Water flows through a horizontal pipe. At one point, the pressure is 2 × 10⁵ Pa and velocity is 2 m/s. At another point, the velocity is 4 m/s. Calculate the pressure at the second point. (Density of water = 1000 kg/m³)

Q12. Explain why the roof of a house sometimes lifts off during a cyclone.

Q13. State and prove Bernoulli's theorem for a non-viscous, incompressible fluid in streamline flow. Discuss the assumptions made and the limitations of the theorem. Explain the following applications:

(i) Speed of efflux (Torricelli's law)

(ii) Dynamic lift on an aeroplane wing

(iii) Magnus effect

(iv) Spray gun and atomiser

Q14. An aeroplane wing has an effective area of 20 m². The air speed over the upper surface is 80 m/s and under the lower surface is 60 m/s. The density of air is 1.2 kg/m³.

(a) Calculate the pressure difference between the lower and upper surfaces.

(b) Calculate the lift force on the wing.

(c) If the mass of the aeroplane is 3000 kg, is this lift sufficient?

(d) What happens if the air speed over the wing decreases?

(e) Explain why aircraft need to maintain minimum speed during takeoff and landing.

Q15. A tank contains water to a height of 4 m. There is a small hole at the bottom.

(a) Calculate the speed of efflux.

(b) If the hole area is 2 cm², calculate the volume flow rate.

(c) Calculate the horizontal distance travelled by the water jet if the hole is 1 m above the ground.

(d) At what height above the bottom should a second hole be made so that the water jet travels the same horizontal distance?

(e) Derive the expression for the range of the water jet as a function of hole depth.

Q16. A horizontal pipe carries water. At point A, the diameter is 10 cm, pressure is 3 × 10⁵ Pa, and velocity is 1 m/s. At point B, the diameter is 5 cm.

(a) Calculate the velocity at point B.

(b) Calculate the pressure at point B.

(c) Calculate the pressure difference between A and B.

(d) If the pipe rises to a height of 5 m at point C (diameter 5 cm), calculate the pressure at C.

(e) Discuss whether the assumptions of Bernoulli's theorem are valid in this situation.

Q17. In a school science fair, students demonstrate Bernoulli's principle using a simple setup.

(a) Design an experiment to show that pressure decreases when air speed increases.

(b) A student blows horizontally over the top of a vertical straw dipped in water. The water rises in the straw. Calculate the minimum air speed needed to raise water by 5 cm.

(c) Explain why perfume spray bottles work on this principle.

(d) Calculate the pressure difference needed to raise water to a height of 10 cm in a vertical tube.

(e) Discuss two limitations of using Bernoulli's principle to explain this demonstration.

Q18. A pitot-static tube is used to measure the speed of an aircraft. The pressure difference measured is 5000 Pa.

(a) Derive the expression for air speed using Bernoulli's theorem.

(b) Calculate the speed of the aircraft. (Air density = 1.2 kg/m³)

(c) If the aircraft flies at the same speed but at high altitude where air density is 0.8 kg/m³, what is the new pressure difference?

(d) Explain why pitot tubes can give false readings in turbulent conditions.

(e) Discuss the importance of pitot tube design in aviation safety.